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arXiv:quant-ph/0401181

Signatures of wave packet revival phenomena in the expectation values of observables

C. Sudheesh, S. Lakshmibala, V. Balakrishnan

Published Jan 29, 2004• 0 citations
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Abstract

Wave packet revivals and fractional revivals are striking quantum interference phenomena that can occur under suitable conditions in a system with a nonlinear spectrum. In the framework of a specific model (the propagation of an initially coherent wave packet in a Kerr-like medium), it is shown that distinctive signatures of these revivals and fractional revivals are displayed by the time evolution of the expectation values of physical observables and their powers, i.e., by experimentally measurable quantities. Moreover, different fractional revivals can be selectively identified by examining appropriate higher moments.

DOI
10.48550/arxiv.quant-ph/0401181

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Wave packet revivals and fractional revivals are striking quantum interference phenomena that can occur under suitable conditions in a system with a nonlinear spectrum. In the framework of a specific model (the propagation of an initially coherent wave packet in a Kerr-like medium), it is shown that distinctive signatures of these revivals and fractional revivals are displayed by the time evolution of the expectation values of physical observables and their powers, i.e., by experimentally measurable quantities. Moreover, different fractional revivals can be selectively identified by examining appropriate higher moments.
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We study the dynamics of superposed wave packets in a specific nonlinear Hamiltonian which models the wave packet propagation in Kerr-like media and the dynamics of Bose–Einstein condensates. We show the dependence of fractional revival times on the initial superposed wave packets using analysis based on the expectation values, Rényi entropy and Wigner function. We also show how the selective identification of fractional revivals using moments of appropriate observables depends on the number of wave packets present in the initial state.
We show in the framework of a tractable model that revivals and fractional revivals of wave packets afford clear signatures of the extent of departure from coherence and from Poisson statistics of an initial state of the radiation field propagating in a nonlinear medium. We establish this by considering a generic Hamiltonian which models wave packet propagation in a Kerr-like medium, and comparing the non-classical effects displayed by an initial photon-added coherent state with that of an inital ideal coherent state.
Treating the ideal coherent state as a reference state, the effects due to departure from coherence of an initial wave packet propagating through a nonlinear medium, were examined, specifically in the context of non-classical effects such as revivals, fractional revivals, squeezing and higher-order squeezing during its temporal evolution. Further, these studies were extended to examine the role of quantum entanglement in bipartite systems. The dynamics of quantum expectation values were tracked carefully in various cases and the conditions under which a wave packet spreads chaotically, were investigated.
Rydberg atomic wave packets have demonstrated striking classical properties. In particular, the wave packets display regions in which they evolve like classical atoms. However, between these regions the wave packet is dispersed and its evolution departs from the classical model. In these nonclassical regions, the wave packet can either be dispersed or coalesced into a number of equally spaced sub-wave-packets. The regions in which the sub-wave-packets appear have come to be known as fractional revivals. This paper reports the observation of these fractional revivals and discusses their implications.
By analyzing the optical tomogram of a linear superposition of coherent states, we show that distinctive signatures of the macroscopic superposition states are displayed directly in the optical tomograms of the states. We also study the effect of decoherence on the optical tomograms of the macroscopic superposition states. Since the wave packet fractional revivals are associated with the generation of macroscopic superposition states, these signatures help in visualizing the revivals and fractional revivals occurring in a nonlinear medium directly in the optical tomogram of the time-evolved state. We found that the optical tomogram of the time-evolved state at the instants of fractional revivals show structures with sinusoidal strands. Using a class of initial superposed wave packets evolving in the Kerr-like medium, we further show that the condition for the occurrence of fractional revival phenomenon depends on the number of wave packets composing the initial superposition state. In the case of a two-mode electromagnetic field, we investigate the entanglement of the state directly using the optical tomogram. We have shown that the signatures of entanglement can be observed directly in the single-mode optical tomogram of the state without reconstructing the density matrix of the system. We also analyze the effect of decoherence on the optical tomograms of the entangled states. Further, we examine the optical tomograms of the entangled states generated using a beam splitter with a Kerr medium placed into one of its input modes. We have found the signatures of entanglement in the optical tomogram for the entangled states generated at the instants of two- and three-subpacket fractional revival times.