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

Journal of Atomic and Molecular Physics

Entropy evolution of the internal and external degree of freedom of a trapped ion in standing wave laser

Zhong Wang

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Starting from the Jaynes-Cummings (J-C) model describing 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,the entropy evolution of the ion are investigated numerically related with Lamb-Dick parameter,the position of the ion in the standing-wave laser field and the initial number of phonon. It is shown that the entropy evolution exhibit nonperiodicity vibration. With the increasing of the parameter, it will increase the frequency of the vibration,therefore the less time of disentanglement between the internal and external degrees of freedom of a trapped ion. When moving the ion from the node of the standing-wave laser to the antinode,the frequency of the vibration becomes less,the longer time of the disentanglement between the internal and external degrees of freedom. With the more initial number of phonon , the entropy evolution of the ion is similar to the field entropy evolution of Jaynes-Cummings model, and the vibration frequency become less gradually.

Related papers

Evolution properties of the field quantum entropy in the nonlinear Jaynes-Cummings model of a trapped ion

Liu Wang-Yun, BI Si-wen, Xi-bo Dou +1 more

The time evolution properties of the field quantum entropy in the system of a trapped ion interacting resonantly with a standing-wave laser field is studied by utilizing the Von Neumann reduced quantum entropy theory, and our attention focuses on the discussion of the influence of the Lamb-Dick parameter, the position of the ion in the standing-wave laser field and the initial state of the trapped ion on the evolution properties of the field quantum entropy. The results obtained from the numerical calculation indicate that: the value of the Lamb-Dick parameter effect the oscillation frequency and amplitude of the quantum entanglement between the trapped ion and the standing-wave laser field, the larger the Lamb-Dick parameter is, the weaker the average entanglement level between the ion and the field will be. When moving the tapped ion from the node of the standing-wave laser to the loop, the vibration frequency of the quantum entanglement between the field and the ion becomes slow gradually, and the entanglement degree gets weaker and weaker. With the decrease of the probability of the trapped ion being in the excited state, the quantum entanglement between the trapped ion and the stanging-wave laser field shows the tendency of increase first and then decrease. These properties have certain reference value for the preparation of entangled states and for the quantum communications with the thapped ion, and so on.

Acta Physica Sinica•Jan 1, 2010•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

PERIODIC ENTANGLEMENT BETWEEN THE INTERNAL AND EXTERANL DEGREE OF FREEDOM OF A TRAPPED ION IN A STANDING WAVE LASER

Mao-Fa Fang, LIU XIANG, 湖南师范大学理学院物理系,长沙410081

We have investigated the quantum entropy and entanglement of the internal and external degrees of freedom of a trapped ion in a standing wave laser by transforming the Hamiltonian to that in the Jaynes-Cummings system for the bare basis of the trapped ion under the Lamb-Dicke limit. Under the off-resonant condition, we have found the periodic entanglement between the internal and external degrees of freedom of a trapped ion.

Acta Physica Sinica•Jan 1, 2001•1 citation

Influence of Squeezing Effects on Nonlinear of a Trapped Ion

Jian Li

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 excited resonantly with single quantum vibrational mode.After solving the time dependent states of this model,we study the ion centroid motion of squeezing effects by utilizing the ion numerical model.It is shown that the ion squeezing effects is related with the Lamb-Dicke parameter and the position of the ion in the standing wave laser field.

Journal of Anhui Normal University•Jan 1, 2012•0 citations

Quantum Entropic Dynamics of a Trapped Ion in a Standing Wave

Mao-Fa Fang, Peng Zhou, S. Swain

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.

Chinese Physics Letters•Dec 1, 2000•13 citations

The Influence of the Micromotion on the Internal Dynamics of an Ion in a Paul Trap

Fang XiMing, Feng Mang, Shi Lei +3 more

For the case of standing wave laser field, we investigate the internal dynamics of a Paul-trapped ion for different cases of the micromotion frequency by means of nonlinear Jaynes–Cummings model and compare our model with the pseudopotential model. The specific calculations show that, when values of dc and ac voltages are fixed, the larger the micromotion frequency is, the smaller the difference between the two models becomes and the larger the Rabi frequency is, for both within and beyond the Lamb–Dicke regime. Moreover, the property of the trapped ion staying whether on the node or on the antinode of the standing wave field is first presented.

Communications in Theoretical Physics•Jul 30, 1999•0 citations
Starting from the Jaynes-Cummings (J-C) model describing 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,the entropy evolution of the ion are investigated numerically related with Lamb-Dick parameter,the position of the ion in the standing-wave laser field and the initial number of phonon. It is shown that the entropy evolution exhibit nonperiodicity vibration. With the increasing of the parameter, it will increase the frequency of the vibration,therefore the less time of disentanglement between the internal and external degrees of freedom of a trapped ion. When moving the ion from the node of the standing-wave laser to the antinode,the frequency of the vibration becomes less,the longer time of the disentanglement between the internal and external degrees of freedom. With the more initial number of phonon , the entropy evolution of the ion is similar to the field entropy evolution of Jaynes-Cummings model, and the vibration frequency become less gradually.
The time evolution properties of the field quantum entropy in the system of a trapped ion interacting resonantly with a standing-wave laser field is studied by utilizing the Von Neumann reduced quantum entropy theory, and our attention focuses on the discussion of the influence of the Lamb-Dick parameter, the position of the ion in the standing-wave laser field and the initial state of the trapped ion on the evolution properties of the field quantum entropy. The results obtained from the numerical calculation indicate that: the value of the Lamb-Dick parameter effect the oscillation frequency and amplitude of the quantum entanglement between the trapped ion and the standing-wave laser field, the larger the Lamb-Dick parameter is, the weaker the average entanglement level between the ion and the field will be. When moving the tapped ion from the node of the standing-wave laser to the loop, the vibration frequency of the quantum entanglement between the field and the ion becomes slow gradually, and the entanglement degree gets weaker and weaker. With the decrease of the probability of the trapped ion being in the excited state, the quantum entanglement between the trapped ion and the stanging-wave laser field shows the tendency of increase first and then decrease. These properties have certain reference value for the preparation of entangled states and for the quantum communications with the thapped ion, and so on.
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.
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 excited resonantly with single quantum vibrational mode.After solving the time dependent states of this model,we study the ion centroid motion of squeezing effects by utilizing the ion numerical model.It is shown that the ion squeezing effects is related with the Lamb-Dicke parameter and the position of the ion in the standing wave laser field.
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.
For the case of standing wave laser field, we investigate the internal dynamics of a Paul-trapped ion for different cases of the micromotion frequency by means of nonlinear Jaynes–Cummings model and compare our model with the pseudopotential model. The specific calculations show that, when values of dc and ac voltages are fixed, the larger the micromotion frequency is, the smaller the difference between the two models becomes and the larger the Rabi frequency is, for both within and beyond the Lamb–Dicke regime. Moreover, the property of the trapped ion staying whether on the node or on the antinode of the standing wave field is first presented.