1. Dynamics of a BEC colliding with a time-dependent dipole barrier (+ Special Bonus Features) Institut D’Optique, Palaiseau, France October 8, 2007 Chris Ellenor Aephraim Steinberg’s group, University of Toronto

2. DRAMATIS PERSONÆ Toronto quantum optics & cold atoms group: Postdocs: An-Ning Zhang(  IQIS) Morgan Mitchell (  ICFO) (HIRING!)Matt Partlow(  Energetiq)Marcelo Martinelli (  USP) Optics: Rob AdamsonKevin Resch(  Wien  UQ  IQC) Lynden(Krister) ShalmJeff Lundeen (  Oxford) Xingxing Xing Atoms: Jalani Fox (  Imperial)Stefan Myrskog (  BEC  ECE) (SEARCHING!)Mirco Siercke ( ...?)Ana Jofre(  NIST  UNC) Samansa ManeshiChris Ellenor Rockson Chang Chao Zhuang Xiaoxian Liu UG’s: Ardavan Darabi, Nan Yang, Max Touzel, Michael Sitwell, Eugen Friesen Some helpful theorists: Pete Turner, Michael Spanner, H. Wiseman, J. Bergou, M. Mohseni, J. Sipe, Daniel James, Paul Brumer,...

3. Talk Outline BEC Experiment: Dynamics of a BEC colliding with a time-dependent dipole barrier –Motivation: Tunneling –The “Muga” Effect –Applications to state measurement / tomography –Some ground (by “ground” I mean “experiment”) breaking data Lattice Experiment: Decoherence and Control of Vibrational States of Atoms in an Optical Lattice

4. Part 1: My BEC

5. Motivation Our long term goal is to study transit times for atoms tunneling through a potential barrier To begin, we will study predictions of non-classical behaviour in collisions with this barrier This effect suggests an interferometric method for measuring the condensate wavefunction / Wigner function

6. Collisional Transitory Enhancement of the High Momentum Components of a Quantum Wave Packet S. Brouard and J. G. Muga, Phys. Rev. Lett. 81, 2621–2625 (1998)

7. Collisional Transitory Enhancement of the High Momentum Components of a Quantum Wave Packet S. Brouard and J. G. Muga, Phys. Rev. Lett. 81, 2621–2625 (1998)

8. More localized = higher momentum components Consider an ensemble of particles with some distribution in phase space approaching a repulsive potential Classically, we can construct the inequality Quantum mechanically, this can be violated, and higher momentum components produced, i.e. G > 0 incomingoutgoing accumulated probability for momentum > p Collisional Transitory Enhancement of the High Momentum Components of a Quantum Wave Packet S. Brouard and J. G. Muga, Phys. Rev. Lett. 81, 2621–2625 (1998)

9. In our experiment we’ll use a small, weak barrier that barely causes any reflection of the BEC to look for these transient effects. (Brouard S., Muga J.G., Annalen der Physik 7 (7-8): 679-686 1998) Momentum distributions: We will switch the barrier off, let the BEC expand and get the momentum distribution from the time of flight Collisional transitory enhancement of the high momentum components

10. This effect can be easily understood by realizing that the barrier writes a Pi phaseshift onto the wavefunction The effect is a single-particle effect, so mean field energy present would make it impossible to use time of flight measurements to extract momentum distributions, and soliton formation would further complicate matters

11. Performing the experiment with an expanded BEC: TOF measurement of momentum distribution at time of collision Variable barrier position = variable drop time before collision 0 ms drop before collision

12. Performing the experiment with an expanded BEC: TOF measurement of momentum distribution at time of collision Variable barrier position = variable drop time before collision 1 ms drop before collision

13. Performing the experiment with an expanded BEC: TOF measurement of momentum distribution at time of collision Variable barrier position = variable drop time before collision 5 ms drop before collision

14. Performing the experiment with an expanded BEC: TOF measurement of momentum distribution at time of collision Variable barrier position = variable drop time before collision 12 ms drop before collision

15. One can think of the expanded BEC as a series of transform- limited wavepackets each with a different phase and velocity The fast wavepackets picked up a total phase of pi, the slow ones no phase, and only the central one exhibits transient enhancement of momentum

