chapter 13 cold atoms and precision measurements · november 22, 2012 12:37 annual review of cold...

November 22, 2012 12:37 Annual Review of Cold Atoms and Molecules, Volume 1 9inx6in b1480-ch13

CHAPTER 13

COLD ATOMS AND PRECISION MEASUREMENTS

Wencui Peng∗,†,‡, Biao Tang∗,†,‡, Wei Yang∗,†,‡, Lin Zhou∗,†,Jin Wang∗,†,§ and Mingsheng Zhan∗,†,¶

∗State Key Laboratory of Magnetic Resonance and Atomicand Molecular Physics, Wuhan Institute of Physicsand Mathematics, Chinese Academy of Sciences,

Wuhan 430071, China†Center for Cold Atom Physics, Chinese Academy of Sciences,

Wuhan 430071, China‡University of Chinese Academy of Sciences,

Beijing 100049, China§[email protected]¶[email protected]

1. General Introduction

Laser cooled atoms are ideal samples for fundamental science researchand technology application. Cold atom physics has become a very importantarea of atomic and molecular physics, this area is attracting more and moreattention. Cold and ultracold atoms have been widely used in experimen-tal investigation of light-atom interaction, atom frequency standards, atom

§,¶Corresponding authors.

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interferometry, fundamental physical constants measurements, fundamentalphysics principle tests, and other precision measurements. Recently, thereis great progress in cold atoms and precision measurements. Techniques ofcold atom preparation are improved rapidly, and some new species of atomare cooled and trapped. Optical dipole traps for single atoms step forward toquantum information processing; ion traps for few ions provide new candi-dates for optical frequency standard. Implementation of cold atom interfer-ometry has made sustained progress, new results of gravity measurementand rotation measurement based on atom interferometry are reported, andnew prospects of gravitational wave detection using atom interferometersare proposed. As the most precise measurement tool of time and frequency,better stabilities are demonstrated in cold atom clocks including microwaveclock, space clock, optical clock and chip clock. New determination offundamental constants using atom interferometers, such as Newton gravi-tational constant and fine structure constant, are comparable with that usingthe classic methods. There are also some better trends in cold atom basedfundamental principle tests, some projects which will offer opportunities toexplore the foundations of modern physics in ground as well as in space areproposed.

In this chapter, we review the recent advances of cold atoms and theirapplications in precision measurements. New progresses in cold atomspreparation, cold atom interferometer, atom gravimeter, atom gravity gra-diometer, atom gyroscope, gravitational wave detection, cold atom clock,determination of the gravitational constant and fine structure constant, pro-posal of test equivalence principle and local Lorentz invariance are reviewedin detail.

2. Progress of Cold Atoms Preparation

There are several different methods to prepare cold atoms. Magneto-optical trap (MOT) is a most popular tool for cooling and trapping neutralatoms, optical dipole trap is usually used to prepare single atoms, and iontrap is a traditional setup for confinement of few ions. There are greatprogresses in cold atom preparation, some new techniques of preparation ofcold atoms are invented, and some new species of atoms for possible newapplications are cooled and trapped.


Cold Atoms and Precision Measurements 475

2.1. Magneto-optical trap

MOT plays an irreplaceable role in cold atom physics. Since the firstMOT was realized by Raab et al. in 1987,1 techniques of laser cooling andtrapping of neutral atoms developed rapidly. Physicists have been trying toimprove and optimize the performance of the MOTs for many years.2 Thereare two main purposes in optimizing of MOTs, the first one is to trap asmany atoms as possible, and another is to cool atoms as colder as possible.Choice of atom species is quite important for better performance of a MOTand for special applications. According to different resonance wavelengthand saturated vapor pressure, some species of atoms, such as rubidium,can be directly captured from the background vapor; while others, espe-cially lighter atoms, such as lithium, need to be heated up to form atomicbeam, decelerated by red detuning laser beam,3–5 and then trapped in MOT.Recently, a double MOT with Zeeman slower for 7Li was realized,6 atomswith velocities less than 100 m/s was pre-cooled from thermal lithium beam,and the capture rate of MOT was 1.7 × 109 atoms per second. Nowadays,most of alkali metal, alkaline earth metal and noble gas atoms can be suc-cessfully trapped in MOT. Other elements, which are used to be difficult tocool, were cooled and trapped recently, Sukachev et al. realized thulium7

MOT and Youn et al. realized dysprosium8 MOT in 2010. Both of thuliumand dysprosium atoms are suitable for study of dipole–dipole interactions.The energy levels of thulium involved in cooling cycle are not perfectlyclosed, so the number of atoms trapped in MOT by Sukachev et al. is only7 × 104. The level structures of lanthanides atoms are more complex, anopen transition was used to cool dysprosium atoms, and a complex opticalsystem was used to compensate atoms loss which was caused by metastablestates, no more than 106 atoms were trapped in Youn’s work.

To optimize MOT, it is necessary to study the factors which could affectthe performance of MOT, and it is also necessary to invent new evaluationmethods for the key characters of MOT. Jhe’s group added an external peri-odic perturbation on the laser intensity; they found that the transverse lasereffect can be used to explain the discrepancies between the measured andtheoretical calculated trap parameters.9 Van Dongen et al. determined thedepth of an atom trap by the collisions of residual gas.10 Liebisch et al. usedstimulated emission during MOT loading,11 atoms emit photons in a givendirection due to stimulated emission, the number of trapped atoms in MOT


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is 13 times more than before and the loading rate of MOT increased bynearly 20 times. Mckay et al. used a new transition to realize low temper-ature and high density potassium MOT,12 a 405 nm laser was used to drivethe open transition, 4S1/2 → 5P3/2. Compared to the previous MOT withclosed transition, the temperature was several folds lower and the densitywas 20 folds higher.

Dual-species MOTs are good candidates for experimental investiga-tion of interaction between different atoms and also candidates for realiza-tion of non-alkali-metal Bose–Einstein condensation (BEC). Dual-speciesalkali metal MOTs, such as Rb−Cs,13Na−K, 14Li−Cs,15Na−Cs,16Na−Rb,17Rb−Cs,18K−Rb,19 85Rb−87Rb,20 135Cs−137Cs (Ref. 21) and He−Rb,(Ref. 22) were realized recently, the trap loss of loading process are inves-tigated. Dual-Fermions MOTs provide good conditions for the study ofs-wave interaction,23 g-factor ratios24 between these two Fermions, andwidth of Feshbach resonance.25 In 2011, Ridinger et al.26 demonstratedthe realization of 6Li−40K MOT, they used a Zeeman slower to provide 6Liatom beam and a two-dimensional MOT to provide 40K atom beam, the cap-ture rate of this dual MOT reached 109 atoms per second. This dual-MOTis very useful to further study Fermions mixture.

2.2. Single atom trap

Single free neutral atom is one of the most promising candidates forstoring and processing quantum information. Although single atom can becaptured in MOT, but the MOT potential is dissipative which leads seri-ous decoherence of single atom. For this reason, ordinary MOT is better fortrapping atom cloud with millions of atoms, but it is not suitable for trappingand manipulating single atom. Optical dipole trap is a better choice for sin-gle atom traps. The first single atom trap was demonstrated by Meschede’sgroup27 in 2000; they combined the red detuned lasers and quadrupole mag-netic field, increased the gradient of quadrupole magnetic field, reduced theloading rate of MOT and finally captured single atom. Hill and McClel-land28 produced single chromium atom using a different way in 2003, theypushed an atom beam pulse to the MOT area until one atom was trappedand detected.

The ability of dipole trap to capture single atom depend on theinteraction between the induced atomic electric dipole moment and the



far off resonance red detuned laser. The dipole trap can capture singleatom both in free space29 and optical cavity.30 MOTs trapping atom mainlydepend on radiation pressure, the dipole traps mainly depend on dipoleforce. Compared to MOTs, dipole traps can capture single atom more effi-ciently. Physicists have been changing the potential field induced by laserto capture single atom. Recently single atoms are trapped in a blue detunedoptical bottle beam trap31 and a blue detuned hollow-beam funnel.32 Ben-efits from application of the spatial light modulator, the trap laser can bemodulated as any designed patterns. In addition, to study the characteristicsof single atoms, one can capture two atoms at the same time to study thetwo-body problems33 and trap several atoms in a ring lattice to study thefew-body problems.34 Besides the application prospects in quantum infor-mation and quantum simulation, due to the lack of the interaction betweenatoms, the single atom trap provides a pure environment for experimentalstudy of atomic physics.

