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

Physical Review Letters

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

Ying Wu, Xiaoxue Yang

Published Apr 21, 1997• 151 citations
Publisher

Abstract

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.
DOI
10.1103/physrevlett.78.3086

Related papers

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

方卯发

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.

中国物理B：英文版•Jun 12, 2005•0 citations

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

Model for Trapped Ion interacting with Standing Wave

Sher Alam, Cleo L. Bentley

We treat the interaction of a trapped ion with a standing-wave light field relaxing the previous condition of the trapping ion being on the node of the standing wave. In addition we work to second order in the Lamb-Dicke parameter $η$, the extension to higher orders in $η$ is also indicated. Only a simple transformation to the ``dressed basis'' [subject to the constraint of Pauli algebra] is required in order to show that the ion interacting with a standing light-wave may be described by the Jaynes-Cummings Hamiltonian.

arXiv:physics/9707004•Jul 4, 1997•0 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

Model for Trapped Ion Interacting with Standing Wave via Gauge-Like Transformations

Sher Alam, Cleo L. Bentley

We treat the interaction of a trapped ion with a standing-wave light field, relaxing the previous condition of the trapping ion being on the node of the standing wave. In addition we work to second order in the Lamb-Dicke parameter η the extension to higher orders in η is also indicated. Only a simple transformation to the “dressed basis” (subject to the constraint of Pauli algebra) is required in order to show that the ion interacting with a standing light-wave may be described by the Jaynes-Cummings Hamiltonian. The ansatz of leaving invariant the Pauli algebra after the transformations amounts to a linear transformation in the su(2) algebra describing the two level system. The outcome is a Jaynes-Cummings like Hamiltonian with effective coupling dependent on the parameter Χ aimed to figure the trapping location in the standing wave. The main idea, namely leaving the Hamiltonian form invariant while changing the physical parameters can pave the way to a new understanding of gauge like transformations in the present context.

Progress of Theoretical Physics•Apr 1, 1998•0 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
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 treat the interaction of a trapped ion with a standing-wave light field relaxing the previous condition of the trapping ion being on the node of the standing wave. In addition we work to second order in the Lamb-Dicke parameter ηηη, the extension to higher orders in ηηη is also indicated. Only a simple transformation to the ``dressed basis'' [subject to the constraint of Pauli algebra] is required in order to show that the ion interacting with a standing light-wave may be described by the Jaynes-Cummings Hamiltonian.
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 treat the interaction of a trapped ion with a standing-wave light field, relaxing the previous condition of the trapping ion being on the node of the standing wave. In addition we work to second order in the Lamb-Dicke parameter η the extension to higher orders in η is also indicated. Only a simple transformation to the “dressed basis” (subject to the constraint of Pauli algebra) is required in order to show that the ion interacting with a standing light-wave may be described by the Jaynes-Cummings Hamiltonian. The ansatz of leaving invariant the Pauli algebra after the transformations amounts to a linear transformation in the su(2) algebra describing the two level system. The outcome is a Jaynes-Cummings like Hamiltonian with effective coupling dependent on the parameter Χ aimed to figure the trapping location in the standing wave. The main idea, namely leaving the Hamiltonian form invariant while changing the physical parameters can pave the way to a new understanding of gauge like transformations in the present context.
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.