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

Chinese Physics Letters

Dynamics of Entanglement for Coherent Motional States of Two Trapped Ions in Cascaded Optical Cavities

Gao‐xiang Li, Zhang Fan, Shaoping Wu

Published Jan 30, 2006• 3 citations
Publisher

Abstract

We study the generation of an entangled motional coherent state of two distant ions trapped in two cascaded cavities, in which the motional mode of the each ion is coupled to the respective cavity field via a linear-mixing interaction. The master equation is solved analytically by using the characteristic function method. It is found that the generated entangled coherent state resulted from the initial preparation of an even coherent state is more robust than that from an odd coherent state under the dissipation of the cavity.

DOI
10.1088/0256-307x/23/2/023

Related papers

Motional entanglement for two trapped ions in cascaded optical cavities

Gao‐xiang Li, Huatang Tan, Shaoping Wu

The time-dependent characteristic function for the vibrational quanta of two ions separately trapped in two cascaded optical cavities is obtained analytically beyond the bad cavity limit, in which the motional mode of the ion in the first cavity is coupled to the cavity field via an effective parametric interaction and that of the ion in the second cavity via a linear-mixing interaction as proposed by Peng and Parkins [Phys. Rev. A 65, 062323 (2002)]. It is found that the two ions develop in a two-mode mixed Gaussian entangled state if there exists a unidirectional coupling from the first cavity to the second one.

Physical Review A•Dec 21, 2004•17 citations

Generation of entanglement and squeezing in the system of two ions trapped in a cavity

Gao‐xiang Li, Shao‐ping Wu, J. F. Hu

The dynamical behavior of the entanglement and the squeezing in the system of two ions trapped in a lossy optical cavity is discussed, in which the vibrational mode of the first ion is coupled to the cavity field via a linear-mixing interaction and the vibrational mode of the second ion is coupled to the cavity field via an effective parametric interaction, respectively. It is found that when the effective strength ${r}_{1}$ of the coupling between the first ion and the cavity field is stronger than the strength ${r}_{2}$ of the coupling between the second ion and the cavity field, the motional state of the two ions develops into a robust two-mode mixed Gaussian entangled state and the two-mode squeezing of phonons appears. But the entanglement between the cavity mode and the vibrational mode of the second ion can only happen periodically in a small time range. When ${r}_{1}<{r}_{2}$, only the entanglement between the two vibrational modes appears but the two-mode squeezing does not exist. And the entanglement between the cavity mode and the motional mode of the second ion can also take place in a small time range.

Physical Review A•Jun 24, 2005•41 citations

Preparation of hybrid entangled states and entangled coherent states for a single trapped ion in a cavity

Jie‐Qiao Liao, Yu Guo, Hao‐Sheng Zeng +1 more

In this paper, we study generation of entangled states in a system which consists of a single trapped ion in a cavity. We obtain a cross-Kerr-like interaction between the cavity field (photons) and the centre-of-mass motion (phonons) of the trapped ion in the Lamb–Dicke and large detuning regime. Based on this cross-Kerr-like interaction, we create hybrid entangled states between the phonon mode and the ionic internal states, and between the cavity field and ionic internal states, respectively. We also show that it is possible to prepare entangled coherent states between the cavity field and the phonon mode. We explicitly obtain an entangled state between two pairs of Schrödinger-cat states.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 7, 2006•14 citations

Generation and stabilization of entangled coherent states for the vibrational modes of a trapped ion

Zhi‐Rong Zhong, Xin-Jie Huang, Zhen‐Biao Yang +2 more

We propose a scheme for preparation of entangled coherent states for the motion of an ion in a two-dimensional anisotropic trap. In the scheme, the ion is driven by four laser beams along different directions in the ion trap plane, resulting in carrier excitation and couplings between the internal and external degrees of freedom. When the total quantum number of the vibrational modes initially has a definite parity, the competition between the unitary dynamics and spontaneous emission will force the system to evolve to a steady state, where the vibrational modes are in a two-mode cat state. We show that the method can be extended to realization of entangled coherent states for three vibrational modes of an ion in a three-dimensional anisotropic trap.

arXiv:1905.04702•Physical Review A•Sep 10, 2018•22 citations

Entanglement in the dispersive interaction of trapped ions with a quantized field