2.3. Ion trap

The interaction between ions and external environment is stronger, andthe depth of MOTs and dipole traps for neutral atoms is not deep enoughto capture ions. So ions are usually trapped by special electronic potential.There are two basic types of ion traps, one is Penning trap35 and the otheris Paul trap.36 Ion trap not only provide the ion source, but also can beused as a mass spectrometer. Allcock et al. demonstrated implementationof a new Paul trap in 2010,37 they designed a symmetric surface-electrodeand applied two-photon process in trap. Zhang et al. studied the effects ofvarying higher-order multi-pole components,38 the magnitude and the scanspeed can influence the mass resolution, and the mass resolution can reacha maximum value under certain condition. Benefits from the technology ofion trap, 171Yb+,39 199Hg+,40 43Ca+ (Ref. 41) and 88Cr+ (Ref. 42) are usedin ion frequency standards.

3. Progress of Atom Interferometry

The de Broglie wavelength of microscopic atom is usually too shortto show wave properties, but for cold and ultracold atoms, their wave-lengths will be longer enough to display interference. Investigation of atom


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interferometers and their application have made great achievements dueto techniques of laser cooling, trapping and manipulation of neutral atoms.Similar to light wave interferometers, atom interferometers need beam split-ting, reflecting and recombining process; these processes can be conductedeither by microstructure or by standing wave of light. The principle of atypical Mach–Zehnder atom interferometer is shown in Fig. 1. Atoms aretrapped in a MOT and are prepared in initial state |a〉, then the first π/2pulse (beam splitter) is applied to atoms, and the atoms are split into PathA and Path B. Atom state in Path A keep unvaried, while atoms in Path Bobtain two-photon recoil momentum, and change to state |b〉. When the πpulse Raman beams interact with atoms in state |a〉 and |b〉, atoms obtaintwo-photon recoil momentum and change their states from |a〉 and |b〉 to |b〉and |a〉, respectively. After the second π/2 pulse is applied to atoms, atomin state |a〉 and |b〉 are split again, and the new states |a〉 and |b〉 overlapspatially. In other words, initial state of atoms is entangled with the path,and detection of population in one of the ground states reveals the interfer-ence fringes. Any effect that affect on atoms will cause the phase shift ofthe interference fringe. If we consider the gravity field, the atoms’ path willbe distorted as dashed line in Fig. 1 due to the free fall of atoms.

The first thermal atom interferometer was realized by Chebotayev et al.in 1985. (Ref. 44). They used nanostructure gratings to split atom beam.The first cold atom interferometer was realized by Kasevich and Chu in1991 (Ref.45), they used standing wave of laser to split and recombine theatom beams. Different from nanostructure grating, stimulated off-resonanceRaman transitions were used as standing wave gratings. After that, othertechniques using laser field, such as Bragg diffraction, Bloch oscillationswere also used to manipulate cold atoms. Laser field can also be used tochoose internal or external states for atom interference; on the other hand,standing wave gratings are easier to be established than artificial nanostruc-ture gratings.

Standing wave based cold atom interferometers are easier to realize andthus are widely used in precision measurements and fundamental physics.Kasevich and Chu considered in 1991 that the atom interferometer can beused to measure gravitational acceleration.45 In 1994, Borde et al. specu-lated that atom interferometers can be used to detect gravitational waves;46

Audretsch and Marzlin believed that the effect induced by space-time



Fig. 1. Schematic diagram of a Mach–Zehnder type atom interferometer. π/2 pulse stand-ing waves act as beam splitters, π pulse acts as reflect mirror. Solid straight lines show theidea interference path of atomic wave packet, dashed curves are interference path in gravityfield.43

curvature can be experimentally measured with Ramsey atom interferom-eter;47 Chu’s group demonstrated that atom interferometer can be used todetermine the fine structure constant. 48 In 1997, Kasevich’s group real-ized an atom interferometer based gyroscope,49 they also measured thegravity gradient using two atom interferometers in 1998,50 two gravimetersshared the same lasers and reflector, and the common noises during themeasurements were greatly reduced. This configuration was proposed todetermine the gravitational constant with similar method. In 1999, Chu’sgroup51 determined the value of gravitational acceleration by atom interfer-ometer, they analyzed the system errors, compared the experimental data ofthe atom interferometer gravimeter with a Michelson optical interferometergravimeter at the same site. They found that, within the experimental error,the macroscopic glass cube in Michelson interferometer and the microscopiccesium atom fall at the same acceleration. That was the first test of weakequivalence principle (WEP) using macroscopic objects and microscopicparticles.

In cold atom interferometers, the interference effect of single atom iscollectively displayed. Therefore, as many as possible atoms are expected to


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participate in the interference process to promote signal to noise ratio (SNR);any divergence of atom state will influence the measurement results. Atomsare also expected to be cooled as colder as possible. But, no matter how coldand how many atoms are, the interference is single-particle interference. In2002, Gupta et al. used BECs in atom interferometer to determine the finestructure constant,52 the application of BECs in atom interferometer openeda new way for precision measurement. In 2004, Fermions were used inatom interferometer to measure gravity, 53 they thought the Fermions willhave better prospect in single-particle-effect type measurement due to theadvantage of non-interaction.

In 2002, a project named as hyper-precision cold-atom interferometry inspace (HYPER) was proposed in Europe.54 According to HYPER, an atominterferometer will be used to detect the Lense-Thirring effect in space. Thatis the second space project on cold atom and precision measurement, andthe first one is on space atomic clock.

In 2004, Weitz’s group dropped the two isotope atoms 85Rb and 87Rb,and then measured the difference of their gravitational acceleration. Theydid not find any difference at the level of 10−7.55 Although the precision oftesting WEP in this work is two orders of magnitude lower than the workof Chu group’s in 1999, they used two kind of microscopic elementaryparticles as the test masses, which had special scientific significance forWEP test.

In 2006, Weel et al. analyzed the influence induced by magnetic fieldgradient in atom interferometer.56 The inhomogeneity of the magnetic fieldalong the trajectory of atoms would induce differential quadratic Zeemanshifts for atoms in different paths, and this difference would induce a phaseshift in the interference fringe. In 2007, Kasevich’s group reported a valueof Newtonian constant of gravity measured via atom interferometer ;57 theyalso proposed a scheme to test the charge neutrality of atoms.58 In 2009,Tino’s group studied the dispersion relation by atom interferometer,59 dueto the applications of atom interferometer in atom recoil measurements,the dispersion relation at Planck-scale level can be studied in terrestriallaboratory. Schmidt et al. designed a portable atom gravimeter;60 it wouldbe more precise than the best classical absolute gravimeter. That means theatom interferometer can be developed as commercial instrument in gravityfield measurements.



Since 1991, atom interferometer has been widely used in geodesy,inertial navigation, test of relativity, determination of fundamental constantand others. All these applications benefit from not only the special propertiesof cold atoms, but also the promotions of the techniques of atom interferom-eters. According to their features, interferometers can be classified as manycategories, such as time domain or space domain interferometers, internalstates or external states interferometers, near-field or far-field interferome-ters, and so on. But the most crucial part is the process of interference. Inaddition to promotion of related technologies, any methods that can enhancethe divergence induced by external field will be helpful to improve the accu-racy of the interferometer.

4. Gravity Measurement Using Atom Interferometry

Precision measurement of gravity is very important for geophysicalresearch, seismology, resources exploration, environmental investigation,earthquake monitoring, metrology and fundamental science. A gravime-ter is an instrument for measuring the local gravitational field. There aretwo types of gravimeters, relative gravimeters and absolute gravimeters.The most common relative gravimeters are spring-based gravimeters,61 andthe most accurate relative gravimeters are superconducting gravimeters.62

Absolute gravimeters directly measure the acceleration of a mass duringfree fall in a vacuum;63 atom interferometric gravimeter51 is a new kind ofgravimeter which uses microscopic atoms as test mass, it has better appli-cation prospects due to its intrinsic higher sensitivity.

