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Physical Review A

Deterministic generation of a pure continuous-variable entangled state for two ions trapped in a cavity

Gao‐xiang Li, Hua-Tang Tan, Shaoping Wu, Guangming Huang

Published Aug 10, 2006• 12 citations
Publisher

Abstract

Two different schemes are proposed for deterministically generating a pure motion-entangled state for two well-separated ions trapped in a cavity. The first one is that through adjusting the amplitudes and the frequencies of transverse lasers, the two ions trapped in a bimodal cavity can unconditionally evolve into a two-mode squeezed vacuum state with the aid of the cavity dissipation. The second one is based on the interactions of two appropriate series of the driving laser pulses with the two ions trapped in a single-mode cavity, it allows us to produce a two-mode squeezed vacuum state for the trapped ions' center-of-mass motion.

DOI
10.1103/physreva.74.025801

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Two different schemes are proposed for deterministically generating a pure motion-entangled state for two well-separated ions trapped in a cavity. The first one is that through adjusting the amplitudes and the frequencies of transverse lasers, the two ions trapped in a bimodal cavity can unconditionally evolve into a two-mode squeezed vacuum state with the aid of the cavity dissipation. The second one is based on the interactions of two appropriate series of the driving laser pulses with the two ions trapped in a single-mode cavity, it allows us to produce a two-mode squeezed vacuum state for the trapped ions' center-of-mass motion.
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.
We propose to generate two-mode squeezed vacuum motional state of an intracavity trapped ion by taking the advantage of the dissipation of the cavity mode. At the first step, the steady and pure two-mode motional entanglement between two motional degrees of the cold ion is obtained by engineering the couplings of both the motional modes of the ion to the cavity field. Based on the first step, a two-mode squeezed vacuum motional state is then generated by manipulating the phases of the external laser pulses incident on the ion.
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.