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Physical Review A

Systems driven by colored squeezed noise: The atomic absorption spectrum

Helmut Ritsch, P. Zoller

Published Nov 1, 1988• 90 citations
Publisher

Abstract

We derive stochastic density-matrix equations for an atom strongly driven by finite-bandwidth squeezed light. The quantum properties of the light are accounted for by a doubling of dimensions of the stochastic process for c-number electric field amplitudes. Saturation properties and the weak-field absorption spectrum of a two-level atom embedded in finite-bandwidth squeezed light and driven by a coherent field are calculated. We discuss the effect of finite bandwidth of the squeezed light in obtaining subnatural linewidth in the atomic absorption spectra, based on nonperturbative solutions of the stochastic optical Bloch equations.

DOI
10.1103/physreva.38.4657

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We derive stochastic density-matrix equations for an atom strongly driven by finite-bandwidth squeezed light. The quantum properties of the light are accounted for by a doubling of dimensions of the stochastic process for c-number electric field amplitudes. Saturation properties and the weak-field absorption spectrum of a two-level atom embedded in finite-bandwidth squeezed light and driven by a coherent field are calculated. We discuss the effect of finite bandwidth of the squeezed light in obtaining subnatural linewidth in the atomic absorption spectra, based on nonperturbative solutions of the stochastic optical Bloch equations.
A stochastic density-matrix equation for an atom strongly driven by finite-bandwidth squeezed light is derived. The quantum properties of the light are accounted for by a doubling of dimensions of the stochastic process for ccc-number electric field amplitudes. The possibility of obtaining reduced atomic linewidths in the absorption spectrum of the atom embedded in colored squeezed light is discussed, based on nonperturbative solutions of stochastic optical Bloch equations.
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.
In this paper, the optical Bloch equations of a two-level atom ensemble driven by squeezed light field are derived. Based on these equations, we calculate the atomic absorption and dispersion. The results show that for different squeezing conditions of the field fluctuations, atomic absorption-lineshape exhibits sub-or super-natural linewidth phenomenon. Atomic dispersion depends on the squeezing direction and coherent excitation direction of the driving field. When these two directions are not parallel or perpendicular to each other, the dispersion zero-point shows a shift to the transition frequency of the atom.
The atomic Bloch equations driven by a quantum noise are investigated in the framework of c-number multiplicative stochastic Rabi amplitudes. It is shown that the stochastic broad-band vacuum fluctuations can be incorporated in such a way that spontaneous absorption is removed. It is shown that the multiplicative stochastic noise with no spontaneous absorption is equivalent to the quantum vacuum noise. A stochastic model of the broad-band squeezed vacuum is introduced and investigated. From such a stochastic description the fast and the slow damping rates of the Bloch polarizations are obtained. The strong-field resonance fluorescence spectrum and the steady-state atomic inversion for the stochastic model of squeezed vacuum fluctuations are derived.
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.
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.