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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 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 1nm E R
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)
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)
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
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
Ramsey spectroscopy of free atoms H = Hint + Hext→ Spectroscopy of two-level Atoms MW Power π/2 T π/2 Time
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)
Ramsey spectroscopy of single eigenstate T MW Power π/2 π/2 Time • For small Perturbation:
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
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 !!!!
De-Coherence Coherence Echo spectroscopy MW Power T T π/2 π π/2 Time Ramsey Echo BUT: it works here !!!!
Echo vs. Ramsey spectroscopy Ramsey H2 H1 Echo H2 H1 H1 H2
Tosc/2 Tosc Calculation for H.O. De-Coherence EHF Coherence Quantum dynamics in Gaussian trap
De-Coherence Coherence Long-time echo signal • 2-D: • 1-D:
Observation of “sidebands” Π-pulse 4π-pulse
Quantum stability in atom-optic billiards <n>~104 D. Cohen, A. Barnett and E. J. Heller, PRE 63, 046207 (2001)
Perturbation strength Quantum dynamics in mixed and chaotic phase-space Incoherent Coherent Perturbation-independent decay
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)
Atom Optics Billiards • Control classical dynamics (regular, chaotic, mixed…) • Quantum dynamics with <n>~106 ???? Tzahi Ariel Nir
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