Classical and quantum periodically driven scattering in one dimension

Photon exchange and entanglement formation during transmission through a rectangular quantum barrier

When a quantum particle traverses a rectangular potential created by a quantum field both photon exchange and entanglement between particle and field take place. We present the full analytic solution of the Schrödinger equation of the composite particle-field system allowing investigation of these phenomena in detail and comparison to the results of a classical field treatment. Besides entanglement formation, remarkable differences also appear with respect to the symmetry between energy emission and absorption, resonance effects and if the field initially occupies the vacuum state.

Classical and quantum chaotic angular-momentum pumps

We study directed transport of charge and intrinsic angular momentum by periodically driven scattering in the regime of fast and strong driving. A spin-orbit coupling through a kicked magnetic field confined to a compact region in space leads to irregular scattering and triggers spin flips in a spatially asymmetric manner which allows us to generate polarized currents. The dynamical mechanisms responsible for the spin separation carry over to the quantum level and give rise to spin pumping. Our theory based on the Floquet formalism is confirmed by numerical solutions of the time-dependent inhomogeneous Schrödinger equation with a continuous source term.

Quantum versus classical dynamics in a driven barrier: The role of kinematic effects

We study the dynamics of the classical and quantum mechanical scattering of a wave packet from an oscillating barrier. Our main focus is on the dependence of the transmission coefficient on the initial energy of the wave packet for a wide range of oscillation frequencies. The behavior of the quantum transmission coefficient is affected by tunneling phenomena, resonances, and kinematic effects emanating from the time dependence of the potential. We show that when kinematic effects dominate (mainly in intermediate frequencies), classical mechanics provides very good approximation of quantum results. In that frequency region, the classical and quantum transmission coefficients are in optimal agreement. Moreover, the transmission threshold (i.e., the energy above which the transmission coefficient becomes larger than a specific small threshold value) is found to exhibit a minimum. We also consider the form of the transmitted wave packet and we find that for low values of the frequency the incoming classical and quantum wave packet can be split into a train of well-separated coherent pulses, a phenomenon that admits purely classical kinematic interpretation.

Escape rate for a quantum particle moving in a time-periodic rapidly oscillating potential: a time-independent approach

We explore, in the quantum regime, the stochastic dynamics of a time-periodic, rapidly oscillating potential (having a characteristic frequency of ω) within the framework of a time-dependent system-reservoir Hamiltonian. We invoke the idea of a quantum gauge transformation in light of the standard Floquet theorem in an attempt to construct a Langevin equation (bearing a time-independent effective potential) by employing a systematic perturbative expansion in powers of ω^{-1} using the natural time-scale separation. The time-independent effective potential (corrected to ω^{-2} in leading order) that acts on the slow motion of the driven particle can be employed for trapping. We proceed further to evaluate the rate of escape of the driven particle from the metastable state in the high-temperature limit. We also envisage a resonance phenomena, a true hallmark of the system-reservoir quantization. This development would thus serve as a model template to investigate the trapping mechanism, as well as an appropriate analog to understand the dynamics of a fluctuation-induced escape process from the trap.

Quantum scattering in driven single- and double-barrier systems

We investigate the quantum transmission through laterally driven single- and double-barrier systems in the nonlinear regime of strong driving. A broad parameter range is explored, distinguishing in particular between different frequency regimes. The applicability of an effective, time independent, potential description in the high-frequency regime is explored. Moreover, we analyze in detail the inelastic processes and their dependence on parameters, resonant tunneling, and photon assisted tunneling. For the single-barrier problem we address driving laws that differ from the purely sinusoidal one. In this context, we encounter reduced spatial and temporal symmetries and demonstrate the corresponding effects on quantum pumping. For the double barrier, the focus of our studies lies on the impact of the variation in the relative phase of the barriers on the transmission.

Dynamical trapping and chaotic scattering of the harmonically driven barrier

A detailed analysis of the classical nonlinear dynamics of a single driven square potential barrier with harmonically oscillating position is performed. The system exhibits dynamical trapping which is associated with the existence of a stable island in phase space. Due to the unstable periodic orbits of the KAM structure, the driven barrier is a chaotic scatterer and shows stickiness of scattering trajectories in the vicinity of the stable island. The transmission function of a suitably prepared ensemble yields results which are very similar to tunneling resonances in the quantum mechanical regime. However, the origin of these resonances is different in the classical regime.

Time independent description of rapidly oscillating potentials

The classical and quantum dynamics in a high frequency field are found to be described by an effective time independent Hamiltonian. It is calculated in a systematic expansion in the inverse of the frequency (omega) to order omega(-4). The work is an extension of the classical result for the Kapitza pendulum, which was calculated in the past to order omega(-2). The analysis makes use of an implementation of the method of separation of time scales and of a quantum gauge transformation in the framework of Floquet theory. The effective time independent Hamiltonian enables one to explore the dynamics in the presence of rapidly oscillating fields, in the framework of theories that were developed for systems with time independent Hamiltonians. The results are relevant, in particular, for exploring the dynamics of cold atoms.