Quantum wave packet revivals

Abstract

The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially localized quantum states which have a short-term, quasi-classical time evolution, which then can spread significantly over several orbits, only to reform later in the form of a quantum revival in which the spreading reverses itself, the wave packet relocalizes, and the semi-classical periodicity is once again evident. Relocalization of the initial wave packet into a number of smaller copies of the initial packet ('minipackets' or 'clones') is also possible, giving rise to fractional revivals. Systems exhibiting such behavior are a fundamental realization of time-dependent interference phenomena for bound states with quantized energies in quantum mechanics and are therefore of wide interest in the physics and chemistry communities.We review the theoretical machinery of quantum wave packet construction leading to the existence of revivals and fractional revivals, in systems with one (or more) quantum number(s), as well as discussing how information on the classical period and revival time is encoded in the energy eigenvalue spectrum. We discuss a number of one-dimensional model systems which exhibit revival behavior, including the infinite well, the quantum bouncer, and others, as well as several two-dimensional integrable quantum billiard systems. Finally, we briefly review the experimental evidence for wave packet revivals in atomic, molecular, and other systems, and related revival phenomena in condensed matter and optical systems.

A Phase-Space Study of the Quantum Loschmidt Echo in the Semiclassical Limit

“…As it is shown in [32], it is also possible to observe fractional revivals, using some elementary properties of integers.…”

“…In Section 3, we consider the (integrable) d = 1 case, and consider the "return probability" in the semiclassical limit. We give a mathematical rigorous presentation of beautiful results on "quantum revivals" obtained by physicists twenty years ago (see [23], [32], [20]). In Section 4 we consider the general d-dimensional case and give a semiclassical calculus of the "return probability" and of the quantum fidelity, with precise error estimates.…”

Quantum spin chains with fractional revival

“…For perfect state transfer (PST), one wishes to have, for example, a one-excitation state localized at the beginning of the chain evolve with unit probability, after some time T , into the state with the excitation localized at the end of the chain. Such a relocalization of the wave packet is what is referred to as revival [4,5]. Fractional revival occurs when a number of smaller packets seen as little clones of the original one form at certain sites and show local periodicities [4,6].…”

Collapse and revival in holographic quenches

“…When revivals appear, they are not isolated, but repeat themselves with or without decay [4][5][6][7]. The focus of this work is set on this last type of effect.…”