Quantum revival patterns from classical phase-space trajectories

Abstract

A general semiclassical method in phase space based on the final value representation of the Wigner function is considered that bypasses caustics and the need to root-search for classical trajectories. We demonstrate its potential by applying the method to the Kerr Hamiltonian, for which the exact quantum evolution is punctuated by a sequence of intricate revival patterns. The structure of such revival patterns, lying far beyond the Ehrenfest time, is semiclassically reproduced and revealed as a consequence of constructive and destructive interferences of classical trajectories. arXiv:1809.04139v2 [quant-ph]

Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

“…Then, considering the semi-classical evolution of W + f (Θ, j) in the continuous limit and applying a subsequent discretization procedure ( 39)- (41), we arrive at the following discretized version of TWA for variable spin systems,…”

“…Multiple attempts to improve the TWA [19,33,34] suggest that more sophisticated methods [35][36][37][38][39][40][41][42][43] should be applied in order to describe the quantum evolution in terms of continuously distributed classical phase-space trajectories. Alternatively, different types of discrete phase-space sampling were proposed [44][45][46][47][48][49][50] in order to emulate evolution of average values using the main idea of the TWA.…”

Peculiarities of Interaction of a Quantum Dot with Non-Classical Light in the Self-Phase Modulation Regime

“…The comparison between figure 6 and figure 1 evidently shows that during the collapse regime when both the excitation probability and the mean number of photons in the field are fixed the dynamics of the system does not stop and manifests itself in the significant change of entanglement. From (14) it can be easily seen that during the collapse regime both the quantum dot and field states are changing dramatically since efficient dynamics of the off-diagonal matrix elements for each subsystem takes place.…”

“…It should be noticed that even the analysis of the Kerr self-phase modulation itself is often restricted to consideration of only coherent states of light and mainly in the limit of extremely small nonlinearity [13,14,15,16]. At the same time the role of the Kerr-nonlinearity during the interaction of light with quantum atomic and semiconductor systems seems to be poorly studied.…”

The role of tunneling in the ionization of atoms by ultrashort and intense laser pulses

“…the initial state is deformed into filaments that are sheared and folded, and the classical position marginals have peaks on the filaments lying perpendicularly to the momentum axis [50,51]. This filamentary structure is usually not enough to reproduce peak heights, and one must resort to semiclassical approximations: Quantum interference is then achieved by a rigorous endowing of classical trajectories with accumulated phases, which superpose and correct peak intensities [52,53]. What is fundamental to our purposes is that only the extremities of the PD in Fig.…”