4.1. Gravity measurement

Commercial absolute gravimeters measure the gravitational accelera-tion by monitoring the trajectory of a free fall mass. The mass includesa retro-reflector and terminates one arm of a Michelson interferometer.Portable absolute gravimeters have been widely used in gravity measure-ment due to their high accuracy and sensitivity. The first real atom gravime-ter was demonstrated in 1999,51 since then, atom gravimeters have beencontinuously improved and enhanced. A lot of works have been done todecrease the measurement errors, and to promote the accuracy and sensitiv-ity of atom gravimeters. The transverse motion of the atoms will induce the


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parasitic acceleration. Besides Coriolis acceleration, the wave-front distor-tion is another effect relative with transverse motion of atoms. Bich et al.64

and Louchet-Chauvet et al.65 investigated the transverse motion of atoms ingravimeters, they tried to evaluate the effects by measuring the temperatureof atoms. The retro-reflect configuration in atom gravimeters will cause anun-negligible delay for Raman beams, Nagornyi and his colleagues stud-ied the delay effect and Doppler effect induced by finite speed of light,66

explained the discrepancy between theory and experiment.Gravity field on Earth’s surface is not uniform, and gravity gradient is

an important systematic error in gravity measurement. No matter how freelythe atoms fall during measurement, the gravity gradient will influence themeasurement results. Within a short distance, the gravitational field can beconsidered as a linear gradient field. Gravity gradient near Earth’s surfaceis approximately equal to 3 × 10−6 s−2. If the falling height of atoms ismore than 3.3 cm, the accuracy of the gravity measurement would not bebetter than 10−7 m/s2. Bertoldi proposed a method to solve this problemby compensating gravity,67 the gravity gradient within 10 cm scale can beflattened by a factor of 1000 after gravity compensation, and the effect ofthe gravity gradient can be ignored.

In 2011, Debs et al. used BEC in atom gravimeters,68 the free evolu-tion time is 3 ms, and the accuracy is lower than 10−3. Hughes et al. useda different method in 87Rb BEC gravimeter,69 equal interval laser pulseswere used to suspend condensate, the information of the gravity can beobtained from the frequency of the laser pulse shining on the condensate.This method does not need space for free fall, the behavior of the atoms wasconsistent, and the suspension of the condensate can be hold for 100 ms.But the relative uncertainty of this measurement did not exceed 10−4 due toserious loss of atoms. Tino’s group measured the gravity with cold atomsin optical lattice,70 the measurement uncertainty is 10−7. They firstly decel-erated strontium atoms with Zeeman slower, then trapped atoms in a bluedetuned trap, and further cooled atoms in a red detuned trap. As an externalforce field, gravity will induce Bloch oscillations, and it can be measuredby determining the period of Bloch oscillations. They compared the mea-surement results between this atom gravimeter and a commercial absolutegravimeter, and two results are consistent.

Portability is the prerequisite for the application of atom gravimeters.A mobile atom gravimeter was designed in 2009,71 the desired accuracy of



this mobile atom gravimeter is 10−10. Tino’s group realized a portable lasersystem for high-precision mobile atom gravimeters.72 Merlet et al. designedand realized a mobile gravimeter for Watt Balance project,73 they demon-strated the comparison between atom interferometric absolute gravimeterand optical interferometric absolute gravimeter. Recently, Zhan’s group inChina also realized a compact cold atom gravimeter,74 which measured thelocal gravitational acceleration.

4.2. Gravity gradient measurement

The gravity gradient is the spatial change of gravitational acceleration.Gravity gradiometers measure the spatial derivatives of the gravity vector; itis widely used in oil prospecting, mineral prospecting, water column densityimaging, water depth determining, geophysics and inertial navigation. Asmentioned above, cold atom interferometers can be used to measure gravitygradient.

Kasevich’s group measured the gravity discrepancy of two atom ensem-bles50 in 1998, which is the first atom gravity gradiometer. The schematicdiagram of atom gravity gradiometer is shown in Fig. 2,50 the upper andlower atom ensembles separated by 1 m from each other, and these twoatom gravimeters shared the same optical system. Data measured by abso-lute gravimeters can be used to determine vertical gravity gradients.75 In2002, Kasevich’s group firstly used ellipse fitting method in coupled atominterferometers to extract phase difference,76 the induced gradient phaseshifts can be rapidly extracted and gravity gradients can be accurately mea-sured in the presence of common-mode vibration phase noise. They alsodemonstrated a absolute-gravity gradiometer, the corresponding sensitivityis 4E/

√Hz.77 Tino’s group presented the status of their high-sensitivity

gravity-gradiometer based on atom interferometry,78 and the precision ofG determination may be below 100 ppm due to the high SNR and the longterm stability of the gravity.

5. Rotation Measurement Using Atom Interferometry

Gyroscope is an instrument to measure changes in angle, or direc-tion. Sagnac effect of interferometer was used in gyroscope in 1913,79,80

the path difference between two lights which propagated clockwise andcounterclockwise respectively was used to measure the rotation of the


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Fig. 2. Schematic diagram of atom gravity gradiometer.50

circular path, that is the principle of laser gyroscope and fiber gyroscope.Since the first demonstration of fiber interferometer,81 compact high-sensitivity optical gyroscope devices have rapidly developed. Sagnac effectof atom interferometer provides principle and technical basis for the devel-opment of atom gyroscopes. The performance of neutron interferometerin 1975 showed that matter wave interferometers can be used to measurethe rotation.82 Atom gyroscopes will have higher sensitivity than opticalgyroscopes due to lower velocity and shorter wavelength of atoms. Con-sider same area of the interference loop, the intrinsic sensitivity of atomgyroscopes may be 10 orders of magnitude higher than laser gyroscopes. In1997, Gustavson et al. demonstrated a precision rotation measurement usingan atom interferometer,49 the short term sensitivity of the atom gyroscopeis 2 × 10−8(rad/s)/

√Hz. Similar to atom gravimeters, atom gyroscopes

also take advantage of collective effect of single atom; the sensitivity of anatom gyroscope is limited by shot noise, which is inversely proportionalto square root of the number of the atom. Dowling analyzed theoreticallyquantum-noise limits of atom gyroscopes,83 if the atoms are entangled, the



sensitivity will exceed the shot noise limit. The gravity field induced effectcannot be distinguished by atom gyroscope. Kasevich’s group designed adual loop atom gyroscope in 1998 to decrease gravity,84 the Sagnac phaseshifts of the counter propagating atoms are opposite, but the gravity inducedphase shifts will be the same, measuring the differential phase shifts willreject the gravity induced systematic error, so the sensitivity of the dual loopatom gyroscope is expected to be improved at least one order of magnitude.They demonstrated an improved sensitivity of 6 × 10−10(rad/s)/

√Hz in

2000.85

The characteristics of atom gyroscopes and atom gravimeters are quitesimilar, such as phase noise due to vibrations.86 A double-loop atom inter-ferometer can be used to measure either gravity or rotation.87 However, thereare still some differences between atom gyroscopes and atom gravimeters.For an atom gravimeter, both the free falling direction of atoms and thepropagating direction of Raman beams are parallel to gravitational field,and the scale factor is proportional to time interval between Raman pulses.While for an atom gyroscope, the angle between propagating direction ofRaman beams and atoms will gradually change due to gravity, and the scalefactor is proportional to distance interval between Raman pulses. As to atomgyroscope, if one only considers the pros and cons of splitting, microstruc-ture seems to be a better splitter; Xia et al. demonstrated a nanometer scaletransmission gratings for atom interferometric gyroscope applications.88

Diamagnetic force was used in gyroscope in 2001.89 Although thismethod was used to improve the gravity induced drift in mechanical gyro-scopes, it is also possible to produce a continuous micro-gravity environ-ment for atom gyroscopes, and thus the systematic errors associated withgravity will be greatly reduced. The sensitivity of atom gyroscopes can beenhanced by increasing the number of atoms or increasing the scaling factor,2keff L2/v sin θ , where, keff is effective wave vector of Raman lasers, L isthe distance interval of Raman pulses, v is the velocity of atoms, and θ is theangle between rotating direction and atom propagating direction. The short-term sensitivity of an atom gyroscope is limited by the shot noise, and thelong-term sensitivity is limited by the optical aberrations.90 The high-fluxatom beam can be achieved,84 and the highest sensitive atom gyroscope wasrealized by thermal atom beams,91 which have much more atoms involvedin measurement.


