Quasiperiodically Driven Ratchets for Cold Atoms

Abstract

We investigate experimentally the route to quasiperiodicity in a driven ratchet for cold atoms and examine the relationship between symmetries and transport while approaching the quasiperiodic limit. Depending on the specific form of driving, quasiperiodicity results in the complete suppression of transport, or in the restoration of the symmetries which hold for a periodic driving. DOI: 10.1103/PhysRevLett.96.240604 PACS numbers: 05.40.Fb, 05.60.Cd, 32.80.Pj The ratchet effect [1-3], i.e., the possibility of obtaining directed transport of particles in the absence of a net bias force, has recently been attracting considerable interest [4 -8]. Initially introduced to point out the strict limitations on directed transport at equilibrium imposed by the second principle of thermodynamics [9], the ratchet effect has subsequently received much attention as it was identified as a model elucidating the working principle of molecular motors [7]. More recently, considerable activity on ratchets by the condensed matter community was stimulated by the possibility of using the ratchet phenomenon to realize new types of electron pumps [10].In order to obtain directed transport in the absence of a net bias, the ensemble of particles has to be driven out of equilibrium, so to overcome the restrictions imposed by the second principle of thermodynamics. Additionally, relevant symmetries of the system have to be broken to allow directed transport. Theoretical work [5,6] precisely identified the relationship between symmetries and transport in the case of periodically driven ratchets, and experiments with cold atoms in optical lattices validated the theoretical predictions [11,12]. The theoretical analysis was then extended to explore the relationship between symmetries and transport for quasiperiodically driven ratchets, and the general symmetries which forbid directed transport were identified [13,14].In the present work we investigate experimentally the route to quasiperiodicity in a driven ratchet for cold atoms, and we examine the relationship between symmetries and transport while approaching the quasiperiodic limit. It will be shown that, depending on the specific form of driving, quasiperiodicity may result in the complete suppression of transport, or in the restoration of the symmetries which hold for a periodic driving.Our experiments are based on caesium atoms cooled and trapped in a near-resonant driven optical lattice [15]. The lattice beam geometry is the same as the one used in our previous experiments [12]: one beam (beam 1) propagates in the z direction; the three other beams (beams 2 -4) propagate in the opposite direction, arranged along the edges of a triangular pyramid having the z direction as axis. We refer to Ref. [12] for further details of the setup, and we summarize here only the essential features. The interference between the lattice fields creates a periodic and spatially symmetric potential for the atoms. The interaction with the light also leads to damping of the atomic motion, and the level of d...

Ratchets from the cold: Brownian motors with cold atoms in optical lattices

“…In the case of quasiperiodically driven ratchet [11], the interesting issue is how the symmetries, and the resulting current generation, are modified following the transition from periodicity to quasiperiodicity. Consider a generic driving force with two frequencies ω 1 , ω 2 .…”

“…Thus, in the experiment of Ref. [11], the transition from periodicity to quasiperiodicity was studied by increasing p,q, so to make the driving effectively more and more quasiperiodic. The measurements across the transition revealed a qualitative change in the conditions on the driving force parameters for which a ratchet current was observed.…”

Symmetries and transport in site-dependent driven quantum lattices

“…Because, originally these systems relied on the rectification of thermal noise they were seen as realizations of Brownian motors the corresponding research field being highly active (see [1] and references therein). As one of the many considered experimental playgrounds for ratchets physics, cold atoms loaded into driven optical lattices have proven to be particularly insightful since they allow for a precise control over the systems parameters [2][3][4][5][6]. While some of these experiments are carried out at moderate temperatures and allow for a classical treatment [2][3][4], others could reach ultracold temperatures and demonstrated the accessibility of Hamiltonian ratchet setups operating deep in the quantum regime [5,6].…”

“…As one of the many considered experimental playgrounds for ratchets physics, cold atoms loaded into driven optical lattices have proven to be particularly insightful since they allow for a precise control over the systems parameters [2][3][4][5][6]. While some of these experiments are carried out at moderate temperatures and allow for a classical treatment [2][3][4], others could reach ultracold temperatures and demonstrated the accessibility of Hamiltonian ratchet setups operating deep in the quantum regime [5,6]. The experimental advancements concerning these newly realized 'quantum ratchets' were accompanied by a substantial body of theoretical works (see [7][8][9][10][11][12][13][14] and references therein).…”

Omnidirectional Transport in Fully Reconfigurable Two Dimensional Optical Ratchets

“…This model can explain the functioning of a number of systems in nature, such as molecular motors [2][3][4] or protein translocation processes [5]. Additionally, schemes based on this mechanism have been implemented to sort biomolecules [6] and inorganic microparticles [7], to rectify the motion of cold atoms in optical lattices [8,9] and vortices in superconductors [10], among others. The rich dynamics arising in ratchets becomes evident from the diverse phenomena that can be observed even in the simplest cases of onedimensional (1D) systems, such as bidirectional transport depending on size, chaotic behavior and current reversals [11][12][13][14][15].…”