Quantum Resonances and Ratchets in Free-Falling Frames

Abstract

Quantum resonance (QR) is defined in the free-falling frame of the quantum kicked particle subjected to gravity. The general QR conditions are derived. They imply the rationality of the gravity parameter $η$, the kicking-period parameter $τ/(2π)$, and the quasimomentum $β$. Exact results are obtained concerning wave-packet evolution for arbitrary periodic kicking potentials in the case of integer $τ/(2π)$ (the main QRs). It is shown that a quantum ratchet generally arises in this case for resonant $β$. The noninertial nature of the free-falling frame affects the ratchet by effectively changing the kicking potential to one depending on $(β,η)$. For a simple class of initial wave packets, it is explicitly shown that the ratchet characteristics are determined to a large extent by symmetry properties and by number-theoretical features of $η$.