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arXiv:0803.4153 · Physical Review A

Demonstration of a multipulse interferometer for quantum kicked-rotor studies

Alexey Tonyushkin, Saijun Wu, Mara Goff Prentiss

Published May 27, 2009• 18 citations
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Abstract

We implemented a multipulse interferometer scheme that allows us to study a quantum kicked rotor by observing dephasing of momentum coherence. Our study shows that momentum coherence can be nearly perfectly preserved under conditions where the mean energy as a function of the kick number is known to increase without bound. The accompanying width narrowing of these coherences may provide a new method for accurate measurement of the recoil frequency.

DOI
10.1103/physreva.79.051402

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Bulletin of the American Physical Society•May 22, 2009•0 citations
We implemented a multipulse interferometer scheme that allows us to study a quantum kicked rotor by observing dephasing of momentum coherence. Our study shows that momentum coherence can be nearly perfectly preserved under conditions where the mean energy as a function of the kick number is known to increase without bound. The accompanying width narrowing of these coherences may provide a new method for accurate measurement of the recoil frequency.
We theoretically investigate a proposed scheme to use an atomic $\ensuremath{\delta}$-kicked rotor resonance for high-precision measurements of accelerations and the photon recoil frequency. Although the technique offers rapid scaling of the measurement sensitivity with pulse number, it also features a high sensitivity to initial atomic momentum. We find that for realistic atom sources, the momentum sensitivity significantly limits the achievable precision. We consider several different variations on the technique, but find similar limitations in all cases.
We investigate the dynamics of the atom-optics δ-kicked rotor in the vicinity of quantum resonance. Although small deviations from resonant conditions lead to a negligible change in the momentum space probability density, they lead to a significant relative phase change between the different momentum states taking part in the dynamics. By adding a tailored pulse to the kicked rotor pulse sequence, one can measure the overlap between the resonant state and any other state, i.e. perform a fidelity measurement. Using this sequence, we predict a narrow peak around quantum resonance with a width that scales as 1/ N 3 with N being the number of pulses in the kicked rotor sequence. This method may be of interest to precision measurements, such as h / M .
The study of quantum resonances in the chaotic atom-optics kicked rotor system is of interest from two different perspectives. In quantum chaos, it marks out the regime of resonant quantum dynamics in which the atomic cloud displays ballistic mean energy growth due to coherent momentum transfer. Secondly, the sharp quantum resonance peaks are useful in the context of measurement of Talbot time, one of the parameter that helps in precise measurement of fine structure constant. Most of the earlier works rely on fidelity based approach and have proposed Talbot time measurement through experimental determination of the momentum space probability density of the periodically kicked atomic cloud. Fidelity approach has the disadvantage that phase reversed kicks need to be imparted as well which potentially leads to dephasing. In contrast to this, in this work, it is theoretically shown that, without manipulating the kick sequences, the quantum resonances through position space density can be measured more accurately and is experimentally feasible as well.
We use an atom interferometer to investigate the dynamics of matter waves in a periodically pulsed optical standing wave: an atom optics realization of the quantum kicked rotor that exhibits chaotic classical dynamics. We experimentally show that a measure of the coherence between the interferometer diffraction orders can revive after a quick initial loss, and can approach a finite asymptote as the number of kicks increases. This observation demonstrates that quantum fidelity of a classically chaotic system can survive strong perturbations over long times without decay.
We have developed a technique for measuring the atomic recoil frequency using a single-state echo-type atom interferometer that manipulates laser-cooled atoms in the ground state. The interferometer relies on momentum-state interference due to two standing-wave pulses that produce density gratings. The interference is modified by applying a third standing-wave pulse during the interferometer pulse sequence. As a result, the grating contrast exhibits periodic revivals at the atomic recoil frequency r as a function of the time at which the third pulse is applied, allowing r to be measured easily and precisely. The contrast is accurately described by a coherence function, which is the Fourier transform of the momentum distribution, produced by the third pulse and by the theory of echo formation. If the third pulse is a traveling wave, loss of grating contrast is observed, an effect also described by a coherence function. The decay of the grating contrast as a function of continuous-wave light intensity is used to infer the cross section for photon absorption.