Minimal Quantum Brownian Rectifiers

Abstract

We consider directed quantum transport in one-dimensional, periodic tight-binding lattices that are driven by unbiased, but asymmetric driving forces which are composed of a fundamental and its second harmonic (harmonic mixing signal). The reduction to a single-band dynamics then yields a formally exactly integrable dynamics. An asymmetric drive generally breaks time-reversal symmetry without causing any dissipation. For an initially localized particle with zero momentum no finite coherent current emerges; in contrast, a directed current occurs, however, when prepared with an initial coherence. The presence of phase fluctuations yields a decaying current, thereby rendering the nondissipative currents a transient phenomenon. In contrast, the presence of quantum dissipation yields at all temperatures a finite asymptotic current independent of preparation.

Artificial Brownian motors: Controlling transport on the nanoscale

“…Directed transport may then take place even though no dissipation mechanisms are present. Trivial examples of this process are provided by integrable regular dynamics subjected to unbiased ac drives with fixed initial phase, i.e., not averaged over Goychuk and Hänggi, 2001͒. Much more intriguing are timedependent driven Hamiltonian quantum Brownian motors exhibiting a nontrivial, mixed classical phase space structure Denisov and Flach, 2001;Schanz et al, 2001.…”

Dissipationless directed transport in rocked single-band quantum dynamics

“…Hence it is not expected that the directed transport survives if the dynamics is averaged over many initial conditions. The second approach relies solely on a driving field that mixes different harmonics of a fundamental frequency [14,15]. However, in addition to the requirement of initial state coherence (consistent with similar findings in "coherent control" [16]), the relative phase between different harmonics should not fluctuate [15].…”

Quantum-Resonance Ratchets: Theory and Experiment

“…These quantities are therefore basically different from trivial currents arising from biased phases in simple classical systems (see e.g. [Goychuk & Hänggi, 2001]). …”

“…Quantized Hamiltonian ratchets may exhibit significant currents also under full-chaos conditions and have been studied in many works [Schanz et al, 2005;Lundh & Wallin, 2005;Gong & Brumer, 2006;Jones et al, 2007;Denisov et al, 2007;Dana & Roitberg, 2007;Sadgrove et al, 2007;Dana et al, 2008;Dana, 2008]. Quantum-chaotic ratchets may be viewed as the deterministic counterpart of the quantum Brownian-motion ratchets [Reimann et al, 1997;Goychuk & Hänggi, 2001]. Particularly interesting cases are strong quantum regimes corresponding to "quantum resonances" (QRs) [Lundh & Wallin, 2005;Dana & Roitberg, 2007;Sadgrove et al, 2007;Dana et al, 2008].…”