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Physical Review A

Spectral and statistical properties of strongly driven atoms coupled to frequency-dependent photon reservoirs

Maciej Lewenstein, THOMAS W. MOSSBERG

Published Mar 1, 1988• 93 citations
Publisher

Abstract

Interesting new aspects of atomic behavior in the presence of strong driving fields appear when the driven atom resides not in free space, but in a region (such as an optical cavity) that displays a frequency-dependent photon-mode density. Under such conditions, it is found that a strong driving field can modify the spontaneous decay properties of an atom, and thereby give rise to interesting new features in the spectrum of strong-field resonance fluorescence. It is also found that a high level of dressed-state polarization can be maintained in a sample of resonantly or nonresonantly driven atoms by appropriate tuning of an enclosing cavity. Furthermore, for appropriate laser and cavity tunings, it is found that the atomic states become highly squeezed. In the course of analyzing these effects, a set of modified Bloch equations is derived that explicitly accounts for the finite response time associated with a frequency-dependent photon-mode density.

DOI
10.1103/physreva.37.2048

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Interesting new aspects of atomic behavior in the presence of strong driving fields appear when the driven atom resides not in free space, but in a region (such as an optical cavity) that displays a frequency-dependent photon-mode density. Under such conditions, it is found that a strong driving field can modify the spontaneous decay properties of an atom, and thereby give rise to interesting new features in the spectrum of strong-field resonance fluorescence. It is also found that a high level of dressed-state polarization can be maintained in a sample of resonantly or nonresonantly driven atoms by appropriate tuning of an enclosing cavity. Furthermore, for appropriate laser and cavity tunings, it is found that the atomic states become highly squeezed. In the course of analyzing these effects, a set of modified Bloch equations is derived that explicitly accounts for the finite response time associated with a frequency-dependent photon-mode density.
We investigate spectral properties of the atomic fluorescence and the output field of the cavity-mode of a single-atom dressed-state laser in a photonic crystal. We pay particular attention to the behavior of the spectra in the presence of the frequency dependent reservoir and search for signatures of the thresholdless lasing. Although the thresholdless behavior has been predicted by analyzing the photon statistics of the cavity field, we find that the threshold behavior still exists in the spectrum of the cavity field. We find that the structure of cavity field spectrum depends strongly on the range of the pumping rate. For low pumping rates, the spectrum is not monochromatic, it is composed of a set of discrete lines revealing the discrete (quantum) structure of the combined dressed-atom plus the cavity field system. We find that for a certain value of the pumping rate, the multi-peak structure converts into a single very narrow line centered at the cavity field frequency. A physical explanation of the behavior of the spectra is provided in terms of dressed states of the system.
We study nonclassical and spectral properties of a strongly driven single-atom laser engineered within a photonic crystal that facilitates a frequency-dependent reservoir. In these studies, we apply a dressed atom model approach to derive the master equation of the system and study the properties of the dressed laser under the frequency-dependent transition rates. By going beyond the secular approximation in the dressed-atom cavity-field interaction, we find that if, in addition, the nonsecular terms are included into the dynamics of the system, then nonlinear processes can occur that lead to interesting aspects of cavity field behavior. We calculate variances of the quadrature phase amplitudes and the incoherent part of the spectrum of the cavity field and show that they differ qualitatively from those observed under the secular approximation. In particular, it is found that the nonlinear processes lead to squeezing of the fluctuations of the cavity field below the quantum shot noise limit. The squeezing depends on the relative population of the dressed states of the system and is found only if there is no population inversion between the dressed states. Furthermore, we find a linewidth narrowing below the quantum limit in the spectrum of the cavity field that is achieved only when the secular approximation is not made. An interpretation of the linewidth narrowing is provided in terms of two phase-dependent noise (squeezing) spectra that make up the incoherent spectrum. We establish that the linewidth narrowing is due to squeezing of the fluctuations in one quadrature phase components of the cavity field.
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.
There is increasing interest in the photon statistics and spectroscopic properties of the radiation from atoms confined in an optical cavity. Effects such as the cavity enhancement and inhibition of spontaneous emission, which were first observed using microwave cavities, have recently been measured at optical frequencies.1 Recent measurements of squeezing and the dynamic effects of single-quantum-level splittings also demonstrate the possibilities for quantum-statistical studies of coupled atom-cavity systems at optical frequencies.2 We study a single two-level atom confined inside an optical cavity which is driven by coherent light in resonance with both cavity and atom. For weak driving field intensities we have calculated the spectrum of the light transmitted by the cavity and fluorescence out the sides of the cavity.