Coherent ratchets in driven Bose-Einstein condensates

📝 Abstract

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 that is strongly governed by the interparticle interaction. Breaking both space and time symmetries is required to produce current flow. For strong driving the behavior becomes chaotic. The resulting effective irreversibility renders the space asymmetry sufficient to produce the ratchet effect, although the system is completely coherent.

💡 Analysis

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 that is strongly governed by the interparticle interaction. Breaking both space and time symmetries is required to produce current flow. For strong driving the behavior becomes chaotic. The resulting effective irreversibility renders the space asymmetry sufficient to produce the ratchet effect, although the system is completely coherent.

📄 Content

arXiv:0908.0692v2 [cond-mat.quant-gas] 3 Nov 2009 Coherent ratchets in driven Bose-Einstein condensates C.E. Creffield and F. Sols Dpto de F´ısica de Materiales, Universidad Complutense de Madrid, E-28040, Madrid, Spain (Dated: October 31, 2018) 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 both 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. PACS numbers: 03.75.Kk, 67.85.Hj, 05.60.Gg, 05.45.-a Introduction – The physics of ratchets, systems that exhibit directed motion in the absence of an external bias, has undergone extremely rapid development in re- cent years [1, 2]. The concept is very general, and ranges from new technological forms of manipulating and direct- ing matter at nanoscale levels, to understanding how sys- tems in nature such as biological molecular motors func- tion. Fundamentally a ratchet must satisfy two essential requirements: the system must be driven out of equilib- rium by an external force, and the relevant space/time symmetries, which would otherwise forbid the generation of directed currents, must be broken. A well-known example is provided by a Brownian par- ticle in a periodic potential. Driving the system from equilibrium by either pulsing the potential (“flashing ratchet”) or tilting it (“rocking ratchet”) produces a cur- rent if the spatial or temporal symmetry of the driving force is broken. In the most commonly studied over- damped regime, the ratchet current arises from the rec- tification of random fluctuations, and accordingly noise and dissipation are essential ingredients. This is not true in general, however, and surprisingly it has been shown recently [3, 4, 5, 6, 7, 8, 9] that ratchet effects can also occur even in completely coherent systems. Considerable progress in this direction has been made by considering the quantum kicked rotor. Experimen- tally this system can be realized extremely well in gases of ultracold atoms held in pulsed optical lattices. While it was originally thought that ratchet effects would only arise in systems with an underlying mixed classical phase- space [3], recent work has shown that they can also arise when the phase-space is globally chaotic. In Ref. [4] a quantum Hamiltonian ratchet of this type was studied both theoretically and experimentally, in which the cur- rent arose from the generation of an asymmetry in the momentum distribution due to the desymmetrization of the system’s Floquet states. An alternative scheme, de- veloped in the context of quantum maps [5], is to use interference effects to produce an imbalance in the phase- space distribution. Quantum resonances, where the pe- riod of the kicks is matched to the inverse recoil velocity of the optical lattice, have also been proposed [6, 7] as a means of producing ratchet accelerators. In this work we consider an optically trapped Bose Einstein condensate (BEC), since the macroscopically protected coherence and excellent controllability of these systems make them ideal subjects for investigating quan- tum transport effects. Instead of kicking the system [8, 10], we use a smoothly varying potential and so can expect to produce less heating effects, which we verify explicitly by evaluating the fraction of non-condensed atoms. By choosing a form for the driving which enables us to separately break space and time symmetries, we find that we can induce a directed current in a BEC start- ing from a symmetric initial state. This occurs by two distinct mechanisms; for weak driving the system under- goes regular oscillations, and both space and time sym- metries in the driving must be broken. Conversely, for strong driving, the system’s dynamics becomes chaotic, and this produces an effective irreversibility which means it is not necessary to explicitly break the time symmetry. Model – We consider a BEC confined in a toroidal trap [11] with a cross-section much smaller than the trap’s ra- dius, R. The system can thus be described by an effective one-dimensional Gross-Pitaevskii equation (GPE) H(t) = −1 2 ∂2 ∂x2 + g |ψ(x, t)|2 + K V (x, t), (1) where x parametrises distance around the trap, and we measure all energies in units of ¯h2/2mR2. The short- range interactions between the atoms in the condensate are described by a mean-field term with strength g, and the condensate is driven by a time-periodic external po- tential with zero mean by modulating the amplitude of the optical potential. The archetypal form of a ratchet potentia

This content is AI-processed based on ArXiv data.