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Chinese Physics Letters

Absorption Spectrum of a Driven Two-Level Atom in a Tunable Cavity with Injected Squeezed Vacuum

Gao‐xiang Li, Huang Guang-ming, PENG JIN-SHENG

Published Jul 1, 2000• 1 citation
Publisher

Abstract

The absorption spectrum of a driven two-level atom in a frequency tunable cavity with injected squeezed vacuum is investigated. The line shape of the spectra depends on the relative phase between the driving field and the squeezed vacuum, and the frequency detuning between the driving field and the cavity mode. Line narrowing and probe gain can occur and be enhanced by adjusting the phase and detuning.

DOI
10.1088/0256-307x/17/7/013

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The absorption spectrum of a driven two-level atom in a frequency tunable cavity with injected squeezed vacuum is investigated. The line shape of the spectra depends on the relative phase between the driving field and the squeezed vacuum, and the frequency detuning between the driving field and the cavity mode. Line narrowing and probe gain can occur and be enhanced by adjusting the phase and 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.
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 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 investigate the modification of squeezing spectrum of resonance fluorescence of a weakly driven two-level atom coupled with a frequency-tunable cavity mode with finite bandwidth. For atom-laser resonance or small atom-laser detuning, as the cavity resonant frequency adjusted, the squeezing switches between the phase quadratures. When the coupling between the atom and the cavity increases, the degree of squeezing in the out-of-phase quadrature decreases, while the noise in the in-phase quadrature decreases and can be squeezed. For proper atom-laser detuning, with the cavity-laser detuning increasing, the degree of squeezing in the in-phase quadrature increases and the squeezing spectrum exhibits two-mode squeezing.
The fluorescence spectrum of a strongly driven two-level atom located inside an optical cavity damped by a narrow-bandwidth squeezed vacuum is studied. We use a dressed atom model approach, first applied to squeezed vacuum problems by Yeoman and Barnett, to derive the master equation of the system and discuss the role of the cavity and the squeezed vacuum in the narrowing of the spectral lines and the population trapping effect. We find that in the presence of a single-mode cavity the effect of squeezing on the fluorescence spectrum is more evident in the linewidths of the Rabi sidebands rather than in the linewidth of the central component. Even in the absence of squeezing, the cavity can reduce the linewidth of the central component almost to zero, whereas the Rabi sidebands can be narrowed only to some finite value. In the presence of a two-mode cavity and a two-mode squeezed vacuum the signature of squeezing is evident in the linewidths of all spectral lines. We also establish that the narrowing of the spectral lines is very sensitive to the detuning of the driving field from the atomic resonance. Moreover, we find that the population trapping effect, predicted for the broadband squeezed vacuum case, may appear in a narrow-bandwidth case only if the input squeezed modes are perfectly matched to the cavity modes and if there is non-zero squeezing at the Rabi sidebands.