Quantum time mirrors for general two-band systems

Abstract

Methods that are devised to achieve reversal of quantum dynamics in time have been named "quatum time mirrors". Such a time mirror can be considered as a generalization of Hahn's spin echo to systems with continuous degrees of freedom. We extend the quantum time mirror protocol originally proposed for Dirac dispersions to arbitrary two-band systems and establish the general requirements for its efficient implementation. We further discuss its sensitivity to various nonhomogeneous perturbations including disorder potentials and the effect of external static magnetic and electric fields. Our general statements are verified for a number of exemplary Hamiltonians, whose phase-coherent dynamics are studied both analytically and numerically. The Hamiltonians considered can be used to describe the low-energy properties of systems as diverse as cold atomoptics setups, direct band gap semiconductors or (mono-or bilayer) graphene. We discuss the consequences of many-body effects at a qualitative level, and consider the protocol feasibility in state-of-the-art experimental setups. arXiv:1805.10160v1 [cond-mat.mes-hall]

Steering Zitterbewegung in driven Dirac systems: From persistent modes to echoes

“…Hence, we have shown that the ZB echo behaves as the quantum time mirror in Ref. [24] where for different band structures the effects of position-dependent potentials in the Hamiltonian, like disorder and electromagnetic fields are discussed additionally. To show that we recover the same results for the ZB echo also in these cases, we discuss the effect of disorder on the ZB echo in App.…”

“…For gapped Dirac systems the transition amplitude A s is independent of s, A s → A. One has [24] A(k, ∆t) = iκM…”

“…The idea is to use the quantum time mirror protocol of Refs. [23,24] to effectively timereverse the sub-wave packet dynamics. Once the latter are brought back together we expect a reconstruction of the interference pattern yielding ZB.…”

“…Our goal is two-fold: (i) to identify non-decaying ZB modes in driven Dirac systems, e.g. graphene; (ii) to consider the possibility of generating ZB "echoes" exploiting the time-mirror protocols put forward in [23,24]. We start in Sec.…”

Time-Reversed Water Waves Generated from an Instantaneous Time Mirror

“…For example, in a gravitycapillary wave field, a sudden change in the water wave speed (or gravity) can be easily generated by accelerating the water tank. Inspired by this new approach, many applications have emerged in different fields, e.g., spatiotemporal light control [12], signal filtration [13], full-duplex communication [14], wave scattering [15,16], temporal control of graphene plasmons [17], focusing beyond the diffraction limit [18,19], and negative refraction [20,21] among others [22,23]. Recently, the ITM protocol is also introduced into quantum systems, generating wave function echoes with high fidelities [24].…”