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Physical Review A

Effect of vibrational heating on the entangled field from an ion trapped in a bimodal cavity

Gao‐xiang Li, Shaoping Wu

Published Dec 12, 2005• 2 citations
Publisher

Abstract

The influence of the vibrational heating of a single cold ion trapped in a bimodal cavity under continuous excitation on the generation of two-mode squeezing and entanglement of the cavity field from the ion is discussed. It is found that the vibrational heating gives a strong limitation for the appearance of the two-mode squeezing, but the two cavity modes can develop into a robust entangled Gaussian state.

DOI
10.1103/physreva.72.064304

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The influence of the vibrational heating of a single cold ion trapped in a bimodal cavity under continuous excitation on the generation of two-mode squeezing and entanglement of the cavity field from the ion is discussed. It is found that the vibrational heating gives a strong limitation for the appearance of the two-mode squeezing, but the two cavity modes can develop into a robust entangled Gaussian state.
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.
By considering vibrational heating of an intracavity trapped ion and cavity damping, we investigate the effects of decoherence on entanglement and two-mode squeezing of output light from the cavity when the ion is excited continuously. It is found that the bright output light with the steady robust entanglement can be always achieved even in the presence of decoherence. Moreover, the entangled output light may not exhibit two-mode squeezing because the heating of the vibrational mode has stronger limitation on the two-mode squeezing than on the entanglement of the output light.
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 analyze the quantum motion of a cold, trapped two-level ion interacting with a quantized light field in a single-mode cavity. We show that in the nonclassical Lamb-Dicke limit the time evolution of the vibrational mode representing the quantized motion of the center of mass of the trapped ion is very sensitive to the quantum statistics of the light field. We also show that the system under consideration may evolve into the maximally entangled three-particle Greenberger-Horne-Zeilinger state. We briefly discuss the dynamics of a cluster of two-level ions trapped in a cavity and interacting with a quantized light field.