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Physical Review A

Extra intracavity squeezing of a degenerate optical parametric oscillator coupling withNtwo-level atoms

Shaozheng Jin, Min Xiao

Published Jan 1, 1994• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.49.499

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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 degenerate optical parametric oscillator (DOPO) in the above threshold regime is a prominent source of squeezed field. In this study, a driven DOPO whose pump mode is coupled to a thermal bath while the signal mode is coupled to a squeezed vacuum reservoir is explored to understand the effect of the external squeezed light and the thermal fluctuations on the squeezing properties of both the intracavity and output pump and signal modes. Our findings showed that the injected squeezed vacuum reservoir enables the intracavity squeezing to surpass the maximum squeezing limit of 50% attainable in a DOPO coupled to an ordinary vacuum reservoir. We also found that the maximum squeezing of the output signal mode shifts from resonance to off-resonance in the presence of the injected squeezed vacuum field. Furthermore, the output pump mode exhibits nearly perfect squeezing for a squeezing parameter of r=2. Unlike the output signal mode, the maximum squeezing of the output pump mode occurs at resonance in the presence of the injected squeezed vacuum reservoir. Moreover, a considerable amount of squeezing is observed even in the presence of thermal fluctuations, as they are counterbalanced by the external squeezed light. Notably, relative damping rate between the pump and signal modes is observed to be a parameter that significantly influences squeezing, indicating the importance of optimizing the amount of damping depending on the intended purpose of the DOPO.
In a recent work,1 the influence of arbitrary values of output-mirror transmission on the quantum noise and squeezing in a degenerate optical parametric oscillator (DOPO) with a single output mirror was studied. The work being presented here is a theoretical extension of that research to the case of a DOPO in a double-sided cavity with arbitrary transmission coefficients for the two output mirrors. Additionally, the pump field will be allowed to have amplitude and phase noise. Both intracavity and extracavity fields will be treated for a variety of squeezing characteristics of the input fields entering the DOPO cavity. The dependence of squeezing of the output and intracavity fields on the spatial phase, which determines the locations of the nodes and antinodes, of the average pump field will also be analyzed. As in Ref. 1, the generalization of the good-cavity results to arbitrary quality cavities is highly nontrivial.
High-Q cavities play a central role in quantum optics for the generation and study of novel quantum mechanical states of light like squeezed states. It is however not widely recognized that even low-Q cavities can produce such states. For example, a degenerate optical parametric oscillator (DOPO) with one nearly perfect mirror can produce perfectly squeezed output light regardless of the second mirror transmission, provided the DOPO is at oscillation threshold. Moreover, the squeezing bandwidth increases with increasing transmission of the second mirror.
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.
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.
Quantum noise and squeezing of the field produced by a degenerate optical parametric oscillator operating below threshold are considered. This analysis extends previously reported calculations for single cavities to double cavities whose mirror transmission coefficients are arbitrary. The double-cavity configuration improves the overall squeezing of the system for both the intracavity field as well as the output field. The double-cavity configuration may be conducive to experimental verification of this and previous work.