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Physical Review A

Exact density matrix for the degenerate-Raman-coupled model in the presence of collisions

Ravinder Rupchand Puri, G. S. Agarwal

Published Apr 1, 1992• 17 citations
Publisher

Abstract

Exact expressions are obtained for the density matrix in the operator form and for the quasiprobabilities for the system of an atom undergoing Raman transitions between two degenerate levels on interaction with a quantized field in a lossy cavity driven by an external field. The model is generalized to include the effects of atomic dephasing collisions. The spectral properties of the radiation are discussed, and the equation of motion of the density matrix is derived in the presence of collisions and an external drive. The equation is found to be of second order with respect to time in the absence of the driving field and also analytically solvable.

DOI
10.1103/physreva.45.5073

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Exact expressions are obtained for the density matrix in the operator form and for the quasiprobabilities for the system of an atom undergoing Raman transitions between two degenerate levels on interaction with a quantized field in a lossy cavity driven by an external field. The model is generalized to include the effects of atomic dephasing collisions. The spectral properties of the radiation are discussed, and the equation of motion of the density matrix is derived in the presence of collisions and an external drive. The equation is found to be of second order with respect to time in the absence of the driving field and also analytically solvable.
The quantum theory of Stokes--anti-Stokes processes in a degenerate system in a cavity is developed. The Raman transition is pumped by a coherent field. Effects of many atoms, cavity losses, and thermal photons are included in the theory. An exact solution for the model is obtained. An explicit expression for the reduced density matrix of the cavity field is given. The spectrum of the cavity field is obtained and is interpreted in terms of the eigenstates of the effective Hamiltonian describing Stokes--anti-Stokes processes. The spectrum develops sidebands due to strong Raman coupling.
We study the dynamics of a collection of two-level atoms interacting with a single mode of a quantized field in a dissipative cavity in the dispersive regime. The quantized mode is driven by a classical driving field. The steady-state density matrix is obtained. The influence of the driving field on the quantized driven field and on atomic properties in both the dissipative and the lossless cases is studied. The atomic decoherence time in the dissipative-driven case is obtained. We show that the external driving field strongly suppresses the atomic coherence (in comparison with the dissipative cavity without the driving field).
An exact analytic solution is presented for a two-state quantum system driven by a time-dependent external field with an exponential temporal shape in the presence of dephasing. In the absence of dephasing the model reduces to the well-known Demkov model originally introduced in slow atomic collisions. The solution is expressed in terms of the generalized hypergeometric function 1F2(a;b1,b2;x){}_{1}{F}_{2}(a;{b}_{1},{b}_{2};x)1​F2​(a;b1​,b2​;x). Various limiting cases are examined in the limits of weak and strong dephasing, strong driving field, and exact resonance.
We consider the radiation from a system of NNN identical two-level atoms coupled to a continuum of quantized em modes, and possibly, to an external driving field near resonance. The atoms can be distributed over a region large in comparison to the resonant wavelength, but smaller than the spontaneous pulse length. Radiation rates and correlation functions are expressed in terms of expectation values of time-dependent atomic operators, which are shown to satisfy coupled first-order differential equations involving similar atomic operators and the initial radiation operators. The corresponding equations for the expectation values simplify considerably if no driving field is present. Similar results are derived for a model in which each atom is replaced by a harmonic oscillator.
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.