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Physical Review A

Bistable behavior in a system of an optical parametric oscillator coupling withNtwo-level atoms

Min Xiao, Shaozheng Jin

Published Jan 1, 1992• 9 citations
Publisher

Abstract

We consider a composite system consisting of a degenerate optical parametric oscillator (DOPO) and a set of N homogeneously broadened two-level atoms. When the atoms are on or near resonance with the subharmonic-frequency field generated through the frequency down-conversion process, bistability appears in the intracavity field near the DOPO threshold. The bistability region will decrease as the detuning between the atomic transition frequency and the frequency of the subharmonic field increases. When the detuning becomes large enough, the atoms decouple from the cavity field and the system behaves like a normal DOPO. There are several features distinguishing this bistable behavior from the usual atomic optical bistability occurring with atoms in an optical cavity driven by an external field.

DOI
10.1103/physreva.45.483

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We consider a composite system consisting of a degenerate optical parametric oscillator (DOPO) and a set of N homogeneously broadened two-level atoms. When the atoms are on or near resonance with the subharmonic-frequency field generated through the frequency down-conversion process, bistability appears in the intracavity field near the DOPO threshold. The bistability region will decrease as the detuning between the atomic transition frequency and the frequency of the subharmonic field increases. When the detuning becomes large enough, the atoms decouple from the cavity field and the system behaves like a normal DOPO. There are several features distinguishing this bistable behavior from the usual atomic optical bistability occurring with atoms in an optical cavity driven by an external field.
We study a composite system consisting of N three-level \ensuremath{\Lambda}-type atoms and a degenerate optical parametric oscillator (DOPO). The standard DOPO threshold is modified by the presence of the three-level atoms. Bistability (in the intracavity field intensity versus pumping intensity for the DOPO) appears for certain atomic detunings and coupling field strengths between the intracavity field and one of the atomic transitions. The effects of the coupling field (for the auxiliary transition in the three-level atomic system) are discussed. The susceptibility of the three-level atoms is calculated for the lower and upper branches of the bistable curve. Both analytical (for certain special cases) and numerical (for more general cases) results are presented.
We study transmitted optical spectra from a realistic system which consists of a degenerate optical parametric oscillator (DOPO) and N two-level atoms. Optical bistability appears when parameters are suitable. Below the modified threshold of the DOPO (lower turning point of the bistable curve), the coherent intensity is always zero at the lower branch, which allows us to describe this system with a set of linear differential equations. By transforming the field and atomic variables into corresponding quadratures, we find that, for the resonance case, one atomic quadrature will only couple to one field quadrature. By separating these two quadratures, we are able to study the effects due to squeezed and unsqueezed quadratures on the atoms. The optical and atomic spectra of this system are obtained, analytically, for arbitrary coupling strength and cavity linewidth.
Although an ideal degenerate optical parametric oscillator (DOPO) can generate perfect squeezing at the output of a one-sided optical cavity when operating just below threshold, its intracavity squeezing is limited to less than one-half (50%) of its perfect value. However, when two-level atoms are introduced into the DOPO cavity, the amount of intracavity squeezing can be enhanced, from its maximum value of 50%, to a maximum value of 75% in the good-cavity limit due to the strong interaction between the two-level atoms and the subharmonic field mode. This extra intracavity squeezing is significant in studying spectroscopy of atoms interacting with a squeezed field mode inside an optical cavity.
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 consider a degenerate optical parametric oscillator (DOPO). A coherent signal is injected with real amplitude ϵ and phase 2iω0t. The cavity has two resonant modes at frequencies ν1 ≃ ω0 and ν2 ≃ 2ω0. A nonlinear crystal converts photons of frequency ν2 into pairs of photons of frequency ν1 = v2/2. A saturable absorber is inserted in the cavity and can absorb photons at the frequency ν1. The absober is described by a collection of N homogeneously broadened two-level atoms with atomic frequency ω ≃ ω0.