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Journal of the Optical Society of America B

Hole-burning and dispersive profiles at line center of the probe absorption spectrum of a two-level atom in a squeezed vacuum

Peng Zhou, Z. Ficek, S. Swain

Published May 1, 1996• 20 citations
Publisher

Abstract

We study the absorption spectra of a weak probe beam that interacts with a driven two-level atom in the presence of a squeezed vacuum. In particular, we focus on the behavior of the central resonance of the probe absorption spectra in the region of intermediate driving intensities and in the large squeezed photon number limit. Squeezing-induced pimples, hole-burning, and dispersive profiles at line center are displayed. These unusual spectral features are highly sensitive to the squeezing phase and to the Rabi frequency of the driving field. We present analytical conditions for the occurrence of these effects and find that they all take place in the vicinity of the critical point dividing the different dynamical regimes, probe absorption and amplification, of the atomic radiation. We also investigate analytically and numerically the two-time correlation functions of the atomic polarization and find that the cross correlations of the two dipole quadratures contribute symmetric (absorptionlike) spectral features to the absorption spectra, whereas the self-correlations contribute asymmetric (dispersionlike) spectral profiles, which disappear for the particular phase values Φ = 0, π. The physical origin of the unusual spectral profiles at line center is also discussed in terms of the coherent population oscillations.

DOI
10.1364/josab.13.000768

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We study the absorption spectra of a weak probe beam that interacts with a driven two-level atom in the presence of a squeezed vacuum. In particular, we focus on the behavior of the central resonance of the probe absorption spectra in the region of intermediate driving intensities and in the large squeezed photon number limit. Squeezing-induced pimples, hole-burning, and dispersive profiles at line center are displayed. These unusual spectral features are highly sensitive to the squeezing phase and to the Rabi frequency of the driving field. We present analytical conditions for the occurrence of these effects and find that they all take place in the vicinity of the critical point dividing the different dynamical regimes, probe absorption and amplification, of the atomic radiation. We also investigate analytically and numerically the two-time correlation functions of the atomic polarization and find that the cross correlations of the two dipole quadratures contribute symmetric (absorptionlike) spectral features to the absorption spectra, whereas the self-correlations contribute asymmetric (dispersionlike) spectral profiles, which disappear for the particular phase values Φ = 0, π. The physical origin of the unusual spectral profiles at line center is also discussed in terms of the coherent population oscillations.
A comprehensive study is made of the absorption spectrum of a weak-probe beam irradiating a two-level atom damped by a broadband squeezed vacuum and driven by a strong laser field. We show that for a resonant driving field whose phase does not coincide with the principal directions of the squeezing ellipse, the absorption spectrum is asymmetric and exhibits absorption-emission profiles at the Rabi sidebands. We find that this feature arises from unequal populations of the dressed states of the system, which occur when all components of the Bloch vector are coupled to the driving field. A symmetric spectrum with dispersionlike profiles at the Rabi sidebands is revealed for an off-resonant driving field. Furthermore, the spectrum may exhibit an emission profile at the central frequency, signifying an amplification of the probe beam. We point out that the amplification at the central component is not attributed to population inversion in both the atomic bare states and in the dressed atomic states. We find that the amplification originates from the coherent population oscillations and is impossible in the absence of the squeezed vacuum. In addition, we examine how these features are affected by the detuning of the driving field and an imperfect squeezed vacuum.
We examine the response of a coherently driven two-level atom interacting with a broadband squeezed vacuum to a probe beam of arbitrary intensity. The equations of motion for the reduced density matrix elements are numerically solved by nonperturbative matrix inversion methods. For large driving intensities, the absorption spectrum exhibits a number of multiphoton absorption peaks with increasing probe strength in a standard vacuum and in a squeezed vacuum with small photon numbers, while the multiphoton absorption peaks are wiped out for large squeezed photon numbers. Strong gain without inversion at line center can be obtained in the presence of the squeezed vacuum when the probe strength does not exceed the driving one. The absorption spectrum is phase sensitive. We also find the presence of remarkable, very narrow structures at line center. In general, the spectrum is symmetric when \ensuremath{\Phi}=0 and \ensuremath{\pi}; otherwise, it is asymmetric and displays a dispersivelike profile at line center.
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 resonance fluorescence system of a coherently driven two-level atom in the presence of a broadband squeezed vacuum field whose central frequency is not in resonance with either the driving field frequency or the atomic transition frequency is analyzed. Solutions of the Bloch equations of the system are presented in terms of continued fractions for arbitrary strength of the coherent driving field. Numerical results are presented for the first-harmonic quadrature components of the absorption spectrum and the fluorescent intensity. The effects of the squeezed vacuum field detuning on the absorption spectrum result in hole burning or a dip structure in the weak-field case and two absorption–amplification peaks in the strong-field case. Results are sensitive to the relative phase of the squeezed vacuum.
The steady-state resonance fluorescence spectrum of a two-level atom driven by a bichromatic field in a broadband squeezed vacuum is studied. When the carrier frequency of the squeezed vacuum is tuned to the frequency of the central spectral line, anomalous spectral features, such as hole burning and dispersive profiles, can occur at the central line. We show that these features appear for wider, and experimentally more convenient, ranges of the parameters than in the case of monochromatic excitation. The absence of a coherent spectral component at the central line makes any experimental attempt to observe these features much easier. We also discuss the general features of the spectrum. When the carrier frequency of the squeezed vacuum is tuned to the first odd or even sidebands, the spectrum is asymmetric and only the sidebands are sensitive to phase. For appropriate choices of the phase the linewidths of only the odd or even sidebands can be reduced. A dressed-state interpretation is provided.
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.