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Quantum dynamics with ultra cold atoms

Quantum dynamics with ultra cold atoms. I. Grunzweig, Y. Hertzberg, A. Ridinger (M. Andersen, A. Kaplan). Nir Davidson Weizmann Institute of Science. BEC. Billiards. Eitan Rowen, Tuesday. Fsec laser pulse. Dynamics inside a molecule: quantum dynamics on nm scale. 1 nm. E. R.

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Quantum dynamics with ultra cold atoms

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  1. Quantum dynamics with ultra cold atoms I. Grunzweig, Y. Hertzberg, A. Ridinger (M. Andersen, A. Kaplan) Nir Davidson Weizmann Institute of Science BEC Billiards Eitan Rowen, Tuesday

  2. Fsec laser pulse Dynamics inside a molecule:quantum dynamics on nm scale 1nm E R

  3. Is there quantum chaos? • Classical chaos: distances between close points grow exponentially • Quantum chaos: distance between close states remains constant Asher Peres (1984): distance between same state evolved by close Hamiltonians grows faster for (underlying) classical chaotic dynamics ??? Answer: yes….but also depends on many other things !!! One thing with many names: survival probability = fidelity = Loschmidt echo R. Jalabert and H. Pastawski, PRL 86, 2490 (2001)

  4. Atom-optics billiards:decay of classical time-correlations …and effects of soft walls, gravity, curved manifolds, collisions….. PRL 86, 1518 (2001), PRL 87, 274101(2001), PRL 90 023001 (2003)

  5. Wedge billiards: chaotic and mixed phase space

  6. Criteria for “quantum” to “classical” transition Old: large state number New: “mixing” to many states by small perturbation But “no mixing” is hard to get • Quantum dynamics with <n>~106: challenges and solutions: • Very weak (and controlled) perturbation –optical traps + very strong selection rules • No perturbation from environment - ultra cold atoms • Measure mixing – microwave spectroscopy • Pure state preparation? - echo

  7. Pulsed microwave spectroscopy Prepare Atomic Sample → MW-pulse Sequence → Detect Populations On Off π-pulse: π/2-pulse: • cooling and trapping ~106 rubidium atoms • optical pumping to optical transition MW “clock”transition

  8. Ramsey spectroscopy of free atoms H = Hint + Hext→ Spectroscopy of two-level Atoms MW Power π/2 T π/2 Time

  9. EHF Microwave pulse H2 Microwave pulse e-iH2t|2,Ψ> |2,Ψ> <Ψ| eiH1te-iH2t|Ψ>… |1,Ψ> H1 e-iH1t|1,Ψ> |1,Ψ> Ramsey spectroscopy of trapped atoms • General case: Nightmare • Short strong pulses: OK (Projection)

  10. Ramsey spectroscopy of single eigenstate T MW Power π/2 π/2 Time • For small Perturbation:

  11. Ramsey spectroscopy of thermal ensemble T MW Power π/2 π/2 Time • For small Perturbation: Averaging over the thermal ensemble destroys the Ramsey fringes

  12. t=T t=2T Echo spectroscopy (Han 1950) MW Power T T π/2 π π/2 Time NOTE: classically echo should not always work for dynamical system !!!!

  13. De-Coherence Coherence Echo spectroscopy MW Power T T π/2 π π/2 Time Ramsey Echo BUT: it works here !!!!

  14. Echo vs. Ramsey spectroscopy Ramsey H2 H1 Echo H2 H1 H1 H2

  15. Tosc/2 Tosc Calculation for H.O. De-Coherence EHF Coherence Quantum dynamics in Gaussian trap

  16. De-Coherence Coherence Long-time echo signal • 2-D: • 1-D:

  17. Observation of “sidebands” Π-pulse 4π-pulse

  18. Quantum stability in atom-optic billiards <n>~104

  19. Quantum stability in atom-optic billiards <n>~104 D. Cohen, A. Barnett and E. J. Heller, PRE 63, 046207 (2001)

  20. Avoid Avoided Crossings

  21. Perturbation strength Quantum dynamics in mixed and chaotic phase-space Incoherent Coherent Perturbation-independent decay

  22. Quantum dynamics in perturbation-independent regime

  23. Shape of perturbation is also important

  24. … and even it’s position

  25. No perturbation-independence

  26. Finally: back to Ramsey (=Loschmidt)

  27. Conclusions • Quantum dynamics of extremely high-lying states in billiards: survival probability = Loschmidt echo = fidelity=dephasing? • Quantum stability depends on: classical dynamics, type and strength of perturbation, state considered and…. • “Applications”: precision spectroscopy (“clocks”) quantum information Can many-body quantum dynamics be reversed as well? (“Magic” echo, Pines 1970’s, “polarization” echo, Ernst 1992)

  28. Atom Optics Billiards • Control classical dynamics (regular, chaotic, mixed…) • Quantum dynamics with <n>~106 ???? Tzahi Ariel Nir

  29. Low density  collisions Atom Optics Billiards • Positive (repulsive) laser potentials of various shapes. Standing Wave Trap Beam • Z direction frozen by a standing wave • “Hole” in the wall  probe time-correlation function

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