helium spectroscopy spectroscopy of a forbidden transition in a 4 he bec and a 3 he degenerate fermi...
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Helium SpectroscopySpectroscopy of a forbidden transition in a 4He BEC and a 3He degenerate Fermi gasRob van Rooij, Juliette Simonet*, Maarten Hoogerland**, Roel Rozendaal,
Joe Borbely, Kjeld Eikema, and Wim Vassen
Institute for Lasers, Life and Biophotonics, VU University, Amsterdam
* École Normale Supérieure, Laboratoire Kastler-Brossel, Paris, France ** University of Auckland, Auckland, New Zealand
He Energy Levels
First excited state: 19.82 eV
All bound states are (1s)(nl)
2 3S1 ( n 2S+1LJ )
He Energy Levels
First excited state: 19.82 eV
All bound states are (1s)(nl)
2 3S1 ( n 2S+1LJ )
What can we learn from helium spectroscopy?
2. determine the fine-structure constant,
1. test 2-electron QED theory
Derived from measurements of the isotope shift.Important for nucelar structure
1970s: ML Lewis and PH Serafino ; M Douglas and NM Kroll O(6mc2)
Modern era of QED began with the discovery of the Lamb shift in 1947(electron self energy and vacuum polarization)
1990s - present: GWF Drake ; K Pachucki O(7mc2) , O(8mc2)
1964: C Schwartz developed a scheme for an O(6mc2) calculation
Coupling strength of electromagnetic interactions between charged elementary particles
proportional to the strengthof the electromagnetic force
3. nuclear charge radius
Argonne National Laboratory, Argonne, Illinois, USA
What can we learn from helium spectroscopy?
1 1S0 –to – 2 1P1 Test 2-electron QED
theory• 58 nm transition in helium
• Lamb shift measurements in helium provide a stringent test of QED effects
• Isotope shift measurement: 3He and 4He
2 3S1 –to – 2 3P0,1,2
Hydrogen n=2
2P3/2
2S1/2
2P1/21.0 GHz
0
0.2
0.4
0.6
0.81
1.2
-6-4
-20
24
6
Natural width 100 MHz=1.6 ns(to 1S)
Helium 23PJ
23P0
2. 3 GHz
00.20.40.60.8
11.2
-6-4
-20
24
6
Natural width 1.6 MHz
23P1
23P2
(60X narrower than H)
(3X larger than H)
(to 23S)
180X better candidate than H!
=98 ns
I. large energy intervals (2.3 GHz and 29.6 GHz)II. long lifetime (= 98 ns)
Why use the 2 3PJ states of helium to determine ?
29. 6 GHz9.9 GHz
2 3S1 –to – 2 3P0,1,2 How does one determine from helium fine structure?
Comparison between theory and experiment for the 29.6 GHz interval is used to determine
The smaller 2.3 GHz interval tests 2-electron QED.
Nonrelativistic Schrödinger equation,
Kinetic energyof the 2 electrons
Potential energyfrom the nucleus and
between the 2 electrons
transformation intocenter-of-mass
frame of the nucleus.(Mass polarization term)
2 3S1 –to – 2 3P0,1,2
The fine-structure energies are expressed as a power series expansion of since 2 ~ 10-4 one can use perturbation theory
How does one determine from helium fine structure?Comparison between theory and experiment
for the 29.6 GHz interval is used to determine The smaller 2.3 GHz interval tests 2-electron QED.
”
Each coefficient, C, is itself a power series expansion of the form (/M ~ 10-4)
30 GHz 50 MHz 1 MHz 50 kHz <15 kHz
2 3S1 –to – 2 3P0,1,2
Relating experiment and theory (K. Pachucki: Phys Rev A 79 062516)
experiment theory
How does one determine from helium fine structure?Comparison between theory and experiment
for the 29.6 GHz interval is used to determine The smaller 2.3 GHz interval tests 2-electron QED.
It is vital to measure using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics.
i) different degrees of reliance on QED expansions of the measured quantitiesii) experiments performed using dissimilar techniques are not affected by the same
systematic errors
Determinations of
AC Josephson
137.036000 137.036005137.035990-1
137.035995
dc vaoltage, V, applied across a superconducting junction leads toan alternating current of frequency f
It is vital to measure using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics.
i) different degrees of reliance on QED expansions of the measured quantitiesii) experiments performed using dissimilar techniques are not affected by the same
systematic errors
Determinations of
AC Josephson
137.036000 137.036005137.035990-1
137.035995
muonium hfs
+ (antiparticle to -)
Ground state HFS
It is vital to measure using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics.
i) different degrees of reliance on QED expansions of the measured quantitiesii) experiments performed using dissimilar techniques are not affected by the same
systematic errors
Determinations of
quantum Hall effect
AC Josephson
137.036000 137.036005137.035990-1
137.035995
muonium hfs
A strong, perpendicular magnetic field is applied to a two-dimensionalelectron gas at a low temperature, the resistance of the gas is quantized with n
It is vital to measure using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics.
i) different degrees of reliance on QED expansions of the measured quantitiesii) experiments performed using dissimilar techniques are not affected by the same
systematic errors
Determinations of
Cs recoil Rb recoil
quantum Hall effect
AC Josephson
137.036000 137.036005137.035990-1
137.035995
muonium hfs
hv
p
It is vital to measure using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics.
