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Physical Review A

Cavity QED with cold trapped ions

Vladimír Bužek, G. Drobný, M. S. Kim, G. Adam, P. L. Knight

Published Sep 1, 1997• 86 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.56.2352

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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.
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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 investigate the dynamics of a cold trapped ion coupled to the quantized field inside a high-finesse cavity, considering exact resonance between the ionic internal levels and the field (carrier transition). We derive an intensity-dependent Hamiltonian in which terms proportional to the square of the Lamb-Dicke parameter $(\ensuremath{\eta})$ are retained. We show that different nonclassical effects arise in the dynamics of the ionic population inversion, depending on the initial states of the vibrational motion and field and on the values of $\ensuremath{\eta}.$
A single two-level atom, with quantized center-of-mass motion, is constrained to move in a one-dimensional harmonic potential while interacting with a single-mode classical traveling-wave light field. When the classical light field is tuned to the atom's lower vibrational sideband, cooling can occur. The strong-sideband and Lamb-Dicke perturbation regimes for the system are defined. The steady-state and time-evolution behaviors in the strong-sideband regime are discussed and, in particular, it is shown that the steady-state average trap number saturates when spontaneous emission is weak and that the steady-state average trap number depends more strongly on the trap frequency in the saturated regime than previously predicted. Finally, the possibility of observing quantum jumps between trap levels is discussed.