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Physics of Particles and Nuclei

EM Field Frequency Down-Conversion in a Quantum Two-Level System Damped by Squeezed Vacuum Reservoir

Nikolay N. Bogolubov, Andrey Vladimirovich Soldatov

Published Jul 1, 2020• 5 citations
Publisher

Abstract

Abstract Down-conversion of high-frequency EM field in a simple quantum two-level system (also known as two-level atom) with broken inversion symmetry driven by a coherent laser field and damped by a squeezed vacuum reservoir is analyzed. It is shown that the squeezing leads to broadening of the low-frequency radiative peak in the fluorescence spectrum of the system. At the same time, changing the reference phase of the squeezed field and the degree of squeezing allows to manipulate the shape of this peak.

DOI
10.1134/s1063779620040164

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Abstract A two-level quantum emitter with broken inversion symmetry driven by external semiclassical monochromatic high-frequency electromagnetic (e.g., laser) field and damped by squeezed vacuum reservoir with finite bandwidth is presented. The squeezed vacuum source is assumed to be either degenerate parametric oscillator (DPO) or a non-degenerate parametric oscillator (NDPO). It is shown that the shape of low-frequency fluorescence spectrum of the emitter can be effectively alternated by controlling the degree of the squeezed vacuum source degeneration and phase of the squeezing.
Abstract A study of the absorption spectrum of a weak-probe beam irradiating a two-level quantum emitter with broken inversion symmetry driven by external monochromatic high-frequency electromagnetic (e.g. laser) field and damped by squeezed vacuum reservoir with finite bandwidth was carried out for the case of the squeezed vacuum source being represented by a non-degenerate parametric oscillator below threshold. It was shown that this atom-driving-field system can either amplify or absorb weak probe electromagnetic radiation beam of much lower frequency than the frequency of the driving field. The shape of the absorption and amplification spectra can be controlled by the degree of the squeezed vacuum source degeneration and by the phase of the squeezing, while the switching between these two modes of operation can only be controlled by the phase of the squeezing.
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.
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.
A single two-level atom in a coherently driven cavity and damped by a broadband squeezed vacuum centered about the atomic transition frequency is studied. A second-order Fokker-Planck equation for this system is obtained without using system size expansion. Effects of detunings and cavity decays are also incorporated in the Fokker-Planck equation. This equation is used to study atomic inversion, fluorescent spectrum, and the intensity correlations of the transmitted and fluorescent photons in the bad-cavity limit. Several interesting effects in the atomic inversion, spectrum, and intensity correlations due to the squeezed vacuum are presented. These results are also compared with an atom that is damped by a thermal reservoir.