Current behavior of a quantum Hamiltonian ratchet in resonance

Abstract

We investigate the ratchet current that appears in a kicked Hamiltonian system when the period of the kicks corresponds to the regime of quantum resonance. In the classical analogue, a spatial-temporal symmetry should be broken to obtain a net directed current. It was recently discovered that in quantum resonance the temporal symmetry can be kept, and we prove that breaking the spatial symmetry is a necessary condition to find this effect. Moreover, we show numerically and analytically how the direction of the motion is dramatically influenced by the strength of the kicking potential and the value of the period. By increasing the strength of the interaction this direction changes periodically, providing us with a non-expected source of current reversals in this quantum model. These reversals depend on the kicking period also, though this behavior is theoretically more difficult to analyze. Finally, we generalize the discussion to the case of a non-uniform initial condition.

6 pages, 4 figures

References in corpus (5)

• Phase-control of directed diffusion in a symmetric optical lattice
• Ratchet effect for cold atoms in an optical lattice
• Quantum ratchets in dissipative chaotic systems
• A classical scaling theory of quantum resonances
• Directed anomalous diffusion without a biased field: A ratchet accelerator

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• Current Reversals and Synchronization in Coupled Ratchets
• Quantum Ratchet Accelerator without a Bichromatic Lattice Potential
• Dissipationless Directed Transport in Rocked Single-Band Quantum Dynamics
• Coherent ratchets in driven Bose-Einstein condensates
• Quantum Parameter Space of Dissipative Directed Transport
• Correspondence behavior of classical and quantum dissipative directed transport via thermal noise
• Chaos and Correspondence in Classical and Quantum Hamiltonian Ratchets: A Heisenberg Approach
• On the environmental stability of quantum chaotic ratchets
• Classical to quantum correspondence in dissipative directed transport
• Transport phenomena in the asymmetric quantum multibaker map
• Behavior of the current in the asymmetric quantum multibaker map