16. The fringes then tell us the phase difference between the central momentum component and the rest of the cloud, allowing reconstruction of the wavefunction

17. Tomography? For a pure state, one shot should be enough For a mixed state, taking measurements at different times (different collision times) should be enough to assemble a Wigner function (but we’re not sure how) Maybe able to achieve excellent position resolution of initial state by measuring phase well Also could watch evolution of “purity,” e.g. in the Mott insulator transition’ Initial position of cloud has been offset by 1  m Could distinguish coherent vs. incoherent addition

18. “Polarization-Gate” Geometry Spectro- meter Frequency-Resolved Optical Gating (FROG) Trebino, et al., Rev. Sci. Instr., 68, 3277 (1997). Kane and Trebino, Opt. Lett., 18, 823 (1993).

19. Simulation of a FROG Benchmark

20. Some preliminary data –5.6ms expansion before collision, 15ms expansion after

21. Comparing to numerical models (Change the phase shift given by the barrier) (Ok – Maybe a bit of wishful thinking!)

22. AOM The Dipole Barrier – Making a Sheet of Light Absorption probe FPGA 200 GHz detuned laser diode

23. AOM The Dipole Barrier – Making a Sheet of Light AOM scans beam Absorption probe FPGA

24. AOM The Dipole Barrier – Making a Sheet of Light Absorption probe Spot is 8um thick by 200um wide With scan - sheet is ~ 0.5mm wide Height is ~ 150nK Intensity flat to < 1% FPGA BEC of about 10 5 87 Rb atoms

25. Next Generation Barrier…

28. Part 1 Summary During the collision of a wavepacket with a barrier transient effects can be observed that are not visible in the asymptotic scattering limits. We may realize an interferometric effect similar to FROG where we infer phase information, and perhaps the Wigner function of our BEC using these transient effects Preliminary results have been achieved, possibly demonstrating a new technique for extraction of phase information from a condensate Possible applications to BEC tomography, and study of entanglement evolution

29. Talk Outline BEC Experiment: Dynamics of a BEC colliding with a time-dependent dipole barrier –Motivation: Tunneling –The “Muga” Effect –Applications to state measurement / tomography –Some ground (by “ground” I mean “experiment”) breaking data Lattice Experiment: Decoherence and Control of Vibrational States of Atoms in an Optical Lattice –Preparing and tomographing quantum states in an optical lattice –Atom (pulse) echoes –Designer excitation pulses –Probing decoherence with 2-D pump-probe spectroscopy –Coherent control of vibrational excitations

30. Part 2: The Optical Lattice

31. Vertical 1D Optical Lattice Experimental Setup Cold 85 Rb atoms T ~ 10μK Lattice spacing : a ~ 0.93μm Effective lattice recoil energy = E R ~ 32nK U o =(18-20)E R = (580-640)nK Controlling phase of AOMs allows control of lattice position Function Generator AOM1 TUI PBS AOM2 Amplifier PBS Spatial filter  Grating Stabilized Laser

32. Quantum CAT scans 1

33. Rb atom trapped in one of the quantum levels of a periodic potential formed by standing light field (30GHz detuning, c. 20 E R in depth) Tomography & control in Lattices [Myrkog et al., PRA 72, 013615 (05) Kanem et al., J. Opt. B7, S705 (05)] Goals: How to fully characterize time-evolution due to lattice? How to correct for “errors” (preserve coherence,...)?

34. Basic Ingredients for Tomography –State Preparation –State Measurement –Unitary operations, i.e. Measure in different bases

35. Measuring State Populations Ground State 1 st Excited State Initial Lattice After adiabatic decrease Well Depth t (ms) 0 t1t1 t 1 +40ms Preparing a ground state t o +30ms 2 bound states 0 toto 7 ms 1 bound state

36. Time-resolved quantum states

37. Designing excitation pulses...

38. Atomic state measurement (for a 2-state lattice, with c 0 |0> + c 1 |1>) left in ground band tunnels out during adiabatic lowering (escaped during preparation) initial statedisplaceddelayed & displaced |c 0 | 2 |c 0 + c 1 | 2 |c 0 + i c 1 | 2 |c 1 | 2

