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Physical Review A

Coupled-channel cavity QED model and exact solutions

Liwei Wang, Ravinder Rupchand Puri, Joseph H. Eberly

Published Dec 1, 1992• 59 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.46.7192

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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 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 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.
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.
In this paper, we present a simple purely algebraic method to solve a coupled-channel cavity QED model with three nondegenerate quantized field modes proposed by Wang, Puri, and Eberly [Phys. Rev. A 46, 7192 (1992)]. By transforming it into one describing a spin-1/2 particle in a magnetic field and utilizing the relations between field variables and an orbital angular momentum, we can easily obtain energy eigenvalues without the need to know concrete expressions for eigenstates in terms of the usual Fock states, and analytical expressions of evolution and atomic inversion operators. The eigenstates of energy and orbital angular momentum are also explicitly expressed in terms of Fock states. \textcopyright{} 1996 The American Physical Society.