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Physical Review A

Super-revivals, chaos, and entanglement of a trapped ion in a standing wave

Mao-Fa Fang, S. Swain, Peng Zhou

Published Dec 12, 2000• 33 citations
Publisher

Abstract

We unitarily transform the Hamiltonian of a trapped ion, situated at any position of a standing-wave laser field, to that for the normal Jaynes-Cummings model in the bare ionic basis, and we obtain the general evolution operator of the trapped ion system. We show the existence of super-revivals of the ionic inversion if the trapped ion is not located at a node of the standing wave, and we examine the degree of entanglement between the vibrational phonons and the trapped ion. For some parameter values, we find chaotic behavior.

DOI
10.1103/physreva.63.013812

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We unitarily transform the Hamiltonian of a trapped ion, situated at any position of a standing-wave laser field, to that for the normal Jaynes-Cummings model in the bare ionic basis, and we obtain the general evolution operator of the trapped ion system. We show the existence of super-revivals of the ionic inversion if the trapped ion is not located at a node of the standing wave, and we examine the degree of entanglement between the vibrational phonons and the trapped ion. For some parameter values, we find chaotic behavior.
By performing a unitary transformation, we transform the Hamiltonian of the trapped ion in any position of standing wave to that of the normal Jaynes-Cummings model in ionic bare basis and we obtain a general evolution operator of the trapped ion system. We study the quantum entropic dynamics of the phonons and trapped ion. Our results show that, when the trapped ion is located at the node of standing wave, the quantum entropic dynamics of phonons and trapped ion are the same as the one of the field in the Jaynes-Cummings model. When the trapped ion deviates from the node of standing wave, the entropies of the phonons and ion keep their maximum value except at the initial stage, and the phonons and trapped ion become extremely entangled.
Starting from the Jaynes-Cummings (J-C) model describing the interaction of a trapped ion with a standing-wave laser field, we derive the interaction Hamiltonian on the nonlinear J-C model of the trapped ion excitated resonantly with 1-quantum vibrational mode. After solving the time-dependent states of this model, we study the evolution of population inversion for the ion numerically. It is shown that the period of the quantum collapse and revival of the population inversionis related with the Lamb-Dick parameter and the position of the ion in the standing-wave laser field. With the increasing of the parameter, it will decrease the period of the collapse and revival. When moving the ion from the node of the standing-wave laser to the antinode, the period of the collapse and revival becomes longer.
We have investigated the position-dependent dynamics of a trapped ion in a standing wave laser by transforming it to the Jaynes-Cummings-type system under the Lamb-Dicke limit. A variety of novel phenomena are exhibited, e.g. periodic collapse and revival features and long-time scaled revivals of the ionic inversion, depending on its position in the standing wave. Our result provides a way of producing a system equivalent to the two-photon Jaynes-Cummings model in the trapped ion system, with its exact periodicities.
We have investigated the position-dependent dynamics of a trapped ion in a standing wave laser by transforming it to the Jaynes-Cummings-type system under the Lamb-Dicke limit.A variety of novel phenomena are exhibited.e.g.periodic collapse and revival features and long-time scaled revivals of the ionic inversion,depending on its position in the standing wave.Our result provides a way of producing a system equivalent to the two-photon Jaynes-Cummings model in the trapped ion system,with its exact periodicities.
We study the dynamical behaviour of the ionic inversion in a trapped ion system in running-wave lasers and we discuss the properties of entanglement between the ion and phonons and the statistics of the vibrational phonon field. It is shown that the appearance of the super-revivals of the ion inversion is dependent on the initial parameters of the vibrational phonon field. The Schrödinger cat and sub-Poissonian statistics of the phonon field can be also exhibited in this system for suitable initial values.
We study the dynamical behaviour of the ionic inversion in a trapped ion system in running-wave lasers,and we discuss the properties of entanglement between the ion and phonons and the statistics of the vibrational phonon field.It is shown that the appearance of the super-revivals of the ion inversion is dependent on the initial parameters of the vibrational phonon field.The Schredinger cat and sub-Poissonican statistics of the phonon field can be also exhibited in this system for suitable initial values.