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

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

Ideal Delta Kicked Rotor

Optical Lattice realization

g

Kicked Rotor

T

ideal lattice implementation

Ideal Rotor

Atom optics realization

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

Discuss classical vs. quantum behaviour of momentumdiffusion?

Classically chaotic: momentum diff. ~ N1/2

Quantum: dynamic localization and/or quantum resonance

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.

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.

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

Raizen reference

And

Reference paper that figure is from

2π 4π

Past experiments with thermal clouds

Our observed resonances

Inset: calculation of resonance-independent quantum diffusion(How much to explain? Make extra slide?)

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

Simulations

interesting conclusion ?

Describe widths used for simulations

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

EXTRAS

a

Windell Oskay/University of Texas at Austin

Energy growth / resonance resolutionQuadratic growth ???