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Compact cold atom gyroscopes should have higher sensitivity thanthermal atom beam gyroscopes, but a relatively small number of atomsinvolved in measurement reduce the SNR of the interference fringes. Thecold atom gyroscope was realized in 2006 with nearly 107 atoms, and theachieved sensitivity was poor.92 Increasing the number of cold atoms isan important trend for the future development of cold atom gyroscope.In 2007, a high-flux cold atom beam for atom gyroscope was demon-strated,93 two-dimensional (2D) MOT was used to generate continuous lowspeed atom beam, and to increase the loading rate of the three-dimensional(3D) MOT, and such a system can provide at least 1010 atoms per second.Recently, high-flux BEC94 and superfluid95 are used as atom sources forgyroscopes.

Gyroscopes can be used for determination of latitude and azimuth, andinertial navigation. The miniaturization of gyroscope is very important forits application. Most of present atom gyroscopes are laboratory prototypes;bulky vacuum system, heavy magnetic shielding and complex optics aredifficult to miniaturize. Cold atoms are more suitable than thermal ones forcompact atom gyroscopes. In 2009, a compact dual-loop cold rubidium atomgyroscope was realized96 by Muller et al., the schematic diagram is shownin Fig. 3. They designed aluminum 2D-MOTs and 3D-MOTs chambers, a20 l/s ion pump and a titanium sublimation pump were used for obtaininghigh-vacuum background. Cold atom beams were generated by 2D-MOTs,

Raman beam splitterstate preparationdetection

/3D-MOT/moving molasses

2D-MOT

/2 /2

90 cm

6 cm6 cm14 cm

Fig. 3. Top view of the compact dual atom gyroscope.96



atom numbers of which were comparable with the thermal atom beams. Thesize of the vacuum system is 120×90 cm2, although the volume of the wholedevice is still big, its portability is better enough for field survey. In practicalfield survey, an atom gyroscope must match the requirements of dynamicmeasurement, for this purpose, a shorter measurement circle is necessary. In2011, Stoner’s group demonstrated an atom gyroscope with short interroga-tion time of millisecond,97 the interaction between Raman lasers and atoms,and the detection of population are completed in MOT region, and the fringecontrast was better than expectation. They found that the measurement islimited by the intensity noise of Raman lasers, and investigated carefullythe dependence of measurement process on laser intensity noise.98 Kase-vich’s group demonstrated an improved atom gyroscope,99 they overcamethe accuracy and dynamic range limitations of previous atom gyroscopes,achieved a sensitivity of 2 × 10−12 rad/s per shot.

6. Gravitational Wave Detection

6.1. Gravitational wave

General relativity predicts that the accelerated motion of the mass willgenerate gravitational waves. Gravitational waves have following proper-ties: they propagate at the speed of light in vacuum; carrying energy andinformation of wave sources; the absorption rate by materials is very low;having two independent polarization states. The energy that gravitationalwaves carry makes them detectable. But due to the very weak strength of thegravitational wave, direct observation of gravitational waves is very diffi-cult. The detection of gravitational waves is of great scientific significance.Once the gravitational wave is proved to really exist, it will open a brandnew page for astronomy and physics.

The sources of gravitational waves can be classified as three kinds.The first kind is pulsed gravitational wave which is generated when uni-verse incidents happen. The second is frequency stable gravitational wavewhich is generated by binary system or neutron star spinning. The third isthe irregular gravitational wave from cosmic background. For more than40 years, physicists have not found any proof of gravitational waves, untilTaylor and his partners calculated the period of the binary pulsar, namedas PSR1913+16, using data of 18 years’ continuous observation, their


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calculation in 1975 agreed well with the theoretical prediction,100 and theirexperiments indirectly proved the existence of gravitational waves andcheered the scientists who are dedicated to the detection of gravitationalwaves.

6.2. Situation and progress

One kind of gravitational wave detectors is Weber detector, which detectgravitational waves through measuring the variation of distance betweentwo objects. There are five Weber detectors around the world, two of themare in Italy,101,102 and the other three are in Switzerland,103 the United Statesof America (USA)104 and Australia105 respectively. Due to the small size oftheir antennas, Weber detectors can only detect high frequency gravitationalwaves, which could only be generated by rare sudden cosmic events. Thewaiting type experiments and continued operation of cryogenic system needexpensive costs to support such research. In the middle of 1970s, scientistsstarted to use laser interferometers as antennas to detect gravitational waves,the antennas is similar to Michelson interferometer, and a pair of mirrorsat each arm is used to form a Fabry–Perot cavity. Multiple reflections canincrease the optical path difference caused by variations of mirrors’ position.There are six high-sensitivity laser gravitational wave detectors in the world.Among them, Virgo is a cooperation project of Italy and France106 with two3-km-long arms and its measurement bandwidth covers 10 Hz to 3 kHz.Laser interferometer gravitational-wave observatory (LIGO) were built andoperated in two places of USA,107 one interferometer’s arm is 4 km long,and the other is 2 km long, two interferometers can simultaneously detecthigh frequency gravitational waves. GEO 600 was built in Germany, and itis a joint project of British and German,108 the arm length is 600 meters.TAMA detector was built in Japan; the baseline is 300 m.109 Australianconsortium for interferometric gravitational astronomy (ACIGA) is theonly laser gravitational-wave detector built in the southern hemisphere,110

its arm length is only 80 m, but it can be extended with high opticalpower in resonant cavity. Above six laser gravitational-wave detectors canonly detect the gravitational waves with frequency from 10−2 to 104 Hz.National Aeronautics and Space Administration (NASA) and EuropeanSpace Agency (ESA) are joining to promote a laser interferometer space



antenna (LISA) for gravitational-wave detection.111 Three ground-baseddetectors are respectively set in three satellites which will form an equilat-eral triangle with a side length of 5×106 km. The regime of the gravitationalwave can be detected by LISA is 10−4 to 10−1 Hz.

Although, so many efforts have been taken, scientists still do not getdirect evidence for gravitational waves. The development of the atom inter-ferometer provides the inspiration for gravitational wave detection. In 2004,Chiao and Speliotopoulos proposed a scheme for matter-wave interfer-ometric gravitational-wave detector,112 further cooled supersonic atomsbeam will be used as matter wave sources, the size of this type detectorwill be much smaller than LIGO type detector, and the detectable band-width of gravitational waves will be wider. Matter-wave interferometricgravitational-wave observatory (MIGO) will become a new generation ofgravitational wave detectors.

6.3. Gravitational wave detection using atom interferometer

Since 1979, scientists had already started to investigate the interactionbetween matter waves and gravitational waves.113 Chiao claimed that forthe same size devices, MIGO type detectors’ sensitivity would be severalorders of magnitude higher than LIGO type detectors,112 but others didnot think so.114 In 2007, Tino and Vetrano carefully analyzed the possibil-ity of atom interferometer based gravitational wave detectors,115 the phaseshifts for different shape interferometers were discussed. They found thatMIGO can be used to detect low frequency gravitational waves, MIGOhas comparable sensitivity with laser gravitational wave detectors whileit does not need so huge device sizes. It seems that MIGO is a potentialdetector which can compensate the LIGO’s defects. In 2011, Hohenseeet al. listed sources and technology for MIGO, the frequency band of grav-itational wave that MIGO can sensor is at mHz∼Hz level.116 In 2009,Ambrosio analyzed major noises of MIGO,117 and he found that the mainlimitation is the noise of the atom interferometers. Charged molecule wasproposed as test mass for gravitational wave detector in 2010 (Ref. 118) byLorek et al., molecules were not spatial split, but oriented in space alongthe two polarization direction of gravitational waves, and the detector willhave a higher sensitivity. In 2011, Lorek et al. further analyzed influence ofa monochromatic gravitational wave over a quarter period,119 this scheme


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can be extended to an atom interferometer; Zhan’s group proposed a newgravitational wave detection scheme which combined Chiao’s and Kase-vich’s proposes,120 standing waves instead of material gratings will be usedto split, reflect and recombine atoms, supersonic atom beams will be used toimprove the SNR. This device would be suitable to detect the gravitationalwaves with frequency range from 10 to 1000 Hz. Another scheme withconfiguration similar to LIGO was proposed,121 two atom interferometers,separated by a distance, act the role of the mirrors in LIGO.

