# Multiple Current Reversals Using Superimposed Driven Lattices
## 1 Introduction  
Originally conceived as a proof of principle behind the working of biological motors [1; 2; 3; 4], the phenomenon of 'ratchet' transport of particles, i.e., the emergence of unidirectional particle transport in an unbiased non-equilibrium environment, has gained widespread applications across various disciplines [5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. The necessary ingredients required for such a rectification of random particle motion into directed transport has been shown to be non-equilibrium, non-linearity and the breaking of certain spatio-temporal symmetries [7; 15; 16]. Since then the ratchet effect has found numerous applications including particle separation based on physical properties [17; 18; 19], design of efficient velocity filters [20; 21], transportation of fluxons in Josephson junctions arrays [22; 23], unidirectional motion of active matter [13; 24], voltage rectification in superconducting quantum interference devices (SQUID) [25; 26; 27], and enhancement of photocurrents in quantum wells [28].  
Due to novel experimental progress in atom trapping techniques, directed transport of atomic ensembles has been realized in ac-driven optical lattices [29; 30] both in the ultracold quantum regime [31] and at micro kelvin temperatures where a classical dynamics approach successfully describes the experiments [32; 14]. Apart from the vast majority of ratchet-based setups in one spatial dimension (1D) [7; 15; 16; 33; 34], recent experiments have significantly progressed the realization of highly controllable two dimensional (2D) setups using ac-driven optical lattices [14; 29; 35; 36] and holographic optical tweezers [37]. Due to such widespread applications of directed particle transport, the different mechanisms to control the transport have been a topic of ongoing research. One such mechanism is 'current reversal' where the direction of the particle transport can be reversed by suitably changing one or more system parameters [38; 39; 40; 41; 42; 43; 44; 45; 25; 35; 36; 46]. Indeed, most of the existing schemes to generate current reversals focus on reverting the direction of asymptotic particle transportdue to a change of system parameter [47; 48; 49; 50]. Only recently has research focused on setups where the current reversal occurs dynamically in time either due to a time-dependent switching of system parameters or due to the presence of interactions and dimensional coupling [33; 38; 51; 52].  
Here, we present a scheme to dynamically generate multiple current reversals due to superimposed driven lattices in two dimensions. The setup employs a 'background lattice' driven by an external bi-harmonic oscillating driving force, whose underlying potential is separable in terms of the spatial coordinates. This allows directed transport of particles along the direction of the driving force and trapped motion in the orthogonal direction. Superimposing a second lattice in a finite region of space along the direction of transport leads to a reflection behavior and hence generates a current reversal. Subsequently, the superposition of a third identical lattice can reflect the transport direction once again yielding a second reversal of transport. The timescales of the current reversals can be controlled by the spatial locations of the superimposed lattices. The underlying principle behind the current reversals lie in the conversion of the particle dynamics from chaotic to ballistic in the setup involving multiple lattices, a phenomenon which is forbidden in the background lattice alone. Our paper is structured as follows. In Section 2, we describe the underlying setup in detail and discuss its relevant symmetries followed by the main results in Section 3. We discuss the cause of the current reversals in terms of the underlying phase space in Section 4. Finally, in Section 5, we provide a possible experimental realization of our setup and conclude our findings in Section 6.