Cold Atoms that interact: nonlinear Dynamics and Spectroscopy

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Cold Atoms that interact(nonlinear) Dynamics
and Spectroscopy

• Nir Davidson
• Weizmann Institute of Science, Rehovot, Israel

Billiards A. Kaplan, M. Andersen, I. Grunzweig
(N. Friedman, L. Khaykovich) BEC N. Katz, E.
Rowen (J. Steinhauer, R. Ozeri, E. Gershnabel)
Interact with themselves BEC
Interact with the walls Billiards
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BEC

• Bogoliubov Excitation spectrum.
• Excitation Dynamics Repulsion and damping.
• Strong excitations

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Experimental set-up

• 87Rb atoms in the ground state.
• N0 1-5x10 5 atoms.
• T 0.3 Tc 100 nK
• 95 of atoms in the ground state
• Chemical potential m/h 2 4 kHz

0.14 mm
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Bogoliubov excitation spectrum
low k limit Phonon regime
high k limit Free particle regime
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Bragg Spectroscopy
Time of flight image of an excited condensate -
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Condensate response to the Bragg pulse
Time of flight image of an excited condensate -
Pulse efficiency vs. Dw
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Excitation Spectrum a roadmap
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High resolution phonon spectroscopy.

• -Numerical solution agrees with data.
• Multiple-branch spectrum.
• different radial modes.

J. Steinhauer, N. Katz, R. Ozeri, N. Davidson, C.
Tozzo and F. Dalfovo PRL 90, 060404 (2002).
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Echo Spectroscopy
E. Gershnabel, N. Katz, R. Ozeri, E. Rowen, J.
Steinhauer, N. Davidson, cond-mat/309584 (2003).
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Condensateexcitation interaction Repulsion
All of the excitation energy is carried by the
released phonons!
R. Ozeri, J. Steinhauer, N. Katz, and N.
Davidson, PRL 88, 220401 (2002).
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Condensateexcitation interaction Damping
N. Katz, J. Steinhauer, R. Ozeri, N. Davidson,
PRL 89, 2120401 (2002).
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Condensateexcitation interaction Damping
Beliaev
k-q
k
q
q
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Measured Beliaev Damping
Simulation
Experiment
N. Katz, J. Steinhauer, R. Ozeri, N. Davidson,
PRL 89, 2120401 (2002).
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Landau damping observed??
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Strong excitation suppression of dephasing
N-i, k
i, 0
Inhomogeneous decay
Gross-Pitaevskii simulation
N. Katz, R. Ozeri, E. Rowen, E. Gershnabel and N.
Davidson, cond-mat/0308492 (2003).
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and measurement of decoherence
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Oscillation dynamics - produces spectral splitting
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and collisional splitting
E. Rowen, N. Katz, R. Ozeri, E. Gershnabel and N.
Davidson, cond-mat/0402225 (2004).
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Low momentum TOF interference fringes
Time-of-flight
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A new spectroscopic tool
Can possibly observe single particle excitations.
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Billiards

• Control classical dynamics (regular, chaotic)
• Quantum dynamics with ltngt108 ????

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Atom Optics Billiards
N. Friedman, A. Kaplan, D. Carasso, and N.
Davidson, PRL 86, 1518 (2001)
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Ramsey Spectroscopy of Trapped Atoms

• Transition Matrix Elements

• Short strong pulses Projection

• Small Perturbation

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Ramsey Spectroscopy of a Thermal Ensemble
H2
MW pulse
MW pulse
e-iH2t?gt
2,?gt
lt? eiH1te-iH2t?gt
1,?gt
H1
e-iH1t?gt
1,?gt
Averaging over the thermal ensemble destroys the
Ramsey fringes
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Echo vs. Ramsey Spectroscopy
MW Power
?T
?T
p/2
p/2
p
Time
M. F. Andersen, A. Kaplan, and N. Davidson, Phys.
Rev. Lett. 90, 023001 (2003)
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Echo vs. Ramsey Spectroscopy
Ramsey
Echo
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Echo Spectroscopy and Dynamics
Calculation
M. F. Andersen, A. Kaplan, and N. Davidson, Phys.
Rev. Lett. 90, 023001 (2003)
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Does Stability Depend on Shape?
Dilation
Stretching
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Quantum Chaos
778.4 nm
779 nm
777.5 nm
777 nm
776 nm
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Perturbation Independent Decay
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Mixed Phase-Space
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And Very Long Times

p
p
MW Power
p
2
2
Time

• Z-motion
• Photon Scattering
• Trap Fluctuations
• Collisions
• ???

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Long Time Echo Signal
M. F. Andersen, A. Kaplan, and N. Davidson, Phys.
Rev. Lett. 90, 023001 (2003)
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Internal Degrees of Freedom
?EHF
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Excitation mixing a dressed state model
Excitation Fock-state manifold
R. Ozeri, N. Katz, J. Steinhauer, E. Rowen, and
N. Davidson Phys. Rev. Lett. 90, 170401 (2003).
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Excitation Spectrum a roadmap
J. Steinhauer, R. Ozeri, N. Katz, and N.
Davidson, PRL 88, 120407 (2002).
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Static Structure Factor
J. Steinhauer, R. Ozeri, N. Katz, and N.
Davidson, PRL 88, 120407 (2002).
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Ramsey Spectroscopy of Free Atoms

• H Hint Hext ? Spectroscopy of two level Atoms

MW Power
p/2
p/2
?T
Time
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Circular and Elliptical Billiards
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Conclusions and outlook

• Bogoliubov and Beliaev theories confirmed
  experimentaly for atomic vapor BEC.
• An excited condensate behaves as a laser which
  is coupled to a quasi-continuum of modes.
• Many analogies to the physics of atom-photon
  systems Natural line-width, Lamb shift, Mollow
  doublets, ac stark shift.
• Spectroscopy Beyond Bogoliubov Beliaev,
  Non-linearity, Strong interactions (Roton).

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Bogoliubov transformation (1947)
Bogoliubov quasi-particle operators -
The Hamiltonian is diagonalized in the new basis
-
Bogoliubov quasi-particles energy spectrum -
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The roton in BEC a calculation

• Jastrow many-particle wavefunction ansatz
• Quantum Metropolis algorithm

J. Steinhauer, R. Ozeri, N. Katz, and N.
Davidson, cond-mat/0303375 (2004).
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The roton in BEC results