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Journal of Modern Optics

Absorption spectrum in a three-level atom with injected squeezed vacuum: ladder case

Sotirios A. Hadjiagapiou, S. M. Spyrou

Published Feb 21, 2005• 1 citation
Publisher

Abstract

The weak probe field spectrum of a three-level atom, in the ladder configuration, is obtained. The lower transition of atom is coupled with squeezed vacuum, while the upper transition is coupled to coherent cavity mode and a bath. In this paper, the effect of the various quantities (detuning, decay rates) on the absorption spectrum is investigated.

DOI
10.1080/09500340512331327534

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Physical Review A•May 1, 1995•62 citations
The weak probe field spectrum of a three-level atom, in the ladder configuration, is obtained. The lower transition of atom is coupled with squeezed vacuum, while the upper transition is coupled to coherent cavity mode and a bath. In this paper, the effect of the various quantities (detuning, decay rates) on the absorption spectrum is investigated.
The behavior of a three level atom in a cascade configuration with the lower transition coherently driven and also coupled to a narrow bandwidth squeezed vacuum field is studied. A master equation treatment based on dressed atom states is used and expressions for probe absorption spectra are obtained via linear response theory and the quantum regression theorem. The expressions obtained also apply to the broad bandwidth squeezed vacuum case. Numerical studies of the modifications caused by the finite squeezed vacuum bandwidth to the Mollow and Autler-Townes probe absorption spectra are made for the case where the squeezed vacuum field center frequency and the driving laser frequency coincide and where upper transition relaxation terms are ignored. The squeezed vacuum source is assumed to be a degenerate parametric amplifier for the numerical calculations. Cases where the driving laser is resonant and detuned are examined. The spectral features are sensitively dependent on the phase of the squeezed vacuum field for a given driving laser phase. Dispersive features in the Mollow probe absorption spectrum can become absorptive, and vice versa. It is found in the probe absorption spectra that for certain choices of the squeezed vacuum phase lines narrower than for the broadband squeezed vacuum are obtained in the finite bandwidth situation. In both the Mollow and Autler-Townes spectra features narrower than for the normal vacuum case are obtained when the laser field is detuned, and in the Autler-Townes case this occurs for resonance also. \textcopyright{} 1996 The American Physical Society.
We consider the interaction of a two-level atom with a squeezed vacuum, both in free space and in a cavity of moderate Q. In the latter case, only vacuum modes coupled to the cavity are squeezed. In both cases we calculate the following quantities for the fluorescent light fields: the second-order intensity correlation function g(2){\mathit{g}}^{(2)}g(2)(\ensuremath{\tau}), the spectrum of squeezing, the coherent spectrum, and the spectrum obtained in a pump-probe absorption measurement. Nonclassical behavior is discussed and comparison to an ordinary vacuum and thermal fields is made. \textcopyright{} 1996 The American Physical Society.
A three-level ladder atom driven by two coherent laser fields with rather different frequencies in various kinds of reservoirs is considered. Making use of the master equation and Bloch equation, we calculate numerically and show graphically the steady-state populations versus two-photon detuning. We also discuss and compare the two-photon and one-photon processes occurring for various cases. For a squeezed vacuum, only when the carrier frequency of the squeezed vacuum equals the average of frequencies of the two driving fields and the phase matching condition is fulfilled, will there be a strong two-photon resonant absorption from the squeezed vacuum, a characteristic different from absorption of photons from a classical field; Otherwise, the two-photon ab-sorption rate from the squeezed vacuum will be greatly diminished.
A theoretical study is made of the steady-state intensity and squeezing properties of the fluorescent light from a three-level-atom system in a ladder configuration, which is subject to spontaneous-emission decay to the electromagnetic-field vacuum. Two cases are examined: in the equispaced (ES) level case, the two atomic transition frequencies are nearly equal and two photon absorption processes occur from a single coherent laser field that couples both transitions and has a small detuning from each; in the non- equispaced (NES) level case, the atomic transition frequencies are rather different and two photon absorption processes occur from two coherent laser fields, each coupled to a single transition and in near resonance with it. In both cases, a situation of small two-photon detuning occurs. Optical Bloch equations for the atomic density matrix in rotating frames are given and matrix expressions for determining the steady-state populations and coherences are obtained. Analytic expressions are also given for special cases. The fluorescent intensity is obtained from the populations of the intermediate and upper states, with the normally ordered variance (NOV) for quadrature components of the fluorescent field involving, in addition, the atomic coherences. The fluorescent intensities are shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases.In both cases, the fluorescent intensities show the well known resonances from the upper state at zero two-photon detuning and from the intermediate state at zero one-photon detuning for the lower transition. However, further resonances are also found. The intermediate-state intensity displays a resonance at zero two-photon detuning. Also, the upper-state intensity shows a resonance at zero one-photon detuning for the upper transition, but only for the NES case; evidently, the transfer rate from upper to lower transition coherences destroys this resonance for the ES case. The time-averaged NOV is also shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases. For the ES case, the quadrature frequency is chosen as the single laser frequency and for the NES case, it is chosen as either the average of the two laser frequencies or the lower transition laser frequency. Squeezing occurs near zero two-photon detuning for both ES and NES cases, though only for the quadrature frequency equal to the average laser frequency in the latter case. It also occurs near zero detuning for the lower transition for both cases, though only for the quadrature frequency equal to the lower transition laser frequency in the NES case. The squeezing minima show a splitting effect for large Rabi frequencies corresponding to two-photon or one-photon Rabi splitting of the dressed atom levels for the situation near two-photon or one-photon resonance, respectively. The large squeezing near two-photon resonance for moderate Rabi frequencies and large one-photon detuning corresponds to essentially pure three-level squeezing, while that near one-photon resonance for weak Rabi frequencies involves two-level squeezing.