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Physical Review A

Single-trapped-ion vibronic Raman laser

C. Di Fidio, W. Vogel, R. L. de Matos Filho, L. Davidovich

Published Dec 13, 2001• 12 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.65.013811

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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.
It is well known that electronic transitions driven by nearly resonant travelling- or standing- wave lasers are often accompanied with vibrational sideband transitions of a single trapped ion undergoing quantized center-of-mass motion [1], Our previous studies showed that quantum statistics of radiation fields can be used to manipulate the vibronic motion of a trapped ion localised within the Lamb-Dicke limit (LDL) [2]. The present paper addresses quantum manipulating vibronic motion of an ion trapped far beyond the LDL.
We present a scheme for the realization of a stationary source of nonclassical light, which approximates very well a continuous single-photon source. It consists of a single four-level atom trapped inside a high-finesse optical cavity and Raman coupled to a cavity mode. A selectivity mechanism, based on a field-dependent Stark shift of electronic levels, prevents the occupation of two or more photon states of the quantized mode being excited. The output light of such a source exhibits sub-Poissonian photon-number statistics and antibunching behavior.
We study a classically driven two-level system in a harmonic trap and a lossy two-mode cavity, with the first mode being resonant to the driving field and an electronic transition, and the second mode being off-resonant, forming a vibrational-assisted Raman transition. Using an exact numerical method, we compute the steady state as well as the time evolution of the photon statistics. We further investigate the photon correlations of both the cavity modes and identify the laser parameters and coupling strength that give the nonclassical sub-Poissonian property. The work is useful for coherent control of photon statistics and photon correlations in the trapped two-level system.
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.
A novel recipe is proposed to generate nonclassical vibrational states of the center-of-mass motions of ions in a quantized trap, based on the quantum conversion between the quantum cavity fields and the quantized trap. It is shown that, when an ion trap system interacts with the eigen mode of a single-mode Fabry-Pérot cavity where the trap was set in, and a particularly selected external laser pulse through Raman transitions, the interchange of the quantum features between the quantum light states and the quantized trap states occurs. This kind of quantum conversion can be used to prepare some nonclassical trap states in an ion trap as well as to measure the properties of initial nonclassical vibrational states.