i) different degrees of reliance on QED expansions of the measured quantitiesii) experiments performed using dissimilar techniques are not affected by the same
systematic errors
Determinations of
Cs recoil Rb recoil
quantum Hall effect
AC Josephson
137.036000 137.036005137.035990-1
137.035995
muonium hfs
ge(electron magnetic moment)(0.37ppb)
one-electron orbit in a Penning trap (amp. & freq. not to scale)
measure trap frequencies yields gs
It is vital to measure using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics.
i) different degrees of reliance on QED expansions of the measured quantitiesii) experiments performed using dissimilar techniques are not affected by the same
systematic errors
Determinations of
Cs recoil Rb recoil
quantum Hall effect
AC Josephson
137.036000 137.036005137.035990-1
137.035995
muonium hfs
20 ppb – dominated by theoryge(electron magnetic moment)
(0.37ppb)
helium spectroscopy
X5 ppb
Nuclear Charge Radius
Drake: Can J Phys 86 45-54 (2008)
Measure “identical” transitions in different isotopes: 3He, 4He, 6He, 8He
”QED terms independent of /M cancel
Radiative recoil ~ 10 kHzcontribute to the uncertainty
2 3S1 –to– 2 3PJ
2 3S1 –to– 3 3PJ
2 3S1 –to– 2 1S0
1 1S0 –to– 2 1P1
Nuclear Charge RadiusMeasure “identical” transitions in different isotopes: 3He, 4He, 6He, 8He
Only relative charge radii can be deduced.
To determine absolute charge radii the radius of the reference nucleus, 4He, must be known with the best possible precision
rc (4He) = 1.681 ± 0.004 fm elastic electron scattering from 4He nucleus
Drake: Can. J. Phys. 83: 311–325 (2005)
2 3S1 –to– 2 1S0
2 3S1 –to– 2 1S0
0
20
22
eV 1s2s 1S0
1s2s 3S1
1557nm
1s2s 3P2
1s2s 1P1
1s1s 1S0
Lifetimes (He*)
2 1S0: 20 ms , 2 = 8 Hz
2 3S1: 8000 s
2 3S1 → 2 3P2 laser cooling / trapping
2 3S1 → 2 1S0 (M1): 1557 nm
QED effects strongestfor low-lying S states
2 3S1 can be trapped at 1557 nm(red detuned from 23S→23P: 1083 nm)
2 1S0 anti-trapped(blue detuned from 21S→21P: 2060 nm)Isotope shift
Experimental setup
Crossed optical dipole trap at 1557 nm
Bose-Einstein condensate of 4He*
Degenerate Fermi gas of 3He* 210
160
170
180
190
200Time of Flight
(ms)
MC
P S
ignal (a
.u.)
TOF on Micro-channel Plate (MCP)
Absorption imaging
Dipole trap laser: 40 MHz detuned from
atomic transition
Mode-locked erbium doped fiber laser (Menlo Systems)Referenced to a GPS-controlled Rubidium clock
Frequency comb
770813 770814 770815770812
f beat
Mode-locked erbium doped fiber laser (Menlo Systems)Referenced to a GPS-controlled Rubidium clock
flaser = nfrep + fceo + fbeat
frep ~ 250 MHz
fceo ~ 20 MHz
fbeat ~ 60 MHz
Load a 4He BEC or 3He DFG from magnetic trap into optical dipole trap
Measurement sequence
160 170 180 190 200 210Time of Flight (ms)
MC
P S
ignal (a
.u.)
Determine remaining atom number
Apply spectroscopy beam
Turn off the trap and record MCP signal
FWHM: 90 kHz
60 60.1 60.2 60.3 60.4Beat frequency (MHz)
12010080
60
40
20
0Rem
ain
ing a
tom
s (%
)
Systematics
Recoil shift: ~20 kHz
2 3S1
MJ=+1MJ= 0
MJ=-1
MJ=+1
MJ=0
MJ=-1
fR FEnerg
y
0
B-field
hv
p
AC Stark shift:
Measure for various powers
Extrapolate to zero power
Mean field: < exp. uncertainty
Zeeman shift
AC Stark shift 4He
Accounted for:
– Recoil shift (20.6 kHz)
– Mean field shift
– Zeeman shift
192 510 702.150 4 (41) MHz
Relative uncertainty: 3 x 10-11
Preliminary result
Quantum statistical effect
4He* BEC
occupy ground state
fluctuating atom number
100
200
300
400
500
600Power
(mW)
0.2F
it T
em
pera
ture
(u
K)
0.6
0.4
3He* DFG, low power
atoms fill up the trap
constant atom number
3He* DFG, P > 300 mW
Trap depth large enough to accommodate full thermal distribution
Measured AC-Stark shift curve non-linear
AC Stark shift 3He
Accounted for:
– Recoil shift (27.3 kHz)
– Mean field shift
– Zeeman shift
192 504 914.431 7 (14) MHz
Relative uncertainty: 8 x 10-12
Preliminary result
Results
Drake
Pachucki
Indirect expt.
Our result
f – 192510700 (MHz)
Helium 4 transition frequency
f – 192502660 (MHz)
Drake
Pachucki
Our result
Indirect expt.
Helium 3 transition frequency
f – 8034 (MHz)
Drake
Pachucki
Our result
Isotope shift
Theoretical uncertainty dominated by nuclear charge radii determined from electron-nucleus scattering experiments
Summary
First time:
spectroscopy on ultracold trapped 4He* and 3He*
direct measurement between triplet and singlet states in He
observation of the 1557 nm 2 3S → 2 1S transition
Observed quantum statistical effects in the dipole trap
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