A space project on atom interferometer based gravitational wave detec-tor was proposed in 2009 (Ref. 122), this detector will probe gravitationalwaves with the same frequency range as LISA and with similar sensitivity,in addition to space plan, a terrestrial 10 m atom interferometer project wasproposed.122 In 2011, a comment on atom type gravitational wave detectorswas reported,123 error sources that had not been concerned before was fur-ther investigated. Another atomic gravitational wave interferometric sensorin low earth orbit (AGIS-LEO) was proposed in 2011 (Ref. 124), threeatom interferometers will be placed in space with 30 km distance betweeneach of pair, and the gravitational waves will be detected by comparing anypair of the atom interferometers. This project is designed for detecting thegravitational waves with frequency range from 50 mHz to 10 Hz, and thesensitivity will be 10−18/

√Hz.

It seems that, atom interferometers have higher sensitivity than laserinterferometers in detection of gravitational waves with special frequencyband, and construction of atom interferometer based gravitational-wavedetectors is necessary. The network of LIGO and MIGO will make asignificant contribution to directly prove the existence of gravitationalwaves.

7. Cold Atom Clock

7.1. Microwave clock

In early days, quartz oscillators, which had fractional frequency insta-bilities of 2 × 10−8, was used to define the second in the InternationalSystem of Units (SI).125 Quartz oscillators are sensitive to temperature, andare individually different from each other; their frequencies usually are notequal and stable. The development of the microwave spectroscopy makes



usage of unperturbed atomic transitions as frequency standards become areality. In atom beam experiments, Doppler shifts and limited interactiontimes restrict both the accuracy and stability of the frequency measurement.To solve these problems, Zacharias126 proposed a fountain type frequencystandard in 1953. Unfortunately, the fountain did not work well. In order toobtain sufficiently strong signal, laser-prepared atomic fountains for opticalfrequency standards applications were proposed in 1989 by Hall et al.,127

Rf spectroscopy was used in fountains by Kasevich et al.128 A lot of primaryclocks are built gradually due to the improvement of key technologies offrequency standard based on atomic transitions. Since the late 1990s, someatom fountains were established successively as primary clocks,129 such asNIST-F1 at the National Institute of Standards and Technology (NIST) inUSA, CSF1 at Physikalisch-Technische Bundesanstalt (PTB) in Germany,CsF1 at the Istituto Elettrotecnico Nazionale (IEN) in Italy, CsF1 at theNational Physical Laboratory (NPL) in UK, FO2 and FOM at the Observa-toire de Paris in France. Other laboratories are developing atom fountainsfor fundamental physics experiments. Ovchinnikov and Marra reported newprogress on rubidium atomic fountain of NPL in 2011,130 Fig. 4 shows asimplified setup of the atomic fountain at NPL. Like most other fountainclocks, it consists of four parts: MOT, state-selection system, the interro-gation system and detection system. But the difference is that it has twoMOTs, the cold 87Rb atoms in the main MOT are all coming from the otherlow-velocity intense source (LVIS). This novel design not only traps more87Rb atoms, but also can get rid of all hot 87Rb atoms in the vacuum cham-ber as well as the high abundance useless 85Rb isotope atoms. Two otherfeatures are water-cooled temperature-stabilized interrogation region andhigh quality factor (Qc ≈ 28500) interrogation cavity. The fractional fre-quency accuracy of the atom clock is estimated to be 3.7 × 10−16 as shownin Table 1, the stability is limited by local oscillator which is estimated to be7×10−16 in one day’s average. Another primary frequency standard at NPL,the NPL-CsF2, also made a good progress in 2011. They evaluated the twomajor sources of uncertainty for the NPL-CsF2 cesium fountain clock, thedistributed cavity phase (DCP) and microwave lensing frequency shifts,131

the DCP uncertainty is reduced to 1.1 × 10−16 and the type B uncertaintyof the NPL-CsF2 clock is reduced to 2.3×10−16. Clairon’s group at Obser-vatoire de Paris also did a great work on evaluating the DCP uncertainty,132


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Fig. 4. Simplified setup of the atomic fountain at NPL.130

they improved their DCP uncertainty to δv/v = ±8.4 × 10−17. In addition,they demonstrated that by using a cavity with four independent, azimuthallydistributed feeds, the DCP uncertainty will probably be reduced to less than±1 × 10−17.

Weyers’ group also evaluated the frequency error from DCP and thefrequency bias and uncertainty due to the microwave lensing of the atomicwavepackets in the cesium fountain clock PTB–CSF2 at PTB,133 theyreported a total systematic uncertainty of 4.1 × 10−16. Dube’s group madean accurate map of the C-field134 in the cesium fountain frequency standardFCs1 at National Research Council of Canada (NRC), as they expected that



Table 1. Frequency shift and their type B uncertainties.130

Effect Frequency shift (10−16) Uncertainty (10−16)

Second order Zeeman 1922.3 1.0Blackbody radiation −133.5 0.6Cavity distributed phase 0 3.0Cavity pulling and collisions −0.6 0.2Collisions with background gas <0.7 1.0Microwave leakage 0.55 1.0Gravity 12.6 0.3Other — 1.0Total uncertainty — 3.7

the inhomogeneity of the magnetic field should give rise to one of the mainsources of uncertainty, and contribute to make the second-order Zeemanshift better than the 10−15 level. Ido’s group reported the total uncertaintyof the NICT–CsF1 at the National Institute of Information and Communica-tions Technology (NICT) in Japan, and it was evaluated as 4.1×10−15, theyalso successfully observed the Ramsey fringe with a linewidth of 0.95 Hzin NICT-CsF2 and its instability is 5×10−13/

√τ .135 Li’s group at National

Institute of Metrology (NIM) in China moved and recovered Cs fountainclock, the preliminary results show a stability of 8 × 10−16 over 1000 saveraging time.136

Müller et al.137 demonstrated a novel compact frequency standard.Their experiment setup and temporal working cycle is shown in Fig. 5. Asit is shown on the left side of Figure 5, the whole equipment is just a littlebit bigger than its microwave cavity, which is wholly made of stainlesssteel. The trapping, repumping, interrogation and detecting procedures areall carried out in the same position as it shows on the right side of Fig. 5.137

There are many advantages of all-in-one configuration in a compact coldatom frequency standard, such as compact structure, small weight and bettermagnetic field shielding. Its stability could reach up to σy(τ ) = (5±0.5)×10−13/

√τ for the clock transition with a linewidth of 47(±5)Hz.

A new principle of microwave frequency standard is coherentpopulation trapping (CPT). CPT clocks have characteristics of small size,low power consumption and good long-term performance. Cold atom CPTclocks will be good candidates for commercial and spatial applications.


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Fig. 5. Simplified setup and temporal working cycle of the compact frequency standard.137

Zhan’s group reported an experimental observation of coherent popula-tion trapping-Ramsey interference in cold 87Rb atoms.138 Esnault et al.139

designed a compact cold-atom CPT frequency standard, their expected fre-quency stability should be better than 10−11/

√τ and an accuracy will be

around 10−13.

7.2. Space clock

Frequency comparisons and fundamental physics in space acquire highaccuracy clocks. Microgravity environment is conducive to improve theperformance of atom clocks. Scientists want to launch atom clocks to spacefor scientific and technology purpose, some space clock projects have pro-posed, such as ACES (Atomic Clock Ensemble in Space)140 and HORACE(Clock with atom cooling in a cell).141

The payload of ACES accommodates two atom clocks, PHARAO (aprimary frequency standard based on samples of laser cooled cesium atoms)and SHM (an active hydrogen maser for space applications). PHARAOwill have fractional frequency instability of 10−13/

√τ and an inaccuracy

of few parts in 1016; SHM will have fractional frequency instability of1.5 × 10−15 after 10,000 s integration. The short-term stability of SHM andthe long-term stability of PHARAO will be used to perform comparisons



of atom frequency standards. Ultimately, researches on general relativity,gravitational redshift, time variations of fundamental constants and so onwill be carried out through precision measurements and comparisons offrequencies. Nearly all the components of ACES have been prepared andtested, it will be launched to International Space Station (ISS) between2013–2014.

