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Physical Review A

Dynamics of a two-channel Raman-coupled cavity-QED model

C. K. Law, Joseph H. Eberly

Published Apr 1, 1993• 32 citations
Publisher

Abstract

We consider a \ensuremath{\Lambda}-type three-level atom interacting simultaneously with two quantized cavity fields and a classical field, all of different frequencies. The classical field is of constant amplitude and the quantized cavity fields are dynamical variables. The effective interactions are Raman type with the two cavity fields regarded as Stokes and anti-Stokes modes. The classical field acts as the pump-mode, so that both the pump--Stokes and the pump--anti-Stokes transitions are included. We present analytic expressions for the dressed states of the system in a general situation where the two channels have different coupling strengths. The dressed states are closely related to the two-mode squeezed number states. We find that two-mode squeezing and nontrivial phase correlation occur in the model. The effects of weak cavity damping are also discussed.

DOI
10.1103/physreva.47.3195

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We consider a two-channel \ensuremath{\Lambda}-type three-level atom interacting simultaneously with two quantized cavity fields and a classically described cw laser field, all of different frequencies. The effective interactions are of the Raman type, in which the two cavity fields are regarded as Stokes and anti-Stokes modes, and the classical field acts as the pump mode, so that both the pump-Stokes and the pump--anti-Stokes transitions are included. We present the analytic solution of the system evolution operator. We also study the time dependence of the atomic inversion and the statistical properties of the cavity fields. We show that strongly correlated photons can be generated in our model.
We present an alternative cavity QED model with three nondegenerate quantized field modes. The atom-field interaction is a cavity analog of Raman scattering, and the three field modes can be associated with pump, Stokes, and anti-Stokes frequencies. Unlike systems based on the Jaynes-Cummings model, this one has two independent channels connecting the two active atomic levels, leading to the possibility of quantum interferences. Despite its complexity, the model has eigenstates and eigenvalues that can be found exactly and fully analytically in finite terms. The most interesting eigenstates have a ``chain'' character unknown in previous cavity QED models. Both Fock-state and coherent-state solutions are presented for a number of quantities, including complex three-mode variables. Heisenberg operator solutions are demonstrated in a few cases, and an example of fourth-order quantum interferences due to the coupled channels is worked out in full.
We investigate the population trapping in a Raman-coupled three-level system interacting with a pump mode and a Stokes mode in a quantized cavity. We show that with an initial atom-field decoupled state and the atomic state prepared in a coherent superposition of two nondegenerate ground states, population trapping occurs when the phase of the atomic dipole is equal to the phase difference of the two modes and the two-mode field state satisfies a specific photon distribution. In the limit of large total photon number, under some specific conditions, the corresponding two-mode trapping state can be identified as a phase difference state. We have studied the variance of superposition mode quadrature and its evolution, statistical properties, and the phase-space properties of the two-mode trapping field state. It has been observed that although under different conditions the two-mode field exhibits both sub- and super-Poissonian statistics, no squeezing is observed in any case.
We describe the dynamics of an exactly solvable Raman coupled model interacting with two modes of a quantized cavity electromagnetic field. The model consists of a three-level atom in the \ensuremath{\Lambda} configuration whose excited state is considered to be far off resonance and is adiabatically eliminated. The effective Hamiltonian for this system contains products of the transition operators between the two ground-state levels and a field annihilation operator from one mode and a creation operator from the other. This Hamiltonian provides an example of a zero-photon process. We study the atomic inversion and investigate the production of nonclassical effects such as antibunched light, violations of the Cauchy-Schwartz inequality, and squeezing.
The population of a three-level system in the lambda configuration interacting with three classical fields is studied. The system is essentially a Raman coupled system with pump, Stokes and anti-Stokes fields. One channel between the two ground states involves the pump and Stokes field while the other involves the pump and anti-Stokes field. Since exact solutions are not generally available the author studies the dynamics numerically. But when the excited state is highly detuned, it may be adiabatically removed so that the system becomes effectively a two-level system but with an effective Rabi frequency that depends on the relative phases of the driving fields. For some choices of the phases this frequency can be made to vanish, an effect of the interference between the two channels. For the special case of equal and opposite detunings, an exact solution of the full three-level equations is presented. The effects of ionization of the excited state are also briefly considered.