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arXiv:quant-ph/0310111 · Physical Review A

Optical bistability in sideband output modes induced by a squeezed vacuum

Leonardo Paulo Maia, Gilberto Aparecido Prataviera, Salomon Sylvain Mizrahi

Published May 3, 2004• 10 citations
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Abstract

We consider $N$ two-level atoms in a ring cavity interacting with a broadband squeezed vacuum centered at frequency ${\ensuremath{\omega}}_{s}$ and an input monochromatic driving field at frequency $\ensuremath{\omega}$. We show that, besides the central mode (at $\ensuremath{\omega}$), an infinity of sideband modes are produced at the output, with frequencies shifted from $\ensuremath{\omega}$ by multiples of $2(\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{s})$. We analyze the optical bistability of the two nearest sideband modes, red shifted and blue shifted.

DOI
10.1103/physreva.69.053802

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We consider NNN two-level atoms in a ring cavity interacting with a broadband squeezed vacuum centered at frequency \ensuremathωs{\ensuremath{\omega}}_{s}\ensuremathωs​ and an input monochromatic driving field at frequency \ensuremathω\ensuremath{\omega}\ensuremathω. We show that, besides the central mode (at \ensuremathω\ensuremath{\omega}\ensuremathω), an infinity of sideband modes are produced at the output, with frequencies shifted from \ensuremathω\ensuremath{\omega}\ensuremathω by multiples of 2(\ensuremathω\ensuremath−\ensuremathωs)2(\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{s})2(\ensuremathω\ensuremath−\ensuremathωs​). We analyze the optical bistability of the two nearest sideband modes, red shifted and blue shifted.
A composite system consisting of a degenerate optical parametric oscillator (DOPO) and N two-level atoms interacting with a broadband squeezed vacuum (SV) centred at frequency ωs and an input monochromatic pumping field with a frequency ωp is analysed. The corresponding explicit analytical steady-state solutions in the central mode ωp = ωs are derived and the result displays optical bistability (OB). In addition, the influence of the broadband SV on the bistable behaviour is analysed in detail.
We discuss the optical bistable behavior of a system of N two-level atoms pumped by a coherent input field and coupled to a squeezed vacuum field by treating the optical bistability of such a system as an input-output problem. We consider the equation of motion for atomic dipole moments, coupled to the cavity field and the squeezed vacuum, and the boundary condition connecting the input and output fields with the atomic lowering operator. A simple analytical expression for the influence of the squeezed vacuum input on the bistable behavior of the output field is derived by this method. The results indicate a strong influence of the squeezed vacuum input on optical bistability. The squeezed (stretched) vacuum input field tends to increase (decrease) the range of optical bistability.
Optical bistability is reexamined as a candidate system for the generation of squeezed states of light. Previous analyses have concluded that significant squeezing can be achieved only in a rather extreme range of parameter space relative to current experimental capabilities and only over a restricted range of frequencies near the carrier.1 By contrast we have identified a new regime in which appreciable squeezing should be obtainable for rather modest operating conditions and without excessive demands on the stability of external control parameters. Following the treatment by Carmichael,2 we have conducted a theoretical search for optimal squeezing in optical bistability in the general case without adiabatic elimination of atomic or cavity variables. Our analysis is based on a linearization of the generalized Fokker-Planck equation for a system of N atoms coupled to a single mode of a high finesse cavity. For comparable atomic and cavity decay rates, there is a mode splitting in the eigenvalue structure of the system which is responsible for the vacuum field Rabi splitting. It is near the spectral features associated with these vacuum field Rabi sidebands that we find significant squeezing. The concepts of optimum squeezing as indicated by Mandel's Q parameter and by the spectrum of squeezing are discussed with reference to the various operating regimes in optical bistability.
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.