Transporting Cold Atoms in Optical Lattices with Ratchets: Mechanisms and Symmetries

Abstract

Thermal fluctuations alone cannot create a steady directed transport in an unbiased system. However, if a system is out of equilibrium, the Second Law of Thermodynamics no longer applies, and then there are no thermodynamical constraints on the appearance of a steady transport [1, 2]. A directed current can be generated out of a fluctuating (time-dependent) external field with zero mean. The corresponding ratchet effect [3–9] has been proposed as a physical mechanism of a microbiologicalmotility more then a decade ago [4,5]. Later on the ratchet idea has found diverse applications in different areas [6–9], from a molecular nanoscale-machine [10] up to quantum systems and quantum devices [11–17]. When the deviation from an equilibrium regime is small (the case of weak external fields) one may use the linear response theory in order to estimate the answer of the system [18–20]. However, due to the linearization of the response, the current value will be strictly zero since the driving field has zero bias. Therefore, one has to take into account nonlinear corrections and then derive the corresponding nonlinear response functional [20, 21], which may become a very complicated task, if the nonadiabatic regime is to be considered.