Quantum wave packet revivals

By R. Robinett. 2004

459 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b7dc9e31f1d33c577ed625a9302b5b3550524611

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Developments in alkali -metal atomic magnetometry (2008, methodology): “Following the general description of quantum revivals in multilevel systems (Robinett, 2004), we write the energy levels given by Equation 3.”
The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics (2013, background): “From this point of view, the Talbot process belongs to a broader family of phenomena exhibiting wave packet revivals [20].”
Colloquium: Looking at a soliton through the prism of optical supercontinuum (2010, background): “This effect is known as quantum bouncing (Robinett, 2004).”
Dynamics of Loschmidt echoes and fidelity decay (2006, background): “[172] and [173], see also the review [174].”
Light propagation and localization in modulated photonic lattices and waveguides (2011, background): “Between subsequent revivals, a collapsed state, corresponding to a kind of ‘incoherent’ superposition of the various wave packet components and leading to a fully delocalized field over a distance d from thewaveguide boundary, is expected on the basis of general considerations [264].”