F. L. Semião, K. Furuya

The mode-mode entanglement between trapped ions and cavity fields is investigated in the dispersive regime. We show how a simple initial preparation of Gaussian coherent states and a postselection may be used to generate motional nonlocal mesoscopic states involving ions in different traps. We also present a study of the entanglement induced by dynamical Stark shifts considering a cluster of $N$ trapped ions. In this case, all entanglement is due to the dependence of the Stark shifts on the ions' state of motion manifested as a cross-Kerr interaction between each ion and the field.

arXiv:quant-ph/0612222•Physical Review A•Apr 16, 2007•11 citations

Dynamics of Entanglement for Coherent Motional States of Two Trapped Ions in Cascaded Optical Cavities

李高翔, Zhang Guoxu Zhang Fan, 吴少平

我们学习在二个串联的洞，每个离子的动的模式经由一个线性混合的相互作用在被联合到各自的洞地套住的二个远离子的一个纠缠的动的协调状态的产生。主人方程是由使用典型功能方法的解决的经分解。产生纠缠的协调状态源于一个甚至协调的状态的起始的准备，这被发现从在洞的驱散下面的一个奇怪的协调状态是比那更柔韧的。

Chinese Physics Letters•Jan 1, 2006•0 citations
We study the generation of an entangled motional coherent state of two distant ions trapped in two cascaded cavities, in which the motional mode of the each ion is coupled to the respective cavity field via a linear-mixing interaction. The master equation is solved analytically by using the characteristic function method. It is found that the generated entangled coherent state resulted from the initial preparation of an even coherent state is more robust than that from an odd coherent state under the dissipation of the cavity.
The time-dependent characteristic function for the vibrational quanta of two ions separately trapped in two cascaded optical cavities is obtained analytically beyond the bad cavity limit, in which the motional mode of the ion in the first cavity is coupled to the cavity field via an effective parametric interaction and that of the ion in the second cavity via a linear-mixing interaction as proposed by Peng and Parkins [Phys. Rev. A 65, 062323 (2002)]. It is found that the two ions develop in a two-mode mixed Gaussian entangled state if there exists a unidirectional coupling from the first cavity to the second one.
The dynamical behavior of the entanglement and the squeezing in the system of two ions trapped in a lossy optical cavity is discussed, in which the vibrational mode of the first ion is coupled to the cavity field via a linear-mixing interaction and the vibrational mode of the second ion is coupled to the cavity field via an effective parametric interaction, respectively. It is found that when the effective strength r1{r}_{1}r1​ of the coupling between the first ion and the cavity field is stronger than the strength r2{r}_{2}r2​ of the coupling between the second ion and the cavity field, the motional state of the two ions develops into a robust two-mode mixed Gaussian entangled state and the two-mode squeezing of phonons appears. But the entanglement between the cavity mode and the vibrational mode of the second ion can only happen periodically in a small time range. When r1<r2{r}_{1}<{r}_{2}r1​<r2​, only the entanglement between the two vibrational modes appears but the two-mode squeezing does not exist. And the entanglement between the cavity mode and the motional mode of the second ion can also take place in a small time range.
In this paper, we study generation of entangled states in a system which consists of a single trapped ion in a cavity. We obtain a cross-Kerr-like interaction between the cavity field (photons) and the centre-of-mass motion (phonons) of the trapped ion in the Lamb–Dicke and large detuning regime. Based on this cross-Kerr-like interaction, we create hybrid entangled states between the phonon mode and the ionic internal states, and between the cavity field and ionic internal states, respectively. We also show that it is possible to prepare entangled coherent states between the cavity field and the phonon mode. We explicitly obtain an entangled state between two pairs of Schrödinger-cat states.
We propose a scheme for preparation of entangled coherent states for the motion of an ion in a two-dimensional anisotropic trap. In the scheme, the ion is driven by four laser beams along different directions in the ion trap plane, resulting in carrier excitation and couplings between the internal and external degrees of freedom. When the total quantum number of the vibrational modes initially has a definite parity, the competition between the unitary dynamics and spontaneous emission will force the system to evolve to a steady state, where the vibrational modes are in a two-mode cat state. We show that the method can be extended to realization of entangled coherent states for three vibrational modes of an ion in a three-dimensional anisotropic trap.
The mode-mode entanglement between trapped ions and cavity fields is investigated in the dispersive regime. We show how a simple initial preparation of Gaussian coherent states and a postselection may be used to generate motional nonlocal mesoscopic states involving ions in different traps. We also present a study of the entanglement induced by dynamical Stark shifts considering a cluster of NNN trapped ions. In this case, all entanglement is due to the dependence of the Stark shifts on the ions' state of motion manifested as a cross-Kerr interaction between each ion and the field.