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Physical Review A

Effects of optical gain and cavity-mode squeezing on the Mollow spectrum

G. S. Agarwal

Published Oct 1, 1989• 10 citations
Publisher

Abstract

A theoretical model for studying the effects of optical gain and the cavity-mode squeezing on the spectrum of radiation produced by coherently driven two-level atoms is developed. The squeezing of the cavity mode dramatically affects the central component leading to a spike in the spectrum which becomes more pronounced with the increase in optical gain and squeezing. The squeezing can also affect the three photon Rabi sideband and can facilitate laser oscillation at such frequencies.

DOI
10.1103/physreva.40.4138

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Physical Review A•Aug 1, 1998•35 citations
A theoretical model for studying the effects of optical gain and the cavity-mode squeezing on the spectrum of radiation produced by coherently driven two-level atoms is developed. The squeezing of the cavity mode dramatically affects the central component leading to a spike in the spectrum which becomes more pronounced with the increase in optical gain and squeezing. The squeezing can also affect the three photon Rabi sideband and can facilitate laser oscillation at such frequencies.
The emission of strongly driven two-level-like Ba atoms into the modes of an optical cavity has been studied as a function of cavity tuning and Ba density. At low densities, the cavity-mode emission viewed as a function of cavity tuning is identical in form to the three-peaked Mollow emission spectrum. At high densities, however, the cavity-mode emission is strongly amplified (attenuated) when the cavity is tuned to the frequency of one (the other) Mollow sideband. It is predicted that modest increases in Ba density will cause lasing to occur in this system.
The fluorescence spectrum of a strongly driven two-level atom located inside an optical cavity damped by a narrow-bandwidth squeezed vacuum is studied. We use a dressed atom model approach, first applied to squeezed vacuum problems by Yeoman and Barnett, to derive the master equation of the system and discuss the role of the cavity and the squeezed vacuum in the narrowing of the spectral lines and the population trapping effect. We find that in the presence of a single-mode cavity the effect of squeezing on the fluorescence spectrum is more evident in the linewidths of the Rabi sidebands rather than in the linewidth of the central component. Even in the absence of squeezing, the cavity can reduce the linewidth of the central component almost to zero, whereas the Rabi sidebands can be narrowed only to some finite value. In the presence of a two-mode cavity and a two-mode squeezed vacuum the signature of squeezing is evident in the linewidths of all spectral lines. We also establish that the narrowing of the spectral lines is very sensitive to the detuning of the driving field from the atomic resonance. Moreover, we find that the population trapping effect, predicted for the broadband squeezed vacuum case, may appear in a narrow-bandwidth case only if the input squeezed modes are perfectly matched to the cavity modes and if there is non-zero squeezing at the Rabi sidebands.
Analysis of the effects of a finite bandwidth squeezed input on the atomic dynamics and radiative properties of a coherently pumped two-level atom trapped in a resonant cavity is presented. It is found that the atom prefers to stay in the lower energy level more often at steady state regardless of the strength of the coherent radiation and squeezed input. Pronounced dipping in the population inversion occurs when the finiteness of the bandwidth of the reservoir modes is taken into consideration. Moreover, due to the narrowing of the bandwidth, the spectral width of the emitted radiation turns out to increase and the height of the central line to decrease with the strength of the squeezed input. The peaks of the sidebands become prominent and shifted side ways with the strength of the amplification constant of the parametric oscillation. It is also found that the emitted radiation exhibits photon anti-bunching, whereas the photon statistics oscillates between sub- and super-Poissonian. Unfortunately, the successively emitted cavity radiation does not exhibit squeezing despite the presence of the squeezed input.
We consider a nondegenerate three-level laser in which the three-level atoms are in a cascade configuration, the laser cavity contains a degenerate parametric oscillator, and one of the cavity modes is driven by coherent light.We have analyzed the effects of the degenerate parametric oscillator and the driving coherent light on the laser using the expectation values of the cavity mode variables at a steady state.The results show that the two-mode light produced by the system under consideration exhibits quadrature squeezing.The presence of nonlinear crystal in the laser cavity generates a single-mode squeezed light and also enhances the degree of squeezing of the two-mode light.Although the driving coherent light has no effect on quadrature squeezing, it increases the intensity of the cavity modes.
The incoherent part of the Mollow spectrum for resonance fluorescence has a subnatural linewidth in the weak-field limit. We show that this is due to squeezing of the fluctuations in the induced atomic dipole. The reduced linewidth persists for driving field intensities of approximately 12% of the saturation intensity, where Rabi sidebands begin to appear. We find a similar linewidth narrowing in the transmitted and fluorescent spectra for a single atom in a weakly driven resonant cavity. In this system single-quantum frequency splitting can produce a two-peaked spectrum. Both peaks have a narrowed linewidth. The spectrum of the transmitted light shows a second nonclassical effect that is due to squeezing. A spectral hole may appear at line center, giving a two-peaked spectrum even when there is no frequency splitting.
A cavity-modified master equation is derived for a coherently driven two-level atom coupled to a single-mode cavity in the bad cavity limit, in which the cavity frequency is tuned to either the center or one of the sidebands of the Mollow triplet. The atomic populations in both the bare- and dressed-state representations are analyzed in terms of the cavity-modified transition rates. In the bare-state basis, the role of the cavity may be interpreted as enhancing the stimulated absorption of the atom while suppressing the stimulated emission. The bare-state population may thus be inverted under appropriate conditions. The dressed-state inversion, however, originates from the enhancement of the atom-cavity interaction when the cavity is resonant with the atomic dressed-state transition. We show that two-phase quadratures of the atomic polarization decay at different rates. The decay of the in-phase (or out-of-phase) quadrature may be greatly inhibited as the driving intensity increases, depending on the cavity resonant frequency. The spectrum of the atomic fluorescence emitted out the side of the cavity is also studied. The spectral profiles are sensitive to the cavity frequency. When the cavity frequency is tuned to the center of the Mollow resonances, the fluorescence spectrum is symmetrical with three peaks whose linewidths and heights are intensity dependent. When the cavity frequency is tuned to one of the Mollow sidebands, however, it is asymmetric, and the central peak and the sideband on resonance with the cavity can be significantly suppressed for strong driving fields. All three spectral lines can be narrowed by increasing the Rabi frequency. The physics of these striking spectral features is explored in the dressed-state basis. We also investigate the probe absorption spectrum. When the cavity frequency is tuned to the center of the Mollow fluorescence triplet, the central component exhibits a Lorentzian line shape, while the side bands show the Rayleigh-wing line shape. Probe gain may occur at line center due to cavity-induced, bare-state population inversion. When the cavity is tuned to resonance with one sideband, only two sidebands, with Lorentzian profiles, dominate. Gain can occur at the sideband far off resonant with the cavity. The sideband gain is a consequence of an unbalanced dressed-state population distribution.