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Theory of 2$δ$-kicked Quantum Rotors

C. E. Creffield·S. Fishman·T. S. Monteiro
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Abstract

We examine the quantum dynamics of cold atoms subjected to {\em pairs} of closely spaced $δ$-kicks from standing waves of light, and find behaviour quite unlike the well-studied quantum kicked rotor (QKR). Recent experiments [Jones et al, {\em Phys. Rev. Lett. {\bf 93}, 223002 (2004)}] identified a regime of chaotic, anomalous classical diffusion. We show that the corresponding quantum phase-space has a cellular structure, arising from a unitary matrix with oscillating band-width. The corresponding eigenstates are exponentially localized, but scale with a fractional power, $L \sim \hbar^{-0.75}$, in contrast to the QKR for which $L \sim \hbar^{-1}$. The effect of inter-cell (and intra-cell) transport is investigated by studying the spectral fluctuations with both periodic as well as `open' boundary conditions.

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C. E. Creffield, S. Fishman, T. S. Monteiro. 2005-10-17. Theory of 2$δ$-kicked Quantum Rotors. https://doi.org/10.1103/physreve.73.066202

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