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Acta Physica Sinica

NON-DEGENERATE TWO-PHOTON FLUORESCENCE SPECTRUM FOR TWO-LEVEL ATOM IN SQUEEZED VACUUM

Lin-sheng He, Feng Xun-Li, WU SHI-XIONG, Zhi‐Ming Zhang, XIA YU-XING, (1)合肥工业大学激光研究所，合肥 230009; (2)上海交通大学应用物理系，上海 200030; (3)西安交通大学应用物理系，西安 710049; (4)中国科学院安徽光学精密机械研究所激光光谱学开放研究实验室，合肥 230031

Published Jan 1, 1998• 0 citations
Publisher

Abstract

In this paper the master equation is derived for the atomic reduced density operator, by means of projection operator technique, starting from the Liouville equation. The nondegenerate two-photon fluorescence spectrum for an atom with two-levels in a squeezed vacuum with broad band has been studied by means of the above equation. We find that there is a new type of oscillation phenomenon, in which there are both super and lower thresholds. Between the two thresholds the atom will exhibit oscillation and the two-photon fluorescence spectrum exhibits single peak. Outside the region between the two thresholds the oscillation will not happen and the two-photon fluorescence spectrum possesses novel negative peak or peaks. The shapes of the spectra depend strongly on the natural two-photon linewidth. However, the spectra are not phase-sensitive, which is unexpected.

DOI
10.7498/aps.47.219

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In this paper the master equation is derived for the atomic reduced density operator, by means of projection operator technique, starting from the Liouville equation. The nondegenerate two-photon fluorescence spectrum for an atom with two-levels in a squeezed vacuum with broad band has been studied by means of the above equation. We find that there is a new type of oscillation phenomenon, in which there are both super and lower thresholds. Between the two thresholds the atom will exhibit oscillation and the two-photon fluorescence spectrum exhibits single peak. Outside the region between the two thresholds the oscillation will not happen and the two-photon fluorescence spectrum possesses novel negative peak or peaks. The shapes of the spectra depend strongly on the natural two-photon linewidth. However, the spectra are not phase-sensitive, which is unexpected.
By using the two photon Bloch equation and quantum regression theorem, the second order correlation function of two photon fluorescence of a two level atom in a broad band squeezed vacuum is obtained. From this, the bunching and the antibunching effects of two photon fluorescence are investigated. We find that the second order correlation function is dependent on the squeezing parameter (|M|) of the squeezed vacuum. There is a critical value (Γ/4g) for |M|,above which the second order correlation function oscillates around 1. This indicates that the two photon fluorescence can exhibit both antibunching and bunching effects. Below the critical value, the second order correlation function does not oscillate and the two photon fluorescence exhibits the antibunching effect only.
The dynamics of a strongly driven two-level atom are examined for the case that the atom is coupled to a ``two-mode'' squeezed vacuum. The source of squeezed light is taken to be a (frequency) nondegenerate parametric oscillator. We consider the situation in which the Rabi sidebands produced by the coherent driving field coincide with the spectral peaks of the parametric oscillator. Approximate analytical results are presented and checked against numerical simulations of the exact equations. For a suitable choice of relative phase, all three spectral lines in the fluorescence triplet are found to exhibit subnatural linewidths. Significant modifications to the fluorescence spectrum are also possible with a nonzero laser-atom detuning.
The authors present analytical and numerical results for resonance fluorescence produced by a two-level atom damped by a broad-band squeezed vacuum. Previous theoretical analyses of this model have assumed that the laser frequency and the carrier frequency of the squeezed vacuum are equal. The authors introduce a non-zero detuning between the laser frequency and the carrier frequency while maintaining resonance between the laser frequency and atomic resonance. In the absence of the driving field there is a squeezing threshold: above threshold the decay rate of the atomic polarization can be reduced, and below threshold a squeezing-induced two peak spectrum and frequency shift, which is analogous to the Bloch-Siegert shift, are predicted. In the presence of the driving field, the spectrum is asymmetric for Rabi frequencies smaller or comparable to the detuning of the squeezed vacuum. A symmetric spectrum is obtained for large Rabi frequencies. An interpretation is predicted by means of a dressed-state analysis. The authors find that for not too large Rabi frequencies a remarkably large population inversion can be induced in the dressed states, even at exact resonance of the driving field, provided that the laser frequency and carrier frequency are detuned. Moreover, for detection times larger than the inverse detuning, the spectrum is insensitive to the phase between the driving field and the squeezed vacuum, in marked contrast to the case of no detuning.
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 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.
In this paper, we investigate the dynamics of fluorescent light emitted by a two-level atom interacts with squeezed vacuum reservoir is studied wisely using two-time correlation function and the master equation fundamentals approaches. We use the pertinent master equation to calculate the time-evolution of cavity filed operators as well as two-time correlation function. The mathematical analysis shows the fluorescent spectrum of light emitted by the atom is turned out to be a single peak at a Lorentz's frequency for both squeezed vacuum reservoir and thermal reservoir. On the other hand, we have identified that the squeezed vacuum reservoir input is responsible to the stimulated emission of photons from the atom. Moreover, it is identified that thermal reservoir is more efficient than squeezed vacuum reservoir to have valuable power spectrum. The power spectrum which characterizes the fluorescent light generated by a two-level atom has been summered as it is observed for both case; (i) when a two-level atom coupled to squeezed vacuum reservoir and (ii) when the two-level atom coupled to thermal reservoir. Finally, we generalized from the paper is that the power spectrum of generated light from a two-level atom coupled to thermal reservoir is greater than the power spectrum generated from a two-level atom coupled to squeezed vacuum reservoir. In contrast, more stimulated and squeezed photons are emitted in the case when the atom is coupled with squeezed vacuum reservoir.