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)

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Cited by in corpus (12)

• Experimental Realization of Quantum-Resonance Ratchets
• Localization, quantum resonances and ratchet acceleration in a periodically-kicked $\mathcal{P}\mathcal{T}$-symmetric quantum rotator
• Controlling the Momentum Current of an Off-resonant Ratchet
• Fidelity of the quantum delta-kicked accelerator
• Fidelity for kicked atoms with gravity near a quantum resonance
• Statistical Approach to Quantum Chaotic Ratchets
• Weak-Chaos Ratchet Accelerator
• Classical and Quantum Transport in One-Dimensional Periodically Kicked Systems
• Tailored particle current in an optical lattice by a weak time-symmetric harmonic potential
• Spinor Dynamics of Quantum Accelerator Modes near Higher Order Resonances
• Kicked Hall Systems: Quantum-Dynamical and Spectral Manifestations of Generic Superweak Chaos
• Quantum Properties of Double Kicked Systems with Classical Translational Invariance in Momentum