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Physical Review A

Two-channel cavity QED: Stokes plus anti-Stokes emission with a classical pump field

C. K. Law, Liwei Wang, Joseph H. Eberly

Published Apr 1, 1992• 23 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.45.5089

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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 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.
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.
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.
We study a cavity QED model where a single three-level atom interacts with four quantized cavity fields in a Raman-type interaction, forming two transition channels for the atom. We show that this system is equivalent to the coupling of three angular momenta, and give its exact eigenenergies and eigenvectors in terms of Clebsch-Gordan coefficients, even if the ac Stark shift is included. Some Heisenberg operators are solved exactly as well as approximately. Dynamical evolution of average photon numbers and the atomic inversion are discussed for several initial conditions and a simple example of model interference is examined.
I study the coherent interaction of a three-level atom in the lambda configuration with pump, Stoke, and anti-Stokes laser fields. The pump laser field drives transitions from the two non-degenerate lower levels to the excited state which is highly detuned for either transition. This excited state is also coupled to each of the lower states by Stokes or anti-Stokes transitions so that this system may represent a model of four-wave mixing. Assuming large detunings, the excited state is adiabatically eliminated from obtaining an effective two-level system with Raman coupling between the levels. Optical Bloch equations are obtained for this effective two-level system, and phenomenological damping terms are added for collisional dephasing of the Raman transitions. The equations are solved for the steady-state as well as by the method of adiabatic following. From these solutions we obtain the polarization.