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Journal of Modern Optics

Three-level Atom in a Squeezed Vacuum II

S. Smart, S. Swain

Published Jun 1, 1994• 22 citations
Publisher

Abstract

The resonance fluorescence of a three-level system is studied in each of its three possible configurations—ladder, lambda and vee—when it also interacts with broad band squeezed vacua and the applied fields are resonant. We obtain general expressions which apply for any configuration and do not make use of the secular approximation. Detailed results are presented which depend upon the degree of squeezing and the squeezing phase, in addition to the intensities of the applied fields. It is shown that asymmetric spectra may be obtained in certain circumstances. These are interpreted in terms of coherent and incoherent transitions induced by the squeezed fields. We also take the opportunity to assess the accuracy of the secular approximation.

DOI
10.1080/09500349414551021

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The resonance fluorescence of a three-level system is studied in each of its three possible configurations—ladder, lambda and vee—when it also interacts with broad band squeezed vacua and the applied fields are resonant. We obtain general expressions which apply for any configuration and do not make use of the secular approximation. Detailed results are presented which depend upon the degree of squeezing and the squeezing phase, in addition to the intensities of the applied fields. It is shown that asymmetric spectra may be obtained in certain circumstances. These are interpreted in terms of coherent and incoherent transitions induced by the squeezed fields. We also take the opportunity to assess the accuracy of the secular approximation.
The fluorescence field from one of the two allowed transitions in a three-level atom can sense squeezed fluctuations of a vacuum field coupled to the other transition. We examine the fluorescence spectra of strongly driven three-level atoms in \ensuremath{\Lambda}, V, and cascade configurations in which one of the two one-photon transitions is coupled to a finite-bandwidth squeezed vacuum field, when the bandwidth is much smaller than the difference in the atomic transition frequencies, though much larger than atomic decay rates and Rabi frequencies of the driving fields. The driving fields are on one-photon resonance, and the squeezed vacuum field is generated by a degenerate parameter oscillator. Details are only given for the \ensuremath{\Lambda} configuration. The extension to the V and cascade configurations is straightforward. We find that in all configurations the fluorescence spectra of the transition not coupled to the squeezed vacuum field are composed of five lines, one central and two pairs of sidebands, with intensities and widths strongly influenced by the squeezed vacuum field. However, only the central component and the outer sidebands exhibit a dependence on the squeezing phase. We also examine the fluorescence spectrum for the cascade configuration with a squeezed vacuum field on resonance with the two-photon transition between the ground and the most excited states and now generated by a nondegenerate parametric oscillator. In this case, where the squeezed vacuum field can be made coupled to both transitions, all spectral lines depend on the squeezing phase. The spectral features are explained in terms of the dressed-atom model of the system. We show that the coherent mixing of the atomic states by the strong driving fields modifies transition rates between the dressed states, which results in the selective phase dependence of the spectral features. \textcopyright{} 1996 The American Physical Society.
The authors calculate the resonance fluorescence spectrum of a two-level atom interacting with a resonant classical applied field and a squeezed vacuum for general values of the squeezing phase. They find that the spectra are asymmetric under the following conditions: (i) the Rabi frequency must not be too large and (ii) the squeezing phase should be of athe order pi /2. Large asymmetries are obtainable, even if the three peaks of the spectrum are clearly resolved. An interpretation is provided by means of a dressed state analysis. Under conditions (i) and (ii), they also find that very large differences in the dressed state populations can occur.
We study fluorescence from a three-level atom in a cascade configuration driven by two coherent fields and damped by a broadband squeezed vacuum. Under the conditions that one or both of these fields are intense, a secular approximation is invoked to derive an analytical solution of the relevant master equation. When the two fields are in exact resonance with their respective transitions, expressions for the fluorescent spectra show a narrowing of the central peak for some specific values of the parameters of the squeezed vacuum and the phases between the driving fields and the squeezed vacuum. We also present analytical expressions for second-order intensity correlations. The inhibition of fluorescence in a squeezed vacuum is reflected in the quantum-jump-like behavior shown by these correlations.
We study the system of a single two-level atom interacting with a braodband squeezed vacuum and a classical applied field. The atom is subject to collisions, and the applied field may possess a finite linewidth. The atomic populations, coherences, resonance fluorescence spectrum, and intensity fluctuation spectrum are calculated. Wherever practicable, analytic expressions are obtained that show the dependence of these quantities on the damping parameters. Numerical plots are presented. Two qualitative results that we obtain are the following: (a) we show that the dependence of the populations on the squeezing phase is increased by increasing the damping parameters, contrary to what might at first have been expected, and (b) we show that, in the absence of external damping, the squeezing induces strong asymmetries in the off-resonant resonance fluorescence spectra.
We review the use of operator reaction field theory in quantum optics by considering the problem of one atom in an isotropic three-dimensional broad-band squeezed vacuum. In these terms we give a quantum electrodynamical analysis of this system exact up to all contributions of order one in the ratio γω 0 -1 , the ratio of the A -coefficient to the atomic resonance frequency. These terms include all of the counter-rotating terms at this order. At zero order, namely in the usual rotating wave approximation, we find the usual Einstein rate equation while we confirm that the fluorescence spectrum consists of two Lorentzian peaks. However, at order one we find an additional oscillating term in the rate equation and additional resonant dispersive terms correct for each of the two Lorentzian peaks in the fluorescence spectrum. Similar results are expected for broad-band correlated squeezed vacua of arbitrary, rather than isotropic, geometry.