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Title: Observation of High-Order Quantum Resonances in the Kicked Rotor

Abstract

Quantum resonances in the kicked rotor are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances occur when the scaled Planck's constant {Dirac_h}/2{pi}-tilde=(r/s)4{pi}, for any integers r and s. However, only the {Dirac_h}/2{pi}-tilde=r2{pi} resonances are easily observable. We have observed high-order quantum resonances (s>2) utilizing a sample of low energy, noncondensed atoms and a pulsed optical standing wave. Resonances are observed for {Dirac_h}/2{pi}-tilde=(r/16)4{pi} for integers r=2-6. Quantum numerical simulations suggest that our observation of high-order resonances indicate a larger coherence length (i.e., coherence between different wells) than expected from an initially thermal atomic sample.

Authors:
; ; ;  [1];  [2];  [1];  [2]
  1. Centre for Quantum Information and Quantum Control, University of Toronto, 60 St. George Street, Toronto, Ontario, M5S 1A7 (Canada)
  2. (Canada)
Publication Date:
OSTI Identifier:
20957681
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevLett.98.083004; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COHERENCE LENGTH; ENERGY ABSORPTION; RESONANCE; ROTORS; SIMULATION; STANDING WAVES

Citation Formats

Kanem, J. F., Maneshi, S., Partlow, M., Steinberg, A. M., Institute for Optical Sciences and Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, M5S 1A7, Spanner, M., and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6. Observation of High-Order Quantum Resonances in the Kicked Rotor. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.083004.
Kanem, J. F., Maneshi, S., Partlow, M., Steinberg, A. M., Institute for Optical Sciences and Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, M5S 1A7, Spanner, M., & Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6. Observation of High-Order Quantum Resonances in the Kicked Rotor. United States. doi:10.1103/PHYSREVLETT.98.083004.
Kanem, J. F., Maneshi, S., Partlow, M., Steinberg, A. M., Institute for Optical Sciences and Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, M5S 1A7, Spanner, M., and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6. Fri . "Observation of High-Order Quantum Resonances in the Kicked Rotor". United States. doi:10.1103/PHYSREVLETT.98.083004.
@article{osti_20957681,
title = {Observation of High-Order Quantum Resonances in the Kicked Rotor},
author = {Kanem, J. F. and Maneshi, S. and Partlow, M. and Steinberg, A. M. and Institute for Optical Sciences and Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, M5S 1A7 and Spanner, M. and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6},
abstractNote = {Quantum resonances in the kicked rotor are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances occur when the scaled Planck's constant {Dirac_h}/2{pi}-tilde=(r/s)4{pi}, for any integers r and s. However, only the {Dirac_h}/2{pi}-tilde=r2{pi} resonances are easily observable. We have observed high-order quantum resonances (s>2) utilizing a sample of low energy, noncondensed atoms and a pulsed optical standing wave. Resonances are observed for {Dirac_h}/2{pi}-tilde=(r/16)4{pi} for integers r=2-6. Quantum numerical simulations suggest that our observation of high-order resonances indicate a larger coherence length (i.e., coherence between different wells) than expected from an initially thermal atomic sample.},
doi = {10.1103/PHYSREVLETT.98.083004},
journal = {Physical Review Letters},
number = 8,
volume = 98,
place = {United States},
year = {Fri Feb 23 00:00:00 EST 2007},
month = {Fri Feb 23 00:00:00 EST 2007}
}
  • We have observed high-order quantum resonances in a realization of the quantum {delta}-kicked rotor, using Bose-condensed Na atoms subjected to a pulsed standing wave of laser light. These resonances occur for pulse intervals that are rational fractions of the Talbot time, and are characterized by ballistic momentum transfer to the atoms. The condensate's narrow momentum distribution not only permits the observation of the quantum resonances at 3/4 and 1/3 of the Talbot time, but also allows us to study scaling laws for the resonance width in quasimomentum and pulse interval.
  • We present experimental measurements of the mean energy in the vicinity of the first and second quantum resonances of the atom-optics kicked rotor for a number of different experimental parameters. Our data are rescaled and compared with the one-parameter ({epsilon}) classical scaling function developed to describe the quantum resonance peaks. Additionally, experimental data are presented for the 'classical' resonance which occurs in the limit as the kicking period goes to zero. This resonance is found to be analogous to the quantum resonances, and a similar one-parameter classical scaling function is derived, and found to match our experimental results. The widthsmore » of the quantum and classical resonance peaks are compared, and their sub-Fourier nature examined.« less
  • The effect of pulse train noise on the quantum resonance peaks of the atom optics kicked rotor is investigated experimentally. Quantum resonance peaks in the late time mean energy of the atoms are found to be surprisingly robust against all levels of noise applied to the kicking amplitude, while even small levels of noise on the kicking period lead to their destruction. The robustness to amplitude noise of the resonance peak and of the fall-off in mean energy to either side of this peak are explained in terms of the occurrence of stable, {epsilon} classical dynamics [S. Wimberger, I. Guarneri,more » and S. Fishman, Nonlinearity 16, 1381 (2003)] around each quantum resonance.« less
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  • We report measurements of the early-time momentum diffusion for the atom-optical delta-kicked rotor. In this experiment a Bose-Einstein condensate provides a source of ultracold atoms with an ultranarrow initial momentum distribution, which is then subjected to periodic pulses (or 'kicks') using an intense far-detuned optical standing wave. We characterize the effect of varying the effective Planck's constant for the system, while keeping all other parameters fixed. The observed behavior includes both quantum resonances (ballistic energy growth) and antiresonances (re-establishment of the initial state). Our experimental results are compared with theoretical predictions.