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Journal of Modern Optics

Optical fluorescence at the combinational frequency in coherently driven three-level systems

Chris O’Brien, Shaoyan Gao, Olga A. Kocharovskaya

Published Aug 9, 2011• 0 citations
Publisher

Abstract

We derive and compare the optical fluorescence spectra for all three transitions for three-level systems coherently coupled with two fields in a cascade or lambda configuration. It is shown that the total intensity of fluorescence at the combinational frequency (the sum or difference of the driving field frequencies in the ladder and lambda systems, respectively) may essentially exceed the fluorescence intensity at the driven transitions under the condition of two-photon resonance. The influence of additional homogeneous and inhomogeneous line broadening on the distribution of intensities between different fluorescence channels is studied. In particular, Doppler broadening is found to suppress fluorescence from the driven transitions but in some cases not from the combinational transition.

DOI
10.1080/09500340.2011.606626

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We derive and compare the optical fluorescence spectra for all three transitions for three-level systems coherently coupled with two fields in a cascade or lambda configuration. It is shown that the total intensity of fluorescence at the combinational frequency (the sum or difference of the driving field frequencies in the ladder and lambda systems, respectively) may essentially exceed the fluorescence intensity at the driven transitions under the condition of two-photon resonance. The influence of additional homogeneous and inhomogeneous line broadening on the distribution of intensities between different fluorescence channels is studied. In particular, Doppler broadening is found to suppress fluorescence from the driven transitions but in some cases not from the combinational transition.
We consider a three-level atomic system interacting with two coherent fields in the ladder configuration. Namely, the pumping field couples the ground and first excited state while the driving field interacts with the two excited states. The intensity spectrum of resonant optical fluorescence at the two-photon transition is studied. It is shown that coherent driving in this scheme allows for efficient control of fluorescence distribution between the one-photon (elastic with respect to pumping field) and two-photon (anti-Stoke Raman with respect to the driving field) channels.
The coherent coupling of atomic levels under the action of driving electromagnetic fields is known to create unusual and interesting effects, such as the well-known population trapping phenomenon and subnatural line narrowing. In this paper we discuss two alternative configurations of three-level atoms, the cascade model and the inverted-V (lambda) model, in an effort to provide alternative options for experimental tests. In both cases we focus on the fluorescent emission spectrum of atom driven by two resonant fields and on the absorption spectrum of a weak probe passing through a gas in such a driven system. Subnatural line narrowing can be obtained from the cascade system but not from the lambda system. The lambda system, however, is characterized by strong population trapping so that it is not suitable for fluorescence studies (except out of resonance) because of its strongly reduced emission rate. The absorption spectrum of a weak probe displays gain features under high field conditions which suggest that useful amplification of a probe or laser-like emission should be possible over appropriate frequency ranges. We give a physical interpretation of the origin of the gain and explain why that in the case of a lambda system, but not a cascade system, steady-state population inversion can be obtained between both excited states relative to the lowest state of the atom. We also discuss the effect of Doppler broadening on the predicted emission and absorption lineshapes.
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.
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.
The resonance fluorescence from a three-level Λ atom is studied, in which each optical transition is driven by a coherent field and the metastable states are coupled to each other via a microwave field. It is shown that the fluorescence depends not only on the relative intensities of the coupling fields but also on the relative phase delay between the envelopes of the amplitudes of the three fields. For the case of equal intensity of the two coherent fields, the fluorescence is completely inhibited once the phase delay is set to be 0 or π, while the fluorescence emerges once the phase delay is changed to π/2; moreover, the fluorescence spectrum ultimately reverts to an ultranarrow triplet by decreasing the relative intensity of the coherent field to the microwave field.