Coherent splitting of a BEC using dressed state potentials

Peter Krüger

Atom chips: micro vs. macrotraps

Atom Chip

87Rb U-MOT

•Complex (=complicated) assemblies

•limited optical access

•frabrication process

Microtraps close to surfaces

Fabrication imperfections lead to fragmentation

Limited trap lifetimes (coherence times) near the surface

Microtraps: possibilities

Complex potentials

Micro scalesSubmicron structures (ebeam lithography)

Tight confinementLarge aspect ratios

100μm

ApplicationsDynamics in low dimensional confinement

Surface probing

Interferometry

High sensitivity, high resolution magnetic field measurements

Wildermuth, Hofferberth, Lesanovsky, Haller, Andersson, Groth, Bar-Joseph, P. K., Schmiedmayer, Nature 2005

Interferometry

Coherent splitting of BECs

Beam splitters

Time dependent beam splitter

Interferometer potential

Electric beam splitter

New type of beam splitter

mF=+1/2

mF=-1/2

resonance condition shifts potential

the crossing is at a position where

controlled by RF frequency

|)(| rBµB

mF=+1/2

mF=-1/2

Ioffe field

‘mF=+1/2

‘mF=-1/2

coupling term creates level repulsion

the levels are repelled bycreating an effectiveIoffe field, cntrolledby RF amplitude

,| |B RF perpµ B

Idea: use DC magnetic trap and couple different magnetic states with RF fields adiabatic potentials

Radio frequency beam splitter

RF coupling term creates

level repulsion

Theory: Zobay, Garraway, PRL 2001 + Andersson, Schumm, Lesanovsky, Hofferberth, P. K., Schmiedmayer comment (submitted 2005) Experiments with thermal atoms: Colombe et al., Europhys. Lett. 2004

•BECs can be split in separated double well over wide range (2-80 μm)

•min. distance of wells given by trap ground state size

•structures can be much larger•state dependent coupling

2 2

F( ) ( ) ( ) / 2eff B F DC RF B F RFV r m g B r g B r

Population of all minima

BECthermal

Atom chip implementation

45°

RF

RFwire

trapwire

atom chip

gravity

100 µm Z wire

50 µm Z wire

10 µm RF antenna

I I 25 µm U wirestransverseimaging

longitudinalimaging

in situ absorption image

BEC double wellsplitting condensates over 80 µmfor different traps by sweeping the RF

limit of optical detection

25µm

400µm

longitudi-nal image

transverseimage

split BEC

RF freq.

•BECs can be split in separated double well over wide range

•min. distance of wells given by trap ground state size (~3μm)

•structures can be much larger

•state dependent coupling

BEC interference

Images taken after 14 ms potential free time-of-flight expansionSmaller double well

separation (3-6 micron)

Deviation is interaction effect (during expansion)

Schumm, Hofferberth, Andersson, Wildermuth, Groth, Bar-Joseph, Schmiedmayer, P. K., Nature Physics (online Sept. 2005, print Oct. 2005)

Coherence of the splitting processRelative phase between the fully split (tunneling suppressed on exp. time scales) BECs in measured in interference experiment – multiple realizations

Result: Well defined phase (spread of distribution σ = 13 degrees)

Phase evolution

Phase evolution during the splitting: As long as the two condensates are connected (tunneling is possible), the phase remains locked at zero (splitting speed 1.4 microns / ms)

Phase control: At lower splitting speed (0.6 microns / ms), the phase evolution reacts more sensitively to imbalances.

Phase spread At remains non-random even for larger splitting, but increases with hold time (1d phase diffusion ?)

Advantages over DC wire splitters•Number of (tightly confining) quadrupole minima is limited by number of wires used (i.e. at least two) for splitting (DC case)

•Splitting region can only be formed by merging two minima to a (weakly confining) higher order minimum (DC case)

•Small scales and surface distances needed for good splitters for DC case

•RF splitter performance equal at larger surface distance (trap frequencies of individual wells at equal barrier height)

•Distance of minima increases as a linear function of control parameter in RF case, as a square root function in the DC case

Lesanovsky, Schumm, Hofferberth, Andersson, P. K., Schmiedmayer, arXiv physics/0510076

Guided matter waver interferometer

Fully integrated wave guide interferometer:

•RF amplitude controls splitting distance

•A single RF current can provide varying RF amplitude if its width is adjusted

Lesanovsky, Schumm, Hofferberth, Andersson, P. K., Schmiedmayer, arXiv physics/0510076

Other applications

Ring potentials

Ring traps: circular polarisation

Lesanovsky, Schumm, Hofferberth, Andersson, P. K., Schmiedmayer, arXiv physics/0510076

Rings can be obtained by adiabatically converting a double well by adjusting the relative phase between two orthogonal (linearly polarized) RF fields

Permanent magnetic ring traps

Fernholz, Gerritsma, P.K., Spreeuw

Dressed state potentials in circular polarization basis

220( / ) / 2

Fm F B F F BE m g B g

Can be used to lift the zero in (perm. magnetic) quadrupole ring

Potential minima on a torus surface

Applying cylindrically symmetric RF fields allows to form and control minima on torus

•circular polarization (in any ρz-plane) results in homogeneous 2d surface (triply connected)

•Elliptic polarization results in two rings (1d)•Phase tuning can be used to rotate minima poloidally

•Added linear field allows to individually form and control (rotate) dimples toroidally

Ring applications

• 1d and 2d traps in multiply connected geometries• adiabatic transfer between regimes• induced rotations in toroidal and poloidal directions• two split rings -> Sagnac type interferometry• controlled independent movement on the ring possible• tunnelling junctions between rings (squids)• …

Conclusion

•atom chips are versatile tools for matter wave (quantum gas) manipulation

•Coherent beam splitter demonstrated: door to quantum dynamics experiments

•Many more applications of RF potentials possible (examples: interferometers & rings)

The team

Experiment:Sebastian HofferberthThorsten SchummStephan WildermuthJose Verdu

Jörg Schmiedmayer

Chips:Israel Bar-JosephSönke Groth

Review on atom chips: Folman, P. K., Schmiedmayer, Denschlag, Henkel, Adv. At. Mol. Opt. Phys. 48, 263 (2002)

Theory:Igor LesanovskyMauritz Andersson

Funding: EU, DFG