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arXiv · 0807.2587

Power-law behavior in the quantum-resonant evolution of the delta-kicked accelerator

P. L. Halkyard·M. Saunders·S. A. Gardiner·K. J. Challis
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Abstract

We consider the atom-optical delta-kicked accelerator when the initial momentum distribution is symmetric. We demonstrate the existence of quantum-resonant dynamics, and derive analytic expressions for the system evolution. In particular, we consider the dynamical evolution of the momentum moments and find that all even-ordered momentum moments exhibit a power law growth. In the ultracold (zero-temperature) limit the exponent is determined by the order of the moment, whereas for a broad, thermal initial momentum distribution the exponent is reduced by one. To demonstrate the power law behavior explicitly we consider the evolutions of the second- and fourth-order momentum moments, and cumulants, for an initially Gaussian momentum distribution corresponding to the Maxwell-Boltzmann distribution of an ideal gas at thermal equilibrium.

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P. L. Halkyard, M. Saunders, S. A. Gardiner, K. J. Challis. 2008-09-25. Power-law behavior in the quantum-resonant evolution of the delta-kicked accelerator. https://doi.org/10.1103/physreva.78.063401

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