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arXiv:1010.4523 · Physical Review A

Tailored particle current in an optical lattice by a weak time-symmetric harmonic potential

Júlio César Santos Júnior, Rafael A. Molina, Juan Ortigoso, Mirta Rodrı́guez

Published Aug 8, 2011• 3 citations
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Abstract

Quantum ratchets exhibit asymptotic currents when driven by a time-periodic potential of zero mean if the proper spatiotemporal symmetries are broken. Recently, there has been debate on whether directed currents may arise for potentials which do not break these symmetries. We show here that in the presence of degeneracies in the quasienergy spectrum, long-lasting directed currents can be induced, even if the time-reversal symmetry is not broken. Our model can be realized with ultracold atoms in optical lattices in the tight-binding regime, and we show that the time scale of the average current can be controlled by extremely weak fields.

DOI
10.1103/physreva.84.023614

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Quantum ratchets exhibit asymptotic currents when driven by a time-periodic potential of zero mean if the proper spatiotemporal symmetries are broken. Recently, there has been debate on whether directed currents may arise for potentials which do not break these symmetries. We show here that in the presence of degeneracies in the quasienergy spectrum, long-lasting directed currents can be induced, even if the time-reversal symmetry is not broken. Our model can be realized with ultracold atoms in optical lattices in the tight-binding regime, and we show that the time scale of the average current can be controlled by extremely weak fields.
We study the response of a Bose-Einstein condensate to an unbiased periodic driving potential. By controlling the space and time symmetries of the driving we show how a directed current can be induced, producing a coherent quantum ratchet. Weak driving induces a regular behavior, and space and time symmetries must both be broken to produce a current. For strong driving, the behavior becomes chaotic and the resulting effective irreversibility means that it is unnecessary to explicitly break time symmetry. Spatial asymmetry alone is then sufficient to produce the ratchet effect, even in the absence of interactions, and although the system remains completely coherent.
We demonstrate that directed transport of bright solitons formed in a quasi-one-dimensional Bose-Einstein condensate can be reliably controlled by tailoring a weak optical lattice potential, biharmonic in both space and time, in accordance with the degree of symmetry breaking mechanism. By considering the regime where matter-wave solitons are narrow compared to the lattice period, (i) we propose an analytical estimate for the dependence of the directed soliton current on the biharmonic potential parameters that is in good agreement with numerical experiments, and (ii) we show that the dependence of the directed soliton current on the number of atoms is a consequence of the ratchet universality.
Classical ratchet potentials, which alternate a driving potential with periodic random dissipative motion, can account for the operation of biological motors. We demonstrate the operation of a quantum ratchet, which differs from classical ratchets in that dissipative processes are absent within the observation time of the system (Hamiltonian regime). An atomic rubidium Bose-Einstein condensate is exposed to a sawtooth-like optical lattice potential, whose amplitude is periodically modulated in time. The ratchet transport arises from broken spatiotemporal symmetries of the driven potential, resulting in a desymmetrization of transporting eigenstates (Floquet states). The full quantum character of the ratchet transport was demonstrated by the measured atomic current oscillating around a nonzero stationary value at longer observation times, resonances occurring at positions determined by the photon recoil, and dependence of the transport current on the initial phase of the driving potential.
Ratchets are devices that operate away from thermal equilibrium and can rectify zero-mean perturbations to achieve directed transport. We implement a ratchet system by using cold atoms in a driven optical lattice. This ratchet system can be precisely controlled experimentally, by adjusting either the driving parameters or the characteristics of the optical lattice. Directed transport in our ratchet is caused by rectification of either the driving force or fluctuations. We demonstrate under which conditions these types of rectification occur. Rectification of the driving force is a deterministic process, while rectification of fluctuations implies that the atoms act as Brownian motors. We show that resonant activation is the underlying mechanism of operation of these Brownian motors. The ratchet transport is controlled by symmetries of the system. The temporal symmetry of the system is normally broken by a time- asymmetric driving force. Here we show that for a system with symmetric driving and a symmetric potential, directed transport can also be caused by dissipation-induced breaking of time-reversal symmetry. This happens in the limit of small driving amplitude and large dissipation. We also study quasiperiodic driving of a cold atom ratchet and examine the relationship between symmetries and transport in this case. When mapping the route to quasiperiodicity we find a characteristic peak spectrum with transport occurring for certain ratios of frequencies. We characterize these peaks spectroscopically, and conclude that their shape is determined by the duration of driving. Finally, we investigate the coherency of transport with quasiperiodic driving and find large coherencies for certain driving parameters.
We report on the successful experimental realization of a quantum ratchet for ultracold atoms in a driven spatially asymmetric optical lattice. Ratchets are usually considered as a tool, which rectify an otherwise undirected, for instance oscillating or fluctuating, motion of particles or objects. In order to observe a directed transport of atoms one has to break the space-time symmetry of the system. Here, we report on the realization of a quantum ratchet in the absence of dissipative processes (Hamiltonian regime) within the interaction time.