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arXiv:physics/0609203 · Physical Review Letters

Exploring the Phase Space of the Quantum δ -Kicked Accelerator

G. Behinaein, Vijayashankar Ramareddy, Peyman Ahmadi, G. S. Summy

Published Dec 13, 2006• 82 citations
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Abstract

We experimentally explore the underlying pseudoclassical phase space structure of the quantum delta-kicked accelerator. This was achieved by exposing a Bose-Einstein condensate to the spatially corrugated potential created by pulses of an off-resonant standing light wave. For the first time quantum accelerator modes were realized in such a system. By utilizing the narrow momentum distribution of the condensate we were able to observe the discrete momentum state structure of a quantum accelerator mode and also to directly measure the size of the structures in the phase space.

DOI
10.1103/physrevlett.97.244101

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We experimentally explore the underlying pseudoclassical phase space structure of the quantum delta-kicked accelerator. This was achieved by exposing a Bose-Einstein condensate to the spatially corrugated potential created by pulses of an off-resonant standing light wave. For the first time quantum accelerator modes were realized in such a system. By utilizing the narrow momentum distribution of the condensate we were able to observe the discrete momentum state structure of a quantum accelerator mode and also to directly measure the size of the structures in the phase space.
We investigate the creation mechanism of quantum accelerator modes which are attributed to the existence of the stability islands in an underlying pseudoclassical phase space of the quantum delta-kicked accelerator. Quantum accelerator modes can be created by exposing a Bose-Einstein condensate to a pulsed standing light wave. We show that constructive interference between momentum states populated by the pulsed light determines the stability island's existence in the underlying pseudoclassical phase space. We generalize this interference model to incorporate higher-order accelerator modes, showing that they are generated if the rephasing occurs after multiple pulses. The model is extended to predict the momentum structure of the quantum accelerator modes close to higher-order quantum resonances. These predictions are in good agreement with our experimental observations.
We report the observation of high-order resonances of the quantum δ-kicked accelerator using a BEC kicked by a standing wave of light. The signature of these resonances is the existence of quantum accelerator modes. For the first time quantum accelerator modes were seen near 1/2, 2/3 and 1/3 of the half-Talbot time. Using a BEC enabled the internal momentum state structure of the modes and resonances to be studied for the first time. This structure has many similarities to that present in the fractional Talbot effect. We present a theory for this system based on rephasing of momentum orders and apply it to predict the behavior of the accelerator modes around a resonance of any order.
We experimentally demonstrate a method for selecting small regions of phase space for kicked rotor quantum chaos experiments with cold atoms. Our technique uses quantum accelerator modes to selectively accelerate atomic wave packets with localized spatial and momentum distributions. The potential used to create the accelerator mode and subsequently realize the kicked rotor system is formed by a set of off-resonant standing-wave light pulses. We also propose a method for testing whether a selected region of phase space exhibits chaotic or regular behavior using a Ramsey type separated field experiment.
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.
The sensitivity of the fidelity in the kicked rotor to an acceleration is experimentally and theoretically investigated. We used a Bose-Einstein condensate exposed to a sequence of pulses from a standing light wave followed by a single reversal pulse in which the standing wave was shifted by half a wavelength. The features of the fidelity "spectrum" as a function of acceleration are presented. This work may find applications in the measurement of temperature of an ultracold atomic sample.
We report the first direct experimental realization of the quantum $\ensuremath{\delta}$-kicked rotor. Our system consists of a dilute sample of ultracold sodium atoms in a periodic standing wave of near-resonant light that is pulsed on periodically in time to approximate a series of delta functions. Momentum spread of the atoms increases diffusively with every pulse until the "quantum break time" after which exponentially localized distributions are observed. Quantum resonances are found for specific values of the pulse period.