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Physics Letters A

Manifestations of wave packet revivals in the moments of observables

C. Sudheesh, S. Lakshmibala, V. Balakrishnan

Published Jul 13, 2004• 28 citations
Publisher
DOI
10.1016/j.physleta.2004.06.085

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The general properties of the time-dependent characteristics of one-dimensional vibrational wave packets in an anharmonic system with the quadratic spectrum are discussed. The local behavior of the autocorrelation function and its square modulus (the survival function) is studied near the moments of fractional revival t=(p/q)Trev, where Trev is the period of the complete revival, p/q is an irreducible fraction, and q is the order of the revival. It is shown that all the wave packets have the same values of the survival function at the moments of fractional revival provided that the number of states in the packet exceeds the order of the revival q. It is also found that for the given packet, all the fractional revivals are identical to each other in the sense that their lifetimes do not depend on the order of the revival. The lifetimes of all fractional revivals are expressed in terms of the parameters of the initial packet (the effective number of states and the period of classical motion of the packet center) and the anharmonicity of the molecular system.
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.
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.