HORACE is a compact cold cesium atom clock developed at ParisObservatory. It has a relatively small size because of performing the wholemeasurement procedures at the same place by using the isotropic light cool-ing techniques. As a candidate for Galileo’s ground segment clocks andonboard Galileo clocks, HORACE has short-term relative frequency insta-bility of 2.2 × 10−13/

√τ and long term instability of about 3 × 10−15 in

104 s integration according to current results.Nissen et al. proposed a novel microwave clock for space purpose,142 it

is suitable for relativity experiments on Earth orbit, and its goal is to reacha frequency discrimination level of about 1 × 10−16 in a single rotationof the satellite roll period which is about 1000 s. Bandi et al. proposedanother space clock, the expected short-term stability is 4 × 10−13/

√τ

for integration time 1 s–1000 s, and a medium-to long-term stability is at1 × 10−14 level.143

7.3. Optical clock

Nowadays, optical clocks based on single ions and neutral atoms havesurpassed the primary microwave frequency standards either on stability oraccuracy, and have a remarkable potential for further developments.144,145

The theoretically achievable fractional frequency instability of the opticalclocks can be scaled as,

σy(τ ) ∝ 1

Q(S/N)

√τ , (1)

where, Q is the line quality factor (the ratio of the transition frequency v0 toits linewidth�v0), S/N is the SNR for a 1 Hz detection bandwidth, and τ isthe averaging time in seconds. From this equation, one can see that changingfrom a microwave transition to an optical transition can lead to an immediateincrease in stability. At the meantime, the reproducibility and interferenceimmunity to environmental disturbances, such as electric or magnetic field,


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ultra-stablelaser

cold ion or atom reference

detectorservo-electronics

single ionend-cap trap

optical lattice trap

femtosecondfrequency comb

counter/clock

optical output

µW output

Loop filter

EOMLaser

ultra-stablereference cavity

Loop filter

EOMLaser

Loop filter

EOMLaser

Loop filterloop filter

EOMlaser

DBM

Fig. 6. Main components of a typical optical clock. EOM is electro-optical modulator,DBM is double-balanced mixer.146

are also needed to be considered in frequency standards. Obviously, opticalfrequency standards can meet the qualification. The candidates for opti-cal frequency standards can be classified as single trapped ions and coldneutral atom cloud. A simplified diagram of a optical clock is shown inFig. 6.146

Single trapped ions are well isolated from environmental perturbations,and thus have narrow linewidth transitions. The future high accurate opticalfrequency standards or clocks will use single trapped ion techniques. Dubédemonstrated the advancement of strontium ion optical frequency standardin NRC,134 they designed an end cap trap which minimized micro motion inthree dimensions, obtained a stability of 6.5×10−16 at 500 s, and a frequencyuncertainty of 5 × 10−17 after one day’s averaging. Peik’s group147 at PTBhas demonstrated that the 2S1/2→2 F7/2 octupole transition in 171Yb+ can beused to realize an optical clock with a systematic uncertainty of 7.1×10−17.

Equation (1) shows that the instability is inversely proportional toSNR, while SNR is proportional to square root of atom number,

√N ,

frequency standards using large numbers of cold atoms potentially have



higher stability than that of using single trapped ions. That is why somany groups construct optical frequency standards based on cold neutralatom ensembles prepared in MOT, optical lattice and continuous beam.Hansch et al.148 have measured the 1S → 2S transition frequency inhydrogen atoms via two-photon spectroscopy, they obtained the valuef1S→2S = 2 466 061 413 187 035(10)Hz, a fractional frequency uncer-tainty is 4.2 × 10−15. Katori used the optical lattice to confine the coldatoms during the clock interrogation cycle in 2001; this greatly promptedthe application of optical lattice technique in time and frequency stan-dards. Katori reviewed the experimental realization, optimal design, andfuture applications of neutral atom optical clocks.149 We know that, asthe number of atoms increases in optical lattice, the collision frequencyshifts also increases. In 2011, Ye’s group proposed a solution for thisproblem by dramatically increasing the strength of atom interactions,150

by suppressing collision shifts in lattice sites containing atoms (N > 1),strong interactions introduced an energy splitting and an evolution to amany-particle state in which collisions is restrained. They demonstratedthat the uncertainty of strontium lattice optical clock is 10−17. Bishofet al. resolved atomic interaction sidebands in 87Sr optical clock tran-sition,151 observed two-body loss of 3 P0

87Sr atoms trapped in a one-dimensional optical lattice and measured loss rate coefficients of atoms.152

Lemke et al. studied ultracold collisions in Fermionic Ytterbium,153 Ludlowet al. demonstrated that the cold-collision shift can be cancelled at the5 × 10−18 level in a 171Yb optical lattice clock.154 Yi et al. found that themagic wavelength for the clock line in neutral Hg is 362.53 (0.21) nm,155

Westergaard et al. presented the frequency shifts associated with the lat-tice potential in a Sr lattice clock by comparing two such clocks witha frequency stability of 5 × 10−17.156 Falke et al. reported their stron-tium optical frequency standard contributes with a fractional uncertainty of1.5 × 10−16.157

Laser stabilization is one of the key techniques in optical frequency stan-dards. Ludlow’s group demonstrated a cavity-stabilized laser system; it hasbeen used as a stable optical source in an ytterbium optical lattice clockto resolve an ultra-narrow 1 Hz transition.158 Tino’s group used two-stagefrequency stabilization techniques to control high-finesse optical cavities,


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the laser frequency noise they measured is 2∼11 Hz, that is about three timeof the cavity thermal noise.159

Femtosecond optical frequency comb is another key technique in opti-cal frequency standards. In 2011, Kippenberg et al. presented a new opticalfrequency comb which used parametric frequency conversion in high res-onance quality factor micro resonators,160 this approach not only causes adramatic reduction in size but also has access to comb generators with arepetition rate up to ∼ 1 THz.

Comparisons are feasible methods to determine the reproducibility offrequency standards. Long distance frequency comparisons are performedvia satellites with a fractional instability of around 10−15 for a measure-ment time of one day. But with fractional instabilities of around 10−15

at 1 s, optical frequency standards are not appropriate for the satellite-based methods. Therefore, transferring stable optical frequency by opti-cal fibers is needed. Recently, Fujieda et al. developed an all-optical linksystem which has the instability less than 2 × 10−15 at 1 s and 7 × 10−17

at 1000 s,161 they performed a 87Sr based optical lattice clock comparisonbetween NICT and University of Tokyo with the fractional instabilities ofaround 7.3×10−16.162 Katori’s group proposed a novel method which madefrequency comparison through synchronously manipulating different iso-topes such as 87Sr (Ref. 149) and 88Sr (Ref. 163), the relative stability theyachieved is 3 × 10−17.

7.4. Chip based clock

Compact and portable frequency standards have potential application inscientific research and technology in future. Atom chips could be an excel-lent carrier to develop the compact high stability clocks. Ramírez-Martínezet al. presented a chip based 87Rb atom frequency standard, the frequencystability is σy = 1.5 × 10−12√τ for 10 < τ < 103 s.164 Farkas et al.demonstrated a chip based atom clock that used all-optical interrogation ofultracold rubidium atoms, the clock inaccuracy is better than 2 × 10−14.165

Although the performances of these chip based clocks, such as the stability,and the shot-noise-level, are not as good as previous clocks, they still havebroad application prospects in the future.



8. Determination of the Fundamental Constant

8.1. Determination of gravitational constant

Newtonian gravitational constant which is known as “capital G” isclosely related to theoretical physics, astrophysics and geophysics. Theexperimental measurement of the gravitational constant can be traced backto the late 18th century.166 Gravitational effect is weak and cannot be iso-lated and shielded. It is so difficult to measure experimentally that aftermore than 200 years’ efforts, the measurement precision of this constanthas only been improved by two orders of magnitude.167

8.1.1. Traditional methods of gravitational constant measurement

In 2006, the recommended value of G by the Committee on Data forScience and Technology (CODATA) is 6.67428(67) × 10−11 m3kg−1s−2,and the relative uncertainty is 1.0×10−4.167 In 2010, the fifth recommendedvalue of G is 6.67384(80)× 10−11 m3kg−1s−2, and the relative uncertaintyis 1.2×10−4.168 We find that, the new recommended measurement precisionof G becomes better, but relative uncertainty of G turns worse. Not onlythe values measured by different methods disagreed with each other, butalso the values measured by the same methods at different time disagreedwith each other. And this worse disagreement made the new recommendedvalue have larger expansion.

