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 $\eta$, the kicking-period parameter $\tau /(2\pi )$, and the quasimomentum $\beta$. Exact results are obtained concerning wave-packet evolution for arbitrary periodic kicking potentials in the case of integer $\tau /(2\pi )$ (the main QRs). It is shown that a quantum ratchet generally arises in this case for resonant $\beta$. The noninertial nature of the free-falling frame affects the ratchet by effectively changing the kicking potential to one depending on $(\beta ,\eta )$. 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 $\eta$.

To appear in Physical Review E (Rapid Communications)

References in corpus (5)

• Quantum resonances and decoherence for delta-kicked atoms
• Directed Chaotic Transport in Hamiltonian Ratchets
• General Quantum Resonances of the Kicked Particle
• Quantum Accelerator Modes from the Farey Tree
• Gravity-Sensitive Quantum Dynamics in Cold Atoms

Cited by in corpus (1)

• Experimental Realization of Quantum-Resonance Ratchets