© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Physical Review A

Coherent coupling between the motional fluctuation of a mirror and a trapped ion inside an optical cavity: Memory, state transfer, and entanglement

Devender Garg, Asoka Biswas

Published Nov 12, 2019• 5 citations

Abstract

We show how the motional fluctuations of two systems of very different sizes---a trapped ion and a mirror---can be coupled coherently, via their common interaction with an optical cavity. Specifically, we show that the fluctuations can be transferred from one system to the other by using pulsed excitation of the cavity mode, and vibrational fluctuations can exhibit entanglement in steady state. We numerically display a sudden death of this entanglement at certain pulse parameters and ambient equilibrium temperature. More interestingly, the state of the driving pulse can also be coherently mapped, in a selective way, into the vibrational mode of the trapped ion or the mirror, which acts as a quantum memory for the optical pulse. We further present a detailed analysis to show that it is also possible to map the state of the pulse into a binomial entangled state of its vibrational fluctuations. We finally investigate how to sympathetically cool the mirror by cooling the ionic vibration, thanks to an effective coupling between the two modes.

DOI: 10.1103/physreva.100.053822

Related papers

Entanglement Between a Moving Mirror and a Trapped Ion

Clóvis Corrêa, A. Vidiella-Barranco

It is presented a scheme for generating entanglement between a moving mirror and the vibrational degree of freedom of a single trapped ion. The system consists of an interferometer with an optomechanical cavity at one arm and a cavity with a single trapped ion at another arm. Because of the radiation pressure, it is possible to entangle the cavity field with the moving mirror at the optomechanical arm and by tuning the cavity field with the internal levels of the ion, it is possible to generate an entangled state comprising the cavity and the ion arm. The cavity fields may be coupled via a beam splitter, making possible to generate entanglement between the moving mirror and the vibrational state of motion of a single trapped ion.

Latin America Optics and Photonics Conference•Jan 1, 2012•0 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

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

Single trapped ions interacting with low‐ and high‐finesse optical cavities

Jürgen Eschner, Ch. Raab, A.B. Mundt +4 more

Abstract The presence of mirrors modifies both the coherent coupling of an atom to a light mode and its spontaneous emission into the mode [1]. We study such cavity QED effects experimentally with single ions and optical cavities. We focus on two examples which are equally interesting as fundamental systems and for application in quantum information processing. (i) By retroreflecting the fluorescence of a single trapped Ba+ ion with a mirror 25 cm away, we observe inhibition and enhancement of the atom's spontaneous emission. When two ions are trapped, the distant mirror creates super‐ and subradiance. (ii) With a single trapped Ca+ ion we demonstrate coherent coupling of its narrow S1/2 – D5/2 “qubit” transition to a mode of a high‐finesse optical cavity. We also achieve deterministic coupling of the cavity standing wave to the ion's vibrational state by controlling the ion's position with nanometer‐precision and selectively exciting vibrational state‐changing transitions.

Fortschritte der Physik•Apr 24, 2003•4 citations

Influence of the vibrational modes in the transmission of electronic states of trapped ions in different coupled cavities

Fabiano Kenji Nohama, José Antonio Roversi

In this paper, we present a system formed by two electromagnetic cavities coupled by an optical fibre, each one interacting with a trapped ion. In the carrier band, we observe the one-qubit state transfer between the internal state of the ions and how the transmission time can be influenced by the vibration motion of the ions.

Journal of Physics B Atomic Molecular and Optical Physics•May 20, 2011•0 citations

Scheme for Implementing Quantum State Transfer in Cavity QED with Trapped Ion

Shao-Hua Xiang, Zheng Qing-yun

We propose a physical scheme for implementing quantum state transfer utilizing the interaction of a two-level trapped ion with a quantum monomode electromagnetic field within an optical cavity.The results show that by controlling the frequency of cavity field to be resonant with the carrier,quantum information can be transferred between cavity field and the internal state of the ion without the need for the selected measurement of the qubits.Quantum information may also be transmitted from the vibrational state of the ion into cavity mode,from the internal state of the ion into its vibration state, and from a single-qubit state into an entangled bipartite state by means of the measurement on the qubits when we tune the light field to the first blue sideband.A practical model of a quantum network is proposed.Finally,we analyze the experimental feasibility of the present scheme.

Journal of Huaihua University•Jan 1, 2005•0 citations

We show how the motional fluctuations of two systems of very different sizes---a trapped ion and a mirror---can be coupled coherently, via their common interaction with an optical cavity. Specifically, we show that the fluctuations can be transferred from one system to the other by using pulsed excitation of the cavity mode, and vibrational fluctuations can exhibit entanglement in steady state. We numerically display a sudden death of this entanglement at certain pulse parameters and ambient equilibrium temperature. More interestingly, the state of the driving pulse can also be coherently mapped, in a selective way, into the vibrational mode of the trapped ion or the mirror, which acts as a quantum memory for the optical pulse. We further present a detailed analysis to show that it is also possible to map the state of the pulse into a binomial entangled state of its vibrational fluctuations. We finally investigate how to sympathetically cool the mirror by cooling the ionic vibration, thanks to an effective coupling between the two modes.

It is presented a scheme for generating entanglement between a moving mirror and the vibrational degree of freedom of a single trapped ion. The system consists of an interferometer with an optomechanical cavity at one arm and a cavity with a single trapped ion at another arm. Because of the radiation pressure, it is possible to entangle the cavity field with the moving mirror at the optomechanical arm and by tuning the cavity field with the internal levels of the ion, it is possible to generate an entangled state comprising the cavity and the ion arm. The cavity fields may be coupled via a beam splitter, making possible to generate entanglement between the moving mirror and the vibrational state of motion of a single trapped 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

{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.

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.

Abstract The presence of mirrors modifies both the coherent coupling of an atom to a light mode and its spontaneous emission into the mode [1]. We study such cavity QED effects experimentally with single ions and optical cavities. We focus on two examples which are equally interesting as fundamental systems and for application in quantum information processing. (i) By retroreflecting the fluorescence of a single trapped Ba+ ion with a mirror 25 cm away, we observe inhibition and enhancement of the atom's spontaneous emission. When two ions are trapped, the distant mirror creates super‐ and subradiance. (ii) With a single trapped Ca+ ion we demonstrate coherent coupling of its narrow S1/2 – D5/2 “qubit” transition to a mode of a high‐finesse optical cavity. We also achieve deterministic coupling of the cavity standing wave to the ion's vibrational state by controlling the ion's position with nanometer‐precision and selectively exciting vibrational state‐changing transitions.

We propose a physical scheme for implementing quantum state transfer utilizing the interaction of a two-level trapped ion with a quantum monomode electromagnetic field within an optical cavity.The results show that by controlling the frequency of cavity field to be resonant with the carrier,quantum information can be transferred between cavity field and the internal state of the ion without the need for the selected measurement of the qubits.Quantum information may also be transmitted from the vibrational state of the ion into cavity mode,from the internal state of the ion into its vibration state, and from a single-qubit state into an entangled bipartite state by means of the measurement on the qubits when we tune the light field to the first blue sideband.A practical model of a quantum network is proposed.Finally,we analyze the experimental feasibility of the present scheme.