Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

中国物理B：英文版

Position-dependent dynamics of a trapped ion in a standing wave laser

方卯发

Published Jun 12, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1009-1963/11/10/011

Related papers

Position-dependent dynamics of a trapped ion in a standing wave laser

Mao-Fa Fang

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.

Chinese Physics•Oct 1, 2002•3 citations

Nonlinear Jaynes-Cummings model of a trapped ion and the evolution of the ion population inversion

Zhongqing Wang, Chang‐Kui Duan, AN Guang-lei +1 more

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.

Acta Physica Sinica•Jan 1, 2006•2 citations

Jaynes-Cummings Model for a Trapped Ion in Any Position of a Standing Wave

Ying Wu, Xiaoxue Yang

It is shown that the dynamics of a two-level ion in any position other than at the antinode of a standing wave that moves in a harmonic trapping potential can be described by Jaynes-Cummings model under the conditions of the rotating-wave approximation, the Lamb-Dicke limit, and the strong confinement limit.

Physical Review Letters•Apr 21, 1997•151 citations

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

Mao-Fa Fang, S. Swain, Peng Zhou

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.

Physical Review A•Dec 12, 2000•33 citations

Jaynes-Cummings Model Dynamics in Two Trapped Ions

Hao‐Sheng Zeng, Le‐Man Kuang, Kelin Gao

We showed that in Lamb-Dicke regime and under rotating wave approximation, the dynamical behavior of two trapped ions interacting with a laser beam resonant to the first red side-band of center-of-mass mode can be described by Jaynes-Cummings Model. An exact analytic solution for this kind of Jaynes-Cummings model is presented. The results showed that quantum collapses and revivals for the occupation of two atoms, and squeezing for vibratic motion of center-of-mass mode existed in both two different types of initial conditions. The maximum momentum squeezing for center-of-mass mode in these two types of conditions are found to be 42.4% and 43.8% respectively. The coherence, in the first type of initial conditions can keeps long times, and in the second type of initial conditions, a concrete form of coherent state is obtained, when the initial average number is very small.

arXiv:quant-ph/0106020•Jun 5, 2001•10 citations

Long-time-scale revivals in ion traps

H. M. Moya-Cessa, A. Vidiella-Barranco, José Antonio Roversi +2 more

In this paper we investigate the interaction of a single ion in a trap with laser beams. Our approach, based on unitary transformating the Hamiltonian, allows its exact diagonalization without performing the Lamb-Dicke approximation. We obtain a transformed Jaynes-Cummings-type Hamiltonian, and we demonstrate the existence of super-revivals in that system.

arXiv:quant-ph/9812047•Physical Review A•Mar 1, 1999•55 citations
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.
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 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.
We showed that in Lamb-Dicke regime and under rotating wave approximation, the dynamical behavior of two trapped ions interacting with a laser beam resonant to the first red side-band of center-of-mass mode can be described by Jaynes-Cummings Model. An exact analytic solution for this kind of Jaynes-Cummings model is presented. The results showed that quantum collapses and revivals for the occupation of two atoms, and squeezing for vibratic motion of center-of-mass mode existed in both two different types of initial conditions. The maximum momentum squeezing for center-of-mass mode in these two types of conditions are found to be 42.4% and 43.8% respectively. The coherence, in the first type of initial conditions can keeps long times, and in the second type of initial conditions, a concrete form of coherent state is obtained, when the initial average number is very small.