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Canadian Journal of Physics

Resonance fluorescence with bichromatic excitation and nonresonant squeezed reservoir: iterative approach

Saad S. M. Hassan, R.A. Alharbey

Published May 1, 2012• 2 citations
Publisher

Abstract

An iterative approach, not restricted to field strength nor to resonance conditions, is used to solve the nonautonomous Bloch equations modeling the interaction of a bichromatically driven two-level atom in the presence of an off-resonant broadband squeezed vacuum (SV) radiation reservoir. The system parameters are chosen such that the absolute difference between the iterative and (exact) numerical solutions is [Formula: see text](10−2) or less. For some limiting cases, range of validity of the iterative procedure is estimated analytically. The derived analytical solutions are used to calculate the transient fluorescent spectrum. Some previously obtained results (both experimental and theoretical) in the normal vacuum case are recovered. In the SV case, with strong resonant (off-resonant) bichromatic field strength, the transient spectrum shows many symmetrical (asymmetrical) resonances of weights and locations dependent on the SV detuning parameter.

DOI
10.1139/p2012-039

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An iterative approach, not restricted to field strength nor to resonance conditions, is used to solve the nonautonomous Bloch equations modeling the interaction of a bichromatically driven two-level atom in the presence of an off-resonant broadband squeezed vacuum (SV) radiation reservoir. The system parameters are chosen such that the absolute difference between the iterative and (exact) numerical solutions is Formula: see text or less. For some limiting cases, range of validity of the iterative procedure is estimated analytically. The derived analytical solutions are used to calculate the transient fluorescent spectrum. Some previously obtained results (both experimental and theoretical) in the normal vacuum case are recovered. In the SV case, with strong resonant (off-resonant) bichromatic field strength, the transient spectrum shows many symmetrical (asymmetrical) resonances of weights and locations dependent on the SV detuning parameter.
The non-autonomous Bloch equations modelling a driven 2-level atom in the presence of an off-resonant broadband squeezed vacuum (SV) field is treated analytically. This concerns iterative solutions valid for large SV detuning parameter but for arbitrary strength of the laser field. Computational results are presented for the averaged atomic variables for various data and compared with the resonant SV field case. The iterated analytical results for nonzero SV detuning are compared with the (exact) numerical solutions of the Bloch equations, hence we have an insight about the range of other system parameters (other than the Rabi frequency) for which the iterated solutions are valid to O(10−2) or less. The main purpose of deriving these analytical results is to calculate analytically the transient fluorescent spectrum. For an initially ground-state atom, both the SV phase and detuning parameters induce pronounced asymmetrical spectrum in the strong field case.
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 present analytical and numerical results for the steady-state resonance fluorescence spectrum produced by a coherently driven two-level atom in the presence of a broadband squeezed vacuum. Here the central frequency of the squeezed vacuum is off-resonant with the driving field frequency, while maintaining resonance between the driving frequency and the atomic resonance. Numerical solutions of the Bloch equations of the system are obtained under the strong driving field approximation which agree well with the analytic results.
We present analytical results for the steady-state resonance fluorescence spectrum produced by a driven two-level atom excited under two strong coherent fields in the presence of a broadband squeezed vacuum. Here the central frequency of the squeezed vacuum is considered to be resonant as well as off-resonant with the average driving field frequency while maintaining resonance between the atomic transition frequency and the average driving field frequency. We observe a ringing phenomenon in the fluorescence spectrum due to the small frequency difference in the bichromatic field and this phenomenon is found to be sensitive to the detuning of the carrier frequency of squeezed vacuum with respect to the central frequency of the bichromatic field.
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 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.