Periodically driven Quantum Ratchets: Symmetries and Resonances

Details Periodically driven Quantum Ratchets: Symmetries and Resonances Periodically driven Quantum Ratchets: Symmetries and Resonances

2007-03-19

arxiv.org/abs/quant-ph/0703169v1

Phys. Rev. A, 75 (2007) 063424

Physics

Quantum Physics

10 pages, 10 figures

Scientific paper

10.1103/PhysRevA.75.063424

We study the quantum version of a tilting and flashing Hamiltonian ratchets, consisting of a periodic potential and a time-periodic driving field. The system dynamics is governed by a Floquet evolution matrix bearing the symmetry of the corresponding Hamiltonian. The dc-current appears due to the desymmetrization of Floquet eigenstates, which become transporting when all the relevant symmetries are violated. Those eigenstates which mostly contribute to a directed transport reside in phase space regions corresponding to classical resonances. Quantum dynamics leads to the dependence of the average velocity on the initial phase of the ac-field. A resonant enhancement (or suppression) of the dc-current, due to avoided crossings between different Floquet states takes place upon tuning some control parameters. Our studies are predominantly aimed at experimental realizations of ac-driven quantum ratchets with cold atoms.

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