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Physical Review A

Time-dependent characteristics of a strongly driven Raman system undergoing quantum jumps

Arundhati S. Jayarao, Richard D’Souza, S. V. Lawande

Published Feb 1, 1990• 2 citations
Publisher

Abstract

We present three additional theoretical signatures of quantum jumps displayed by the behavior of the Mandel Q(T) function, transient squeezing, and the time-dependent spectra, for a Raman system resonantly driven by coherent fields. As in our earlier formalism we assume that one or both of the driving fields are intense and invoke the secular approximation to derive a Markovian master equation for the atomic-density operator. This is then used to obtain analytical expressions for Q(T), transient squeezing parameters, and the time-dependent spectra. These analytical results provide further characteristics of the quantum jumps.

DOI
10.1103/physreva.41.1533

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We present three additional theoretical signatures of quantum jumps displayed by the behavior of the Mandel Q(T) function, transient squeezing, and the time-dependent spectra, for a Raman system resonantly driven by coherent fields. As in our earlier formalism we assume that one or both of the driving fields are intense and invoke the secular approximation to derive a Markovian master equation for the atomic-density operator. This is then used to obtain analytical expressions for Q(T), transient squeezing parameters, and the time-dependent spectra. These analytical results provide further characteristics of the quantum jumps.
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Early results of Agarwal and Jha [Z. Phys. B 35, 391 (1979)] are used to examine the question of quantum jumps in a Raman (\ensuremath{\Lambda}) system driven by two coherent fields. We discuss both short-time (${\ensuremath{\gamma}}_{1}$t\ensuremath{\lesssim}1) and long-time (${\ensuremath{\gamma}}_{2}$t\ensuremath{\approxeq}1) behavior of the intensity correlations assuming that the Stokes transition is very weak, ${\ensuremath{\gamma}}_{2}$\ensuremath{\ll}${\ensuremath{\gamma}}_{1}$. We calculate the counting statistics of the dark periods using the higher-order intensity correlations. The results differ from those obtained using arguments based on population trapping which predict only a very rare ``jump'' event. The intermittence in fluorescence produced by a coherently driven \ensuremath{\Lambda} system is interpreted in terms of an equivalent two-state Markov process.
We study analytically the effect of the dipole-dipole interaction on the statistics of the fluorescent radiation emitted from a system of two two-level atoms resonantly driven by a coherent field. For some interatomic separations, an inhibition of fluorescence occurs, which is reminiscent of the recently discussed quantum-jump phenomenon in a single three-level atom. This is reflected in the behaviors of the intensity correlation function, Mandel's Q parameter, and the time-dependent fluorescence spectrum. It is argued that this quantum-jump-like behavior arises from the coupling between the symmetric states and the antisymmetric state caused by the dipole-dipole interaction.
The Hamiltonian and the equations of motion for various modes involving spontaneous and stimulated Raman processes are derived. The coupled differential equations involving these modes are solved analytically by using an intuitive approach (IA). The solution of the present paper does not require any short time approximation. As a matter of fact, the present solution for field operators and hence the squeezing for various modes are valid for all interaction time t. In this way, the present paper is more general compared to the earlier investigations where short-time approximations were found a must. By exploiting the solutions for the field operators, we obtain the squeezing effects of input coherent light for pure and for mixed field modes. The IA employs the perturbation theory and hence we came across the secular terms in the solution. Of course, for small coupling constants these secular terms could be summed for all orders. To establish our claim, we remove the secular terms at least for one occasion.
We present numerical and analytical results for the Mollow probe absorption spectrum of a coherently driven two-level system in a narrow bandwidth squeezed vacuum field. The spectra are calculated for the case where the Rabi frequency of the driving field is much larger than the natural linewidth and the squeezed vacuum carrier frequency is detuned from the driving laser frequency. The driving laser is on resonance. We show that in a detuned squeezed vacuum the standard Mollow features are each split into triplets. The central components of each triplet are weakly dependent on the squeezing phase but the sidebands strongly depend on the phase and can have dispersive or absorptive/emissive profiles. We also derive approximate analytical expressions for the spectral features and find that the multi-peak structure of the spectrum can be interpreted either via the eigenfrequencies of a generalized Floquet Hamiltonian or in terms of three-photon transitions between dressed states involving a probe field photon and a correlated photon pair from the squeezed vacuum field.