Topological energy conversion through the bulk or the boundary of driven systems

Abstract

Combining physical and synthetic dimensions allows a controllable realization and manipulation of high dimensional topological states. In our work, we introduce two quasiperiodically driven 1D systems which enable tunable topological energy conversion between different driving sources. Using three drives, we realize a 4D quantum Hall state which allows energy conversion between two of the drives within the bulk of the 1D system. With only two drives, we achieve energy conversion between the two at the edge of the chain. Both effects are a manifestation of the effective axion electrodynamics in a 3D time-reversal invariant topological insulator. Furthermore, we explore the effects of disorder and commensurability of the driving frequencies, and show the phenomena is robust. We propose two experimental platforms, based on semiconductor heterostructures and ultracold atoms in optical lattices, in order to observe the topological energy conversion. arXiv:1801.05811v2 [cond-mat.mes-hall]

Robust temporal pumping in a magneto-mechanical topological insulator

“…While spatial topological pumps can address these concerns, the introduction of time as a pumping parameter offers unprecedented control and reconfigurability over the transport of energy in space [14,15] and even in frequency [38]. Moreover, the use of alternative pumping protocols or multiple incommensurate temporal drives can potentially open up a wide configuration space [39,40], allowing the synthesis of larger Chern numbers for increased pumping capacity [41][42][43][44][45], the generation of higher Chern numbers in higher synthetic dimensions [46], and the exploration of dynamic phase transitions between topological phases in time [47][48][49].…”

Photon pumping in a weakly-driven quantum cavity–spin system

“…Temporal analogs of topological models can provide a new platform for the efficient transfer of photons from one electromagnetic mode to another. In such systems, novel types of topological order are realized by subjecting a trivial quantum system to periodic driving [18][19][20][21][22] . In particular, driving a spin-1/2 with two elliptically polarized periodic waves of incommensurate frequencies generates the dynamical analog of a 2D topological insulator, where the Hall current corresponds to a quantized pumping of energy between the two sources 23,24 .…”

Universal nonadiabatic energy pumping in a quasiperiodically driven extended system

“…In fact, the concept of synthetic dimensions has recently emerged as a powerful way to emulate topological phases of matter, which are now of great interest across many areas of physics [21]. Among various approaches to engineer synthetic dimensions, the idea based on quasiperiodic drives was pursued and generalized by several theorists [22][23][24][25][26][27][28][29], as well as realized in experiments [30,31].…”

“…The amplitudes for the harmonics form new degrees of freedom, thereby effectively raising the dimensionality of the system from d to d + n. Furthermore, different driving frequencies, if collected into a vector, resemble a homogeneous electric field operating in the synthetic space. In an extended system, when the external drives are not homogeneous in the physical dimensions, a synthetic magnetic field can also be realized [22].…”

“…Understanding the quantum dynamics beyond the adiabatic limit is important because it greatly expands the parameter regime where the energy pumping device operates. On the other hand, an extended-system-based device is favorable, as its energy pumping power can be manipulated by changing the system size [22], which adds more controllability.…”