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 A

Collapse and revival dynamics of two entangled trapped ions

Atle Svandal, J. P. Hansen

Published Feb 8, 2002• 6 citations
Publisher

Abstract

We study the long-time dynamics of two entangled ions coupled by a single vibrational mode and two lasers with different frequencies as proposed by M\o{}lmer and S\o{}rensen [Phys. Rev. Lett. 82, 1835 (1999)]. It is shown that the time development involves collapses and revivals well known from the dynamics of a single atom in a cavity or in a trap. The revival time is found to be insensitive to the details of the initial collective vibrational state. Therefore, revival and collapse phenomena are obtained for coherent, thermal as well as other vibrational states.

DOI
10.1103/physreva.65.033406

Related papers

Observing different phases for the dynamics of entanglement in an ion trap

Cecilia Cormick, Juan Pablo Paz

The evolution of the entanglement between two oscillators coupled to a common thermal environment is nontrivial. The long time limit has three qualitatively different behaviors (phases) depending on parameters such as the temperature of the bath [J. P. Paz and A. J. Roncaglia, Phys. Rev. Lett. 100, 220401 (2008)]. The phases include cases with nonvanishing long-term entanglement, others with a final disentangled state, and situations displaying an infinite sequence of events of disappearance and revival of entanglement. We describe an experiment to realize these different scenarios in an ion trap. The motional degrees of freedom of two ions are used to simulate the system while the coupling to an extra (central) ion, which is continuously laser cooled, is the gateway to a decohering reservoir. The scheme proposed allows for the observation and control of motional entanglement dynamics and is an example of a class of simulations of quantum open systems in the non-Markovian regime.

arXiv:0912.1602•Physical Review A•Feb 9, 2010•15 citations

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 pure multipartite entangled vibrational states for ions trapped in a cavity

Gao‐xiang Li

We propose schemes for the deterministic preparation of pure multipartite entangled vibrational states for $N$ ions trapped in a single-mode cavity. Through sequentially sending lasers with appropriate phases and amplitudes to drive the ions, two kinds of pure multipartite entangled continuous variable entangled states respectively suggested by van Loock and Braunstein [Phys. Rev. Lett. 84, 3482 (2000)] and Pfister et al. [Phys. Rev. A 70, 020302(R) (2004)] can be unconditionally prepared with the help of cavity dissipation.

Physical Review A•Nov 10, 2006•30 citations

Quantum collapse and revival in the motion of a trapped ion for high detuning

Zhong Wang

The quantum dynamics of a trapped ion which acts with two standing light fields with different frequency is investigated on the condition of high detuning. Evolution of the quantum mean energy of the ion with time displays the characteristic of collapse revival which implies the vibration states of the ion have squeezing effect. The higher the value of the squeezing parameter G 3 . The higher the degree of squeezing of the vibration states of the ion can be observed. If G 3 is greater than a particular value, the degree of squeezing will become smaller.

Chinese journal of atomic and molecular physics•Jan 1, 2001•0 citations

Generation of Superpositions of Two-Mode Coherent States for the Motion of Two Trapped Ions

Zheng Zheng, Shi-Biao

We propose a method for the generation of superpositions of two-mode coherent states for the center-of-mass and relative vibrational modes of two trapped ions. In the scheme the ions are driven by a single travelling-wave laser field tuned to the carrier. Then a measurement of the internal states collapses the vibrational modes to the entangled coherent state.

理论物理通讯：英文版•Jan 1, 2005•0 citations

Collapses and revivals of the coherence of a mesoscopic superposition of motional states.

Shi‐Biao Zheng

A scheme is proposed to observe the collapses and revivals of a mesoscopic superposition of coherent states in the motion of a trapped ion. In the scheme the ion motion in the x -axis is first prepared in a Schrödinger cat state, and then coupled to the motion in the z -axis. With the vibrational excitation exchange between the two modes, the mesoscopic quantum coherence collapses and revives periodically, providing an example for complementarity.

Australian Journal of Physics•Jun 22, 2000•1 citation
We study the long-time dynamics of two entangled ions coupled by a single vibrational mode and two lasers with different frequencies as proposed by M\o{}lmer and S\o{}rensen [Phys. Rev. Lett. 82, 1835 (1999)]. It is shown that the time development involves collapses and revivals well known from the dynamics of a single atom in a cavity or in a trap. The revival time is found to be insensitive to the details of the initial collective vibrational state. Therefore, revival and collapse phenomena are obtained for coherent, thermal as well as other vibrational states.
The evolution of the entanglement between two oscillators coupled to a common thermal environment is nontrivial. The long time limit has three qualitatively different behaviors (phases) depending on parameters such as the temperature of the bath [J. P. Paz and A. J. Roncaglia, Phys. Rev. Lett. 100, 220401 (2008)]. The phases include cases with nonvanishing long-term entanglement, others with a final disentangled state, and situations displaying an infinite sequence of events of disappearance and revival of entanglement. We describe an experiment to realize these different scenarios in an ion trap. The motional degrees of freedom of two ions are used to simulate the system while the coupling to an extra (central) ion, which is continuously laser cooled, is the gateway to a decohering reservoir. The scheme proposed allows for the observation and control of motional entanglement dynamics and is an example of a class of simulations of quantum open systems in the non-Markovian regime.
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.
We propose schemes for the deterministic preparation of pure multipartite entangled vibrational states for NNN ions trapped in a single-mode cavity. Through sequentially sending lasers with appropriate phases and amplitudes to drive the ions, two kinds of pure multipartite entangled continuous variable entangled states respectively suggested by van Loock and Braunstein [Phys. Rev. Lett. 84, 3482 (2000)] and Pfister et al. [Phys. Rev. A 70, 020302(R) (2004)] can be unconditionally prepared with the help of cavity dissipation.
The quantum dynamics of a trapped ion which acts with two standing light fields with different frequency is investigated on the condition of high detuning. Evolution of the quantum mean energy of the ion with time displays the characteristic of collapse revival which implies the vibration states of the ion have squeezing effect. The higher the value of the squeezing parameter G 3 . The higher the degree of squeezing of the vibration states of the ion can be observed. If G 3 is greater than a particular value, the degree of squeezing will become smaller.