Observation of High-order Quantum Resonances in the Kicked Rotor
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Transcript of Observation of High-order Quantum Resonances in the Kicked Rotor
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Jalani F. Kanem1, Samansa Maneshi1, Matthew Partlow1, Michael Spanner2
and Aephraim Steinberg1
Center for Quantum Information & Quantum Control,
Institute for Optical Sciences,1Department of Physics,
2Department of Chemistry,University of Toronto
Observation of High-order Quantum Resonances in the Kicked Rotor
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Outline:
• Kicked Rotor analogue with optical lattice• Quantum resonances• Experimental setup• Data & simulations
• The quantum kicked rotor is a rich system for studying quantum-classical correspondence, decoherence, and quantum dynamics in general
• Atom optics systems provide excellent analogue:Atom Optics Realization of the Quantum Delta-Kicked Rotor
Raizen group - PRL 75, 4598-4601 (1995)
• Possible probe of lattice inter-well coherence ?
INTRODUCTION
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Ideal Delta Kicked Rotor
Optical Lattice realization
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g
Kicked Rotor
T
ideal lattice implementation
Ideal Rotor
Atom optics realization
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g
Kicked Rotor
Stochasticity parameter: system becomes chaotic when strength or period of kicks are large enough that atoms (rotor) travel more than one lattice spacing (2 between kicks.→Force on atom is a random variable
T
ideal lattice implementation
Scaled quantum Schrödinger’s:
Scaled Planck's constant is a measure of how 'quantum' the system is. The smaller , the greater the quantum classical correspondence
~ ratio of quantized momentum transfer from lattice to momentum required to move one lattice spacing in one kick period, T
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Discuss classical vs. quantum behaviour of momentumdiffusion?
Classically chaotic: momentum diff. ~ N1/2
Quantum: dynamic localization and/or quantum resonance
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Quantum Resonances• Resonances → dramatically increased energy absorption• Due to rephasing of momentum states coupled by the lattice potential whose
momentum differ by a multiple of :
• 2π, 4π, etc. ‘easy’ to observe: all momentum states rephase e.g. wavepacket revival
• High-order resonance, s>1, fractional revival, only some quasimomentum states rephase.
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TUIPBS
PBS PBS
AOM1
AOM2
Amplifier
Grating Stabilized Laser
Function Generator
Individual control of frequency and phase of AOMs allows control of lattice velocity and position.
Spatial filter
Experimental Setup
Note: optical standing wave is in vertical direction‘hot’ un-bound atoms fall out before kicking begins
~3 recoil energies
1m
Tilted due to gravity
A tilted lattice would affect the dynamics of the experiment, therefore we accelerate the lattice downward at g to cancel this effect.
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The System
Preparation:
● 85Rb vapor cell MOT
● 108 atoms
● Cooled to ~10K
● Load a 1-D optical lattice supporting 1-2 bound states (~14 recoil energies)
● Initial rms velocity width of ~5mm/s (255nK)
Typical pulse parameters:
● 50-150s pulse period
● 5-15s pulse length
● Depth of 30-180 recoil units (~2-12K)
● chaos parameter = 1-10
● scaled Planck's constant =1-10
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Raizen reference
And
Reference paper that figure is from
2π 4π
Past experiments with thermal clouds
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Our observed resonances
Inset: calculation of resonance-independent quantum diffusion(How much to explain? Make extra slide?)
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Quantum, not classical: resonance position insensitive to kick strength
/π = 0.47±0.01, 0.72±0.01, 1, 1.25±0.02, 1.54±0.02
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Simulations
interesting conclusion ?
Describe widths used for simulations
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Conclusions• have observed high-order quantum resonances in atom-optics implementation of the kicked rotor
• visibility due to using lattice to select out cold atoms
• possibly greater coherence across lattice than we expect?
•give credit to other observation
•in the future, control and measurement of quasimomentum
This work: arXiv:quant-ph/0604110
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EXTRAS
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a
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Windell Oskay/University of Texas at Austin
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Energy growth / resonance resolutionQuadratic growth ???