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arXiv:physics/0502061 · Physical Review A

Experimental verification of a one-parameter scaling law for the quantum and “classical” resonances of the atom-optics kicked rotor

Sandro Wimberger, Mark Sadgrove, A. S. Parkins, R. Leonhardt

Published May 12, 2005• 29 citations

Abstract

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 $(ϵ)$ 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 widths of the quantum and classical resonance peaks are compared, and their sub-Fourier nature examined.

DOI: 10.1103/physreva.71.053404

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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

(ϵ)

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 widths of the quantum and classical resonance peaks are compared, and their sub-Fourier nature examined.

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 [Nonlinearity 16, 1381 (2003)]] around each quantum resonance.

We examine the effect of the initial atomic momentum distribution on the dynamics of the atom-optical realisation of the quantum kicked rotor. The atoms are kicked by a pulsed optical lattice, the periodicity of which implies that quasi-momentum is conserved in the transport problem. We study and compare experimentally and theoretically two resonant limits of the kicked rotor: in the vicinity of the quantum resonances and in the semiclassical limit of vanishing kicking period. It is found that for the same experimental distribution of quasi-momenta, significant deviations from the kicked rotor model are induced close to quantum resonance, while close to the classical resonance (i.e. for small kicking period) the effect of the quasi-momentum vanishes.

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 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 .