Coherent splitting of a BEC using dressed state potentials

1. Peter Krüger Coherent splitting of a BEC using dressed state potentials

2. Atom Chip 87Rb U-MOT Atom chips: micro vs. macrotraps • Complex (=complicated) assemblies • limited optical access • frabrication process

3. Microtraps close to surfaces Fabrication imperfections lead to fragmentation Limited trap lifetimes (coherence times) near the surface

4. 100μm Microtraps: possibilities Complex potentials Submicron structures (ebeam lithography) Micro scales Tight confinement Large aspect ratios

5. Applications Dynamics in low dimensional confinement High sensitivity, high resolution magnetic field measurements Surface probing Wildermuth, Hofferberth, Lesanovsky, Haller, Andersson, Groth, Bar-Joseph, P. K., Schmiedmayer, Nature 2005 Interferometry

6. Coherent splitting of BECs Interferometry

7. Time dependent beam splitter Electric beam splitter Interferometer potential Beam splitters

8. mF=+1/2 mF=+1/2 Ioffe field mF=-1/2 mF=-1/2 resonance condition shifts potential coupling term creates level repulsion the crossing is at a position where controlled by RF frequency ‘mF=+1/2 the levels are repelled by creating an effective Ioffe field, cntrolled by RF amplitude ‘mF=-1/2 New type of beam splitter Idea: use DC magnetic trap and couple different magnetic states with RF fields adiabatic potentials

9. Radio frequency beam splitter RF coupling term creates level repulsion • 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 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

10. Population of all minima thermal BEC

11. gravity Atom chip implementation atom chip 100 µm Z wire trap wire RF wire 45° RF transverse imaging 25 µm U wires I I in situ absorption image 10 µm RF antenna 50 µm Z wire longitudinal imaging

12. 400µm 25µm BEC double well transverse image splitting condensates over 80 µm for different traps by sweeping the RF longitudi- nal image split BEC RF freq. limit of optical detection • 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

13. BEC interference Deviation is interaction effect (during expansion) Images taken after 14 ms potential free time-of-flight expansion Smaller double well separation (3-6 micron) Schumm, Hofferberth, Andersson, Wildermuth, Groth, Bar-Joseph, Schmiedmayer, P. K., Nature Physics (online Sept. 2005, print Oct. 2005)

14. Coherence of the splitting process Relative 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)

15. 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 ?)

16. 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

17. 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

18. Ring potentials Other applications

19. Ring traps: circular polarisation Rings can be obtained by adiabatically converting a double well by adjusting the relative phase between two orthogonal (linearly polarized) RF fields Lesanovsky, Schumm, Hofferberth, Andersson, P. K., Schmiedmayer, arXiv physics/0510076

20. Permanent magnetic ring traps Dressed state potentials in circular polarization basis Can be used to lift the zero in (perm. magnetic) quadrupole ring Fernholz, Gerritsma, P.K., Spreeuw

21. 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

22. 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) • …

23. 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)

24. The team Experiment: Sebastian Hofferberth Thorsten Schumm Stephan Wildermuth Jose Verdu Theory: Igor Lesanovsky Mauritz Andersson Chips: Israel Bar-Joseph Sönke Groth Jörg Schmiedmayer Funding: EU, DFG Review on atom chips: Folman, P. K., Schmiedmayer, Denschlag, Henkel, Adv. At. Mol. Opt. Phys. 48, 263 (2002)