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

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.

15 pages, 4 figures (changed content)

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Cited by in corpus (9)

• Quantum resonances in an atom-optical delta-kicked harmonic oscillator
• Pseudo-classical theory for fidelity of nearly resonant quantum rotors
• Quantum resonant effects in the delta-kicked rotor revisited
• Fractional resonances in the atom-optical delta-kicked accelerator
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• Kicked-rotor quantum resonances in position space: Application to situations of experimental interest
• Driving the resonant quantum kicked rotor via extended initial conditions