39. Extracting a superoperator: prepare a complete set of input states and measure each output Likely sources of decoherence/dephasing: Real photon scattering (100 ms; shouldn't be relevant in 150  s period) Inter-well tunneling (10s of ms; would love to see it) Beam inhomogeneities (expected several ms, but are probably wrong) Parametric heating (unlikely; no change in diagonals) Other

40. Wait… Quantum state reconstruction Shift…  x Cf. Poyatos,Walser,Cirac,Zoller,Blatt, PRA 53, 1966 ('96) & Liebfried,Meekhof,King,Monroe,Itano,Wineland, PRL77, 4281 ('96) Measure ground state population (former for HO only; latter requires only symmetry) Q(0,0) = P g 1  W(0,0) =  (-1) n P n 1 

41. Husimi distribution of coherent state

42. Data:"W-like" [P g -P e ](x,p) for a mostly-excited incoherent mixture

43. Atom echoes 2

44. Oscillations in lattice wells (Direct probe of centre-of-mass oscillations in 1  m wells; can be thought of as Ramsey fringes or Raman pump-probe exp’t.)

45. 0 500  s 1000  s 1500  s 2000  s Towards bang-bang error-correction: pulse echo indicates T2 ≈ 1 ms... Free-induction-decay signal for comparison echo after “bang” at 800  s echo after “bang” at 1200  s echo after “bang” at 1600  s coherence introduced by echo pulses themselves (since they are not perfect  -pulses) (bang!)

46. time ( microseconds ) single-shift echo (≈10% of initial oscillations) double-shift echo (≈20-30% of initial oscillations) Echo from compound pulse Ongoing: More parameters; find best pulse. E.g., combine amplitude & phase mod. Also: optimize # of pulses. Pulse 900 us after state preparation, and track oscillations

47. Cf. Hannover experiment Buchkremer, Dumke, Levsen, Birkl, and Ertmer, PRL 85, 3121 (2000). Far smaller echo, but far better signal-to-noise ("classical" measurement of ) Much shorter coherence time, but roughly same number of periods – dominated by anharmonicity, irrelevant in our case.

48. Why does our echo decay? Present best guess = finite bath memory time: So far, our atoms are free to move in the directions transverse to our lattice. In 1 ms, they move far enough to see the oscillation frequency change by about 10%... which is about 1 kHz, and hence enough to dephase them. 3D lattice (preliminary results) Except for one minor disturbing feature: These data were first taken without the 3D lattice, and we don’t have the slightest idea what that plateau means. (Work with Daniel James to relate it to autocorrelation properties of our noise, but so far no understanding of why it’s as it is.)

49. Our thinking shows one-dimensionality 3

50.  exc  det  exc

53. And finally, towards coherent control 4

54. 0 (ground) 1 (desired excitation) 2 (loss) PM 2 AM 22 PM  May expect loss  cos (  AM - 2  PM - some phase) One scheme for reducing leakage? Classical explanation as “sideband engineering,” or something more?

55. Preliminary evidence for 1+2 coherent control

56. 1We can prepare a variety of quantum states of vibration of atoms in lattice wells, and carry out quantum state & process tomography on them. 2Decoherence occurs in 3-5 cycles due at least in part to inhomogeneous broadening. 3Pulse echo can let us probe decoherence and/or the memory function of the inhomogeneities. We are surprised by the “fidelity freeze” in 1D and 3D lattices, and by the rapidity of the initial fidelity decay in the 3D case. 4We have been able to excite as many as 70% of our atoms, and are continuing to work on optimizing pulses for control (& echo “error correction”). 5We have apparently seem some 1-vs-2 coherent control, but have a lot more to understand. 6There remain many other strategies to try, starting with ARP. Summary

58. To understand this, consider the Fourier transform of our symmetric envelope with a discontinuous phase profile

59. Do we have an interferometer? Well, vary the phase! We notice from our data that fringes translate as a function of phase shift from the barrier (Ok – Maybe a bit of wishful thinking!)