Quantum Echoes and revivals in two-band systems and Bose-Einstein condensates

In this thesis, we address the long-standing question of time-reversal protocols for the quantum mechanical wave function for continuous degrees of freedom. We propose two new mechanisms - quantum time mirrors - one for two-band systems, the other one for systems described by the nonlinear Schrödinger equation like Bose-Einstein condensates. In both cases, a homogeneous pulse is applied to the system that is supposed to flip the velocity direction and thus invert the motion of the system. In a two-band system, the pulse induces a transition from one band to the other. For bands with opposite group velocity directions, e.g. Dirac cone systems like graphene, the band-transition directly leads to an inversion of the motion. By generalizing the results for arbitrary bands and additionally investigating the effects of perturbations like disorder or electro-magnetic fields, we are able to determine for any (effective) two-band system at hand with a given pulse whether it is a suited candidate for the quantum time mirror. In the Bose-Einstein condensates, the inversion of motion is achieved by quickly varying the nonlinear term. The phases in the wave function acquired during the pulse affect the velocity and for certain parameters it switches sign. Although echoes are induced by this mechanism, the fidelity is rather low. However, time lenses, i.e. refocusing the wave packet by a time-dependent pulse, can be achieved with high fidelity in this setup. Even solitary waves can be created whose refocus fidelity stay above 99% for more than 100,000 pulses. In the last part of the thesis, we investigate zitterbewegung in two-band systems with time-dependent potentials. In the driven setup, we find persistent, i.e. undamped, modes of the zitterbewegung that would decay for a wave packet in a static environment. Moreover, using the quantum time mirror pulses described above, echoes of the zitterbewegung can be achieved that are in some sense similar to the well-known and highly exploited spin echo

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

Although Zitterbewegung—the jittery motion of relativistic particles—was known since 1930 and was predicted in solid-state systems long ago, it has been directly measured so far only in so-called quantum simulators, i.e., quantum systems under strong control, such as trapped ions and Bose-Einstein condensates. A reason for the lack of further experimental evidence is the transient nature of wave-packet Zitterbewegung. Here, we study how the jittery motion can be manipulated in Dirac systems via time-dependent potentials with the goal of slowing down/preventing its decay or of generating its revival. For the harmonic driving of a mass term, we find persistent Zitterbewegung modes in pristine, i.e., scattering free, systems. Furthermore, an effective time-reversal protocol—the “Dirac quantum time mirror”—is shown to retrieve Zitterbewegung through echoes

Floquet oscillations in periodically driven Dirac systems

Electrons in a lattice exhibit time-periodic motion, known as Bloch oscillation, when subject to an additional static electric field. Here, we show that a corresponding dynamics can occur upon replacing the spatially periodic potential by a time-periodic driving: Floquet oscillations of charge carriers in a spatially homogeneous system. The time lattice of the driving gives rise to Floquet bands that take on the role of the usual Bloch bands. For two different drivings (harmonic driving and periodic kicking through pulses) of systems with linear dispersion we demonstrate the existence of such oscillations, both by directly propagating wave packets and based on a complementary Floquet analysis. The Floquet oscillations feature richer oscillation patterns than their Bloch counterpart and enable the imaging of Floquet bands. Moreover, their period can be directly tuned through the driving frequency. Such oscillations should be experimentally observable in effective Dirac systems, such as graphene, when illuminated with circularly polarized light

Quantum time mirrors for general two-band systems

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 atom-optics 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

Overcoming dispersive spreading of quantum wave packets via periodic nonlinear kicking

We propose the suppression of dispersive spreading of wave packets governed by the free-space Schrodinger equation with a periodically pulsed nonlinear term. Using asymptotic analysis, we construct stroboscopically-dispersionless quantum states that are physically reminiscent of, but mathematically different from, the well-known one-soliton solutions of the nonlinear Schrodinger equation with a constant (time-independent) nonlinearity. Our analytics are strongly supported by full numerical simulations. The predicted dispersionless wave packets can move with arbitrary velocity and can be realized in experiments involving ultracold atomic gases with temporally controlled interactions

Towards a quantum time mirror for non-relativistic wave packets

We propose a method – a quantum time mirror (QTM) – for simulating a partial time-reversal of the free-space motion of a nonrelativistic quantum wave packet. The method is based on a short-time spatially-homogeneous perturbation to the wave packet dynamics, achieved by adding a nonlinear time-dependent term to the underlying Schroedinger equation. Numerical calculations, supporting our analytical considerations, demonstrate the effectiveness of the proposed QTM for generating a time-reversed echo image of initially localized matter-wave packets in one and two spatial dimensions. We also discuss possible experimental realizations of the proposed QTM

Dynamical Spin-Orbit-Based Spin Transistor

Spin-orbit interaction (SOI) has been a key tool to steer and manipulate spin-dependent transport properties in two-dimensional electron gases. Here we demonstrate how spin currents can be created and efficiently read out in nano- or mesoscale conductors with time-dependent and spatially inhomogenous Rashba SOI. Invoking an underlying non-Abelian SU(2) gauge structure we show how time-periodic spin-orbit fields give rise to spin-motive forces and enable the generation of pure spin currents of the order of several hundred nano-Amperes. In a complementary way, by combining gauge transformations with "hidden" Onsager relations, we exploit spatially inhomogenous Rashba SOI to convert spin currents (back) into charge currents. In combining both concepts, we devise a spin transistor that integrates efficient spin current generation, by employing dynamical SOI, with its experimentally feasible detection via conversion into charge signals. We derive general expressions for the respective spin- and charge conductances, covering large parameter regimes of SOI strength and driving frequencies, far beyond usual adiabatic approaches such as the frozen scattering matrix approximation. We check our analytical expressions and approximations with full numerical spin-dependent transport simulations and demonstrate that the predictions hold true in a wide range from low to high driving frequencies

Simulating time-dependent thermoelectric transport in quantum systems

International audienceWe put forward a gauge-invariant theoretical framework for studying time-resolved thermoelectric transport in an arbitrary multiterminal electronic quantum system described by a noninteracting tight-binding model. The system is driven out of equilibrium by an external time-dependent electromagnetic field (switched on at time $t_0$) and possibly by static temperature or electrochemical potential biases applied (from the remote past) between the electronic reservoirs. Numerical simulations are conducted by extending to energy transport the wave-function approach developed by Gaury et al. and implemented in the t-Kwant library. We provide a module that allows us to compute the time-resolved heat currents and powers in addition to the (already implemented) charge currents, and thus to simulate dynamical thermoelectric transport through realistic devices, when electron-electron and electron-phonon interactions can be neglected. We apply our method to the noninteracting Resonant Level Model and verify that we recover the results reported in the literature for the time-resolved heat currents in the expected limits. Finally, we showcase the versatility of the library by simulating dynamical thermal transport in a Quantum Point Contact subjected to voltage pulses