Two kinds of methods used to measure G are torsion balance and beambalance. The group at University of Washington measured G with fibertorsion balance,169 the value they measured in 2000 is 6.674255(92) ×10−11 m3kg−1s−2. The group at University of Zurich measured G withbeam balance,170 the value they measured in 2006 is 6.67425(12) × 10−11

m3kg−1s−2.Both torsion balance and beam balance used macroscopic objects as

test mass, microscopic particles was not used in G measurement until atominterferometry was applied in precision measurement.

8.1.2. Determination of gravitational constant with cold atoms

Cold atoms can be used in high sensitivity gravity measurementand have potential to determine the Newtonian gravitational constant. In


500 W. Peng et al.

2003, Tino’s group proposed a feasible scheme to measure G for anexpected accuracy of 10−4,171 two atom clouds were launched and formeda configuration of gradiometer.50 To reach the accuracy of 10−4, the grav-ity measurement must achieve accuracy of 10−11 g with single atom cloudlaunched scheme, which seems difficult. Differential measurement willgreatly suppress common mode noise and thus increase the accuracy ofgravity gradient measurement, heavy source masses can be used to changethe local gravitational acceleration, this method is similar to beam balance,two atom clouds are test masses, and the source masses are field masses.Atom interferometric method has two advantages: the properties of certainatoms are well known; and the gravity variation can be directly measuredwithout any other gravimeters. While, characterizing the source masses andprecise positioning of the test mass is still a problem.

In 2007, the first value of G measured by cold atom interferometer wasreported by Kasevich’s group.57 The schematic of experiment is shown inFigure 7; a 540 kg lead was used as the source mass which can move alongthe vertical direction. Upper and lower gravimeters share the same Ramanlasers. The inferred value of G is (6.693±0.027)×10−11 m3kg−1s−2, witha relative uncertainty of 4.0 × 10−3. Similar to beam balance method, thelimitation of measurement accuracy of this method are determination ofinitial location, velocity of atoms and positioning of the source mass. In2008, Tino’s group determined a new value of G,172 two high density tung-sten source masses were used to induce gravitational field, and their gravitygradiometer was formed with successively launched atom ensembles withdifferent launch heights. The value of G they measured is 6.667 × 10−11

m3kg−1s−2 with a relative uncertainty of 1.6 × 10−3. Until now, only twogroups have experimentally determined the G using cold atoms.

Recently, Tino’s group upgraded their atom preparation system andRaman laser system,78 a 2D-MOT was used to provide high flux atombeam, which can promote the loading rates and preserve a low backgroundpressure. A new Raman lasers system was used, which has lower intrinsicfrequency noise with an output power of 1 W. The measurement uncertaintyunder 120 hours’ integration is 4.0 × 10−4.

Within just eight years, the measurement precision of G using coldatoms has reached a comparable level with the traditional measurements’.Although the accuracy of atom interferometric method has not been



Fig. 7. Schematic diagram of atom gravity gradiometer.57

accepted by CODATA yet, there is still great space for this new methodto optimize and to improve.

8.2. Determination of fine structure constant

8.2.1. Traditional methods of fine structure constant determination

The fine structure constant,α, is a dimensionless constant and appears indifferent domains of physics, its value can be measured by three methods.The first method is combination of electron anomaly measurement andquantum electrodynamics (QED) calculation, the second is measuring thequantum Hall effect, and the third is measuring the ratio of Plank constant


502 W. Peng et al.

and atomic mass. The most precision value of α was determined by thefirst method, and the most precision measurement using electron anomalywas realized by Gabrielse’s group at Harvard University,173 combiningthis measurement and the QED calculation, the determined value of α−1

is 137.035999084, with a relative uncertainty of 3.7×10−10. The most pre-cision value of α determined by quantum Hall effect is 137.0360037, witha relative uncertainty of 2.4×10−8.174 The most precision value of α deter-mined by the ratio of Plank constant and atomic mass is 137.035999037,with a relative uncertainty of 6.6 × 10−10.175 And the recommended valueof α−1 by CODATA in 2010 is 137.035999074, with a relative uncertaintyof 3.2 × 10−10.176

8.2.2. Determination fine structure constant with cold atoms

For a long period of time, the fine structure constant was mainly deter-mined by the method of combination of electron anomaly measurementand QED calculation. The determination using only one kind of methodsis unreliable, especially the determination of α had been shifted becauseof a mistake of the calculation. So other methods that are independent onQED are needed. In turn, comparing the values of α inferred from differentmethods can test QED theory. A well known relationship on determinationof fine structure constant is,

α2 = 2R∞c

ma

e

h

ma, (2)

where, R∞ is the Rydberg constant, c is the speed of light, ma is the massof atom, me is the mass of electron, and h is Planck constant. The last termof the right side of the equation decides the precision of α so far. Due tothe relationship, vr = h̄k/ma, vr is the recoil velocity, h̄ is reduced Plankconstant, k is the wave vector of light, one can infer the last term in Eq. (2)by measuring the value of recoil velocity.

In 1994, Chu’s group measured the velocity variation of cesium atom,48

they carefully analyzed the errors during measurements, and obtained thevalue of h/mCs (mCs is the mass of cesium atom), the disagreement withwell known value of α is 0.1 parts per million. They improved their experi-ments in 2002, and determined that the value of α−1 is 137.036000, with arelative uncertainty of 7.4 ×10−9.176 In 2006, they proposed a new feasible



scheme to measure α with an expected precision of 5×10−10,177 the Braggdiffraction will be used instead of the stimulate Raman transition, atomswould stay in the same internal states which can avoid the influence inducedby differential of the internal states; two conjugate interferometers will beused in to reduce some systematic errors, especially the gravity inducedphase shift. In addition, lower noises during the measurements, enhancethe velocity variation due to photon kicking will intrinsically promote theprecision of the measurements. In 2008, they improved the precision ofmeasurement of α to 3.7 × 10−10.178 Recently, the atom’s momentum canbe changed up to 102 photon recoil momentums,179 this would greatly helpto determine the value of fine structure constant.

Another group also measured the value of α with cold atoms, two con-jugate interferometers were also used to detect the velocity variation of theatom, and Bloch oscillations were used to split atoms, which can efficientlytransfer large number of photon recoil momentums. In 2008, they achieved1600 photon momentums transfer,180 the more momentum transfer waslimit by their device’s size. The determined value of α−1 is 137.03599945,with a relative uncertainty of 4.6 × 10−9. In this experiment, atoms keeposcillating in laser induced potential field, so the requirements for laserquality are very strict. The experiment results are limited by wave front cur-vature, frequency stabilization of lasers and the alignment of laser beams.They obtained an improved value of α−1 , which is 137.035999037, with arelative uncertainty of 6.6×10−10,175 this is the most accurate value of finestructure constant inferred by cold atoms.

Until now, two groups measured the value of α with precision of 10−10

by cold atoms. This may totally change the situation of determination of α,and provide a possibility to stringently test QED theory. Larger area interfer-ometer will be used to promote the precision, and the uncertainty of ma/me

will be the major limitation of determination of α with cold atoms.

9. Testing Fundamental Physics

Einstein’s equivalence principle (EP) is a cornerstone of general rela-tivity, and EP contains three assumptions: (1) the universality of free fall(UFF), known as weak equivalence principle (WEP), which states that freelyfalling bodies have the same acceleration in the same gravitational field


504 W. Peng et al.

independent of their compositions; (2) Local Lorentz invariance (LLI),which assumes that clock rates are independent of the clock velocities; (3)Local position invariance (LPI), which assumes that clock rates are inde-pendent of their space-time positions. Some theory predicted the possibilityof the violation of EP. The violation of the EP seems to be the requirementof the unified theory. This situation greatly inspired physicists to further testEP. Usually the test of EP starts from the test of WEP.

