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Journal of Optics B Quantum and Semiclassical Optics

Quantum control of light and motion with a trapped ion in a leaky cavity

C. Di Fidio, W. Vogel

Published Sep 9, 2002• 2 citations
Publisher

Abstract

We propose a method for controlling the number of photons and motional quanta using a trapped ion in a leaky cavity. A Raman interaction is used to entangle the atomic motion and cavity field. Motional Fock states can be obtained upon detection of the photons leaking out of the cavity. The motional state can be converted upon request into a fixed number of photons, freely propagating outside the cavity.

DOI
10.1088/1464-4266/4/5/317

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We propose a method for controlling the number of photons and motional quanta using a trapped ion in a leaky cavity. A Raman interaction is used to entangle the atomic motion and cavity field. Motional Fock states can be obtained upon detection of the photons leaking out of the cavity. The motional state can be converted upon request into a fixed number of photons, freely propagating outside the cavity.
We investigate how superpositions of motional coherent states naturally arise in the dynamics of a two-level trapped ion coupled to the quantized field inside a cavity. We extend our considerations, including a more realistic setup where the cavity is not ideal and photons may leak through its mirrors. We found that a detection of a photon outside the cavity would leave the ion in a pure state. The statistics of the ionic state still keeps some interference effects that might be observed in the weak-coupling regime.
We propose a scheme to generate a particular kind of tripartite entangled states using a single two-level trapped ion coupled to a quantized monomode electromagnetic field within an optical cavity. The resulting state involves motional Schr\\"odinger-cat states of the trapped ion, its internal electronic states, and Fock states of the cavity field. By means of a measurement of the internal state of the ion, it is also possible to generate either entangled bipartite states involving light and motion or single motional Schr\\"odinger-cat states. Our proposal is based on a previously introduced intensity dependent Hamiltonian [Phys. Rev. A 66, 063403 (2002)] for a trapped ion in a cavity.
The dynamics of the interaction of a quantized cavity field and the vibronic degrees of freedom of a trapped ion is studied under realistic conditions by including cavity losses, spontaneous electronic transitions, and atomic nonlinearities. As long as spontaneous electronic transitions are negligible, analytical results are derived for describing the interaction of the trapped ion and the damped cavity field in the secular approximation. Under more general conditions, when the secular approximation breaks down and spontaneous emission effects become important, the dynamics of the system is studied by quantum-trajectory methods. As an example we demonstrate that, by exploiting the nonlinearities inherent in the dynamics of the system, one may prepare correlated vibronic states and vibrational Fock states. Moreover, we study the generation of an entangled Greenberger-Horne-Zeilinger state. Taking into account the decoherence due to electronic and cavity losses, the best fidelity is obtained under conditions far from the Lamb-Dicke regime.
We propose a model for a single-trapped-ion vibronic Raman laser and study its dynamics by using quantum-trajectory methods. In our treatment, it is essential that both the cavity field of the high-finesse optical cavity and the center-of-mass vibrational motion of the trapped ion be quantized. A transition from a super-Poissonian light source to a Poissonian lasing regime is obtained by increasing the Raman coupling constant. Furthermore, we demonstrate that a nonclassical regime can be realized, where the photon statistics becomes sub-Poissonian and the photons leak out of the cavity in an antibunched manner. This is achieved by exploiting nonlinear Stark shifts inherent in the model, which depend on both the number of cavity photons and the number of vibrational quanta.
We propose a generation method of Bell-type states involving light and the vibrational motion of a single trapped ion. The trap itself is supposed to be placed inside a high-QQQ cavity sustaining a single mode, quantized electromagnetic field. Entangled light-motional states may be readily generated if a conditional measurement of the ion's internal electronic state is made after an appropriate interaction time and a suitable preparation of the initial state. We show that all four Bell states may be generated using different motional sidebands (either blue or red), as well as adequate ionic relative phases.