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Physical Review A

Analytical solution for the Mollow and Autler-Townes probe absorption spectra of a three-level atom in a squeezed vacuum

M. Bosticky, Z. Ficek, Bryan J. Dalton

Published May 1, 1998• 8 citations
Publisher

Abstract

The Mollow and Autler-Townes probe absorption spectra 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 are studied. Analytical studies of the modifications caused by the finite squeezed-vacuum bandwidth to the spectra are made for the case when the Rabi frequency of the driving field is much larger than the natural linewidth. The squeezed vacuum center frequency and the driving laser frequency are assumed equal. We show that the spectral features depend on the bandwidth of a squeezed vacuum field and whether the sources of the squeezing field are degenerate (DPA) or nondegenerate (NDPA) parametric amplifiers. In a broadband or narrow bandwidth squeezed vacuum generated by a NDPA, the central component of the Mollow spectrum can be significantly narrower than that in the normal vacuum. When the source of the squeezed vacuum is a DPA, the central feature is insensitive to squeezing. The Rabi sidebands, however, can be significantly narrowed only in the squeezed vacuum produced by the DPA. The two lines of the Autler-Townes absorption spectrum can be narrowed only in a narrow bandwidth squeezed vacuum, whereas they are independent of the phase and are always broadened in a broadband squeezed vacuum.

DOI
10.1103/physreva.57.3869

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Physical Review A•Feb 15, 2000•14 citations
The Mollow and Autler-Townes probe absorption spectra 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 are studied. Analytical studies of the modifications caused by the finite squeezed-vacuum bandwidth to the spectra are made for the case when the Rabi frequency of the driving field is much larger than the natural linewidth. The squeezed vacuum center frequency and the driving laser frequency are assumed equal. We show that the spectral features depend on the bandwidth of a squeezed vacuum field and whether the sources of the squeezing field are degenerate (DPA) or nondegenerate (NDPA) parametric amplifiers. In a broadband or narrow bandwidth squeezed vacuum generated by a NDPA, the central component of the Mollow spectrum can be significantly narrower than that in the normal vacuum. When the source of the squeezed vacuum is a DPA, the central feature is insensitive to squeezing. The Rabi sidebands, however, can be significantly narrowed only in the squeezed vacuum produced by the DPA. The two lines of the Autler-Townes absorption spectrum can be narrowed only in a narrow bandwidth squeezed vacuum, whereas they are independent of the phase and are always broadened in a broadband squeezed vacuum.
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 present numerical and analytical results for the Mollow probe absorption spectrum of a coherently driven two-level system in a narrow bandwidth squeezed vacuum field. The spectra are calculated for the case where the Rabi frequency of the driving field is much larger than the natural linewidth and the squeezed vacuum carrier frequency is detuned from the driving laser frequency. The driving laser is on resonance. We show that in a detuned squeezed vacuum the standard Mollow features are each split into triplets. The central components of each triplet are weakly dependent on the squeezing phase but the sidebands strongly depend on the phase and can have dispersive or absorptive/emissive profiles. We also derive approximate analytical expressions for the spectral features and find that the multi-peak structure of the spectrum can be interpreted either via the eigenfrequencies of a generalized Floquet Hamiltonian or in terms of three-photon transitions between dressed states involving a probe field photon and a correlated photon pair from the squeezed vacuum field.
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.
We examine subnatural phase-dependent linewidths in the fluorescence spectrum of a three-level atom damped by a narrow-bandwidth squeezed vacuum in a cavity. Using the dressed-atom model approach of a strongly driven three-level cascade system, we derive the master equation of the system from which we obtain simple analytical expressions for the fluorescence spectrum. We show that the phase effects depend on the bandwidths of the squeezed vacuum and the cavity relative to the Rabi frequency of the driving fields. When the squeezing bandwidth is much larger than the Rabi frequency, the spectrum consists of five lines with only the central and outer sidebands dependent on the phase. For a squeezing bandwidth much smaller than the Rabi frequency the number of lines in the spectrum and their phase properties depend on the frequency at which the squeezing and cavity modes are centered. When the squeezing and cavity modes are centered on the inner Rabi sidebands, the spectrum exhibits five lines that are completely independent of the squeezing phase with only the inner Rabi sidebands dependent on the squeezing correlations. Matching the squeezing and cavity modes to the outer Rabi sidebands leads to the disappearance of the inner Rabi sidebands and a strong phase dependence of the central line and the outer Rabi sidebands. We find that in this case the system behaves as an individual two-level system that reveals exactly the noise distribution in the input squeezed vacuum.
The resonance fluorescence of a two-level atom driven by a coherent laser field and damped by a finite bandwidth squeezed vacuum is analysed. We extend the Yeoman and Barnett technique to a non-zero detuning of the driving field from the atomic resonance and discuss the role of squeezing bandwidth and the detuning in the level shifts, widths and intensities of the spectral lines. The approach is valid for arbitrary values of the Rabi frequency and detuning but for the squeezing bandwidths larger than the natural line-width in order to satisfy the Markoff approximation. The narrowing of the spectral lines is interpreted in terms of the quadrature-noise spectrum. We find that, depending on the Rabi frequency, detuning and the squeezing phase, different factors contribute to the line narrowing. For a strong resonant driving field there is no squeezing in the emitted field and the fluorescence spectrum exactly reveals the noise spectrum. In this case the narrowing of the spectral lines arises from the noise reduction in the input squeezed vacuum. For a weak or detuned driving field the fluorescence exhibits a large squeezing and, as a consequence, the spectral lines have narrowed linewidths. Moreover, the fluorescence spectrum can be asymmetric about the central frequency despite the symmetrical distribution of the noise. The asymmetry arises from the absorption of photons by the squeezed vacuum which reduces the spontaneous emission. For an appropriate choice of the detuning some of the spectral lines can vanish despite that there is no population trapping. Again this process can be interpreted as arising from the absorption of photons by the squeezed vacuum. When the absorption is large it may compensate the spontaneous emission resulting in the vanishing of the fluorescence lines.
Using the coupled-system approach we calculate the optical spectra of the fluorescence and transmitted fields of a two-level atom driven by a squeezed vacuum of bandwidths smaller than the natural atomic linewidth. We find that in this regime of squeezing bandwidths the spectra exhibit unique features, such as a hole burning and a three-peak structure, which do not appear for a broadband excitation. We show that the features are unique to the quantum nature of the driving squeezed vacuum field and do not appear when the atom is driven by a classically squeezed field. We find that a quantum squeezed-vacuum field produces squeezing in the emitted fluorescence field which appears only in the squeezing spectrum while there is no squeezing in the total field. We also discuss a nonresonant excitation and find that depending on the squeezing bandwidth there is a peak or a hole in the spectrum at a frequency corresponding to a three-wave-mixing process. The hole appears only for a broadband excitation and results from the strong correlations between squeezed-vacuum photons.