9.1. Equivalence principle test

The WEP states that the gravitational mass is equal to inertial mass.Usually it is tested by comparing the gravitational acceleration of differentfree falling test bodies. The earliest test of WEP can be traced back tothe famous Galileo’s leaning tower experiment,181 that experiment kindlyproved the WEP, but the precision was quite low.

Eötvös suspended two balls which were made of different materialson two sides of a torsion balance. The two balls were affected not only bygravitational force, but also by the inertial centrifugal force. If the WEP wasviolated, the torsion of the balance would not be zero. Eötvös’ experimentgreatly improved the precision of WEP test. To commemorate his contri-bution to WEP test, a dimensionless Eötvös-parameter, η , is used to scalethe precision of the WEP test,

η = 2(a1 − a2)

a1 + a2, (3)

where, a1 and a2 are the acceleration of the two test masses respectively.The most precision test of WEP with a torsion balance was reported in

2008, the precision of η is 10−13.182 Another method to test WEP, LunarLaser-Ranging (LLR), also achieved the precision of 10−13 (Ref. 183), inthe Sun–Earth–Moon system, the Earth and the Moon can be consideredas two test masses which are free falling to the Sun. With new APOLLOfacility, the precision of LLR will reach millimeter level range, and that willlead to a test of WEP at the level of 10−14.

The high precision measurements of gravity with atom interferometersmake cold atoms the most suitable test masses. Besides that, the gravityinduced quantum effect is the best combination of gravity and quantummechanics. In 1999, Chu’s group compared the values of the gravitational



acceleration measured by cold atoms with that measured by an absolutegravimeter FG-5.51 The two kinds of test masses showed the same acceler-ation at the level of 10−9. That comparison is called as modern version ofGalileo’s “Leaning Tower” experiment. Demonstration of WEP test withtwo kinds of atoms was in 2004,54 85Rb and 87Rb atoms were used astest masses. Not only the accelerations of the two kinds of atoms weremeasured, but also the accelerations of 85Rb at different hyperfine groundstates were measured. They both proved the WEP is founded at the level of10−7. Although the precision of this test is much lower than the test withmacroscopic bodies, it showed that both particles with different internalnuclear structure and particles with different orientation of nuclear to elec-tron spin, obey the law of free fall. Another terrestrial high precision atomicinterferometer-based WEP test experiment has been prepared at StanfordUniversity. They will build a 10 meter atom interferometer, the differen-tial acceleration of free falling 85Rb and 87Rb atoms will be measured totest WEP,184 the expected precision is 10−15. A different 10 m interferom-eter was designed and developed in China,185 the test masses could eitherbe 85Rb and 87Rb, or be rubidium and lithium atoms with more differentcompositions and qualities. An airborne interferometer testing WEP wasdesigned in 2009,186 they planned to use potassium and rubidium atoms asthe test masses, and put the whole device in a plane to produce a 0 g envi-ronment. Recently they had successfully achieved gravity measurement onthe aircraft.187

Space offers unique experimental conditions to explore the foundationsof modern physics with accuracy far beyond that of ground-based experi-ments, such as better seismic conditions, micro-gravity environment. Sometheories considered that, the violation of EP may be more obvious in spacethan on the ground. Six space projects on precision WEP test have beenproposed. In accordance with the expected precision from low to high, theyare MicroSCOPE (Micro-Satellite à tranînée pour l’Obeservation du Princi-ple d’Equivalence) with targeted precision of 10−15,188 POEM (Principle ofEquivalence Measurement) with targeted precision of 10−16,189 MWXG(Matter wave explorer of gravity) with targeted precision of 10−16,190

STUFF (Space Test of Universality of Free Fall) with targeted precisionof 10−17,191 GG (Galileo Galilei) with targeted precision of 10−17,192 STEP(Satellite Test of the Equivalence Principle) with targeted precision of


506 W. Peng et al.

10−18.193 Among them, the MWXG project is the atom interferometricWEP test space project.

9.2. Local Lorentz invariance test

LLI is not only one of basic parts of the equivalence, but also the basichypothesis of special relativity. The nonvanishing parameter δ = |c2/c2

i −1|is used to test the violation of LLI, where c is the speed of light and ci isthe maximum speed of the particles. And the nonvanishing parameterizedpost-Newtonian parameter α3 can also be used to test the violation of LLI.So the LLI can be test by method in high-energy field or by method incosmophysics. There are still many other parameters in different model totest LLI.

According to the description of LLI, consequent comparison of the ratesof two clocks will test LLI. Atom clock can achieve a very high precision,LLI test experiment by atom clocks was demonstrated in 1997,194 a cesiumclock and a rubidium clock carried on global positioning system (GPS)satellites were compared with a hydrogen maser, the upper limit value ofδc/c is not more than 10−9, where, δc is the difference between the observedspeed of light that propagates along a particular direction with the clock,and c is the speed of light in vacuum. ACES takes the LLI test as one of itstasks,140 a rubidium clock and a hydrogen maser will be launched to the ISSin 2013 or 2014. Due to the development of the femtosecond laser frequencycombs, optical clocks came into the sight of precision measurement of timeand frequency. Not only the laser cooled neutral atoms, but also the trappedions are used in optical clocks. This new generation clocks show higheraccuracy and stability, and are better candidates for space missions.

Besides the comparison of clocks, the test of LLI with atom interfer-ometers had been proposed,195,196 and the expected accuracy will be higherdue to their high sensitivity in gravity measurement.

9.3. Test of local position invariance

The description of LPI states that the rate of a free falling clock will bethe same with the rate of a standard one. In other words, comparison of twoclocks with different acceleration can also test the LPI. The precision of LPItest is at the same level as the measurement of the gravitational redshift,



it will not be better than the precisions of UFF and LLI test. In 1980, thecomparison between two hydrogen clocks was performed to test LPI,197

one clock was carried on a suborbital rocket, and the other one was on theground. The relative frequency shift of two clocks, �v/v , was disagreedwith the prediction value at the level of 10−5, where�v is the gravitationalredshift, v is the frequency shift due to free fall. LPI test is also one task ofACES, and the expected test precision is 10−6.

In 2010, Müller claimed that the atom interferometer can be used to mea-sure gravitational redshift,198 furthermore this measurement would achievean accuracy of 10−9, which is much higher than current accuracy measuredwith atom clocks. And this announcement caused a lively discussion.199–201

9.4. Other tests

The atom interferemetry is a powerful tool to sensor the phase change,any phase shifts induced by interactions between the atoms and the environ-ment can be measured by atom interferometers. Recently, the phase shiftinduced by the atom-surface van der Waals interaction was measured withatom interferometers,202 the berry phase and Aharonov–Anandan phase,203

polarizability of Na, K and Rb204 were also measured with atom interferom-eters. Due to high precision of gravity measurement, atom interferometerswill be a good tool to test the violation of the Newton’s inverse square lawin mid-distance range.205 The measurements of variation of α with atomclocks may be used to infer the violations of fundamental symmetries.206

Other potential applications of cold atoms are too numerous to mentionindividually.

10. Summary

Benefits from the technology of laser cooling and trapping of neutralatoms, cold atoms provide more opportunities in precision measurements.Atom transitions can provide the best frequency standards. Atoms clocks inspace will perform unprecedented improvements and have an irreplaceablecontribution to the GPS. Cold atom microwave clocks had achieved remark-able performance, while optical clocks have the best performances eitherin stability or in accuracy, and have great potential for further improve-ment. The rest mass that the matters have but the photons do not have


508 W. Peng et al.

lead a great difference between matter waves and light waves, so that atominterferometers will be widely used in gravity measurements. The quan-tum effects induced by gravity will provide a good platform for mergingthe gravity and quantum mechanics together. The main factors that limitthe sensitivity of an atom interferometer are the uncertainties of the laserswhich are used to manipulate the atoms, and the vibration of the mirrorswhich is used to reflect the laser beams. The parasitic accelerations, suchas the inertial acceleration and relative acceleration of the reference, are themain factors that limit the accuracy of an atom interferometer. To promotethe precision of measurements, some space atom interferometer projectsare proposed. Miniaturization is an important development trend of atominterferometers. Cold atoms and BECs will be used in fundamental phys-ical constants measurements, fundamental physics principle test and otherprecision measurements.

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