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arXiv:physics/9808022 · Physical Review A

Quantum noise reduction and generalized two-mode squeezing in a cavity Raman laser

Kai J. Drühl, Claude Windenberger

Published Oct 1, 1998• 3 citations
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Abstract

We study a generalized notion of two-mode squeezing for the Stokes and anti-Stokes fields in a model of a cavity Raman laser, which leads to a significant reduction in decoherence or quantum noise. The model comprises a lossless cavity with classical pump, unsaturated medium, and arbitrary homogeneous broadening and dispersion. Allowing for arbitrary linear combinations of the two modes in the definition of quadrature variables, we find that there always exists a combination of the two output modes that exhibits quadrature squeezing with noise reduction below the vacuum level. The number of noise photons for this combination mode is proportional to the square root of the number of Stokes noise photons.

DOI
10.1103/physreva.58.3268

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We investigate two-mode squeezing of compound Stokes-anti-Stokes modes propagating in a Raman coupler with a broad reservoir phonon system. Three types of squeezing: principal squeezing, generalized squeezing and sum squeezing are examined and their relations are identified. The definition of generalized squeezing is extended to an arbitrary number of modes, and a multimode uncertainty product is introduced. The quantum statistical properties of the optical fields propagating in the coupler are treated within the framework of the generalized superposition of the coherent signal and quantum noise. According to this model, generalized squeezing appears whenever the Glauber-Sudarshan quasidistribution does not exist as an ordinary function.
We investigate the dynamics of a two-mode stimulated Raman scattering model including propagation and the quantum correlations that develop between the Stokes and anti-Stokes fields. For example, under certain conditions two-mode squeezed states can result. We report results for quadrature squeezing and sum squeezing. Quadrature squeezing only occurs when the anti-Stokes coupling constant is larger than the Stokes coupling constant. The amount of squeezing increases as the damping of the material polarization is increased. \textcopyright{} 1996 The American Physical Society.
We consider a \ensuremath{\Lambda}-type three-level atom interacting simultaneously with two quantized cavity fields and a classical field, all of different frequencies. The classical field is of constant amplitude and the quantized cavity fields are dynamical variables. The effective interactions are Raman type with the two cavity fields regarded as Stokes and anti-Stokes modes. The classical field acts as the pump-mode, so that both the pump--Stokes and the pump--anti-Stokes transitions are included. We present analytic expressions for the dressed states of the system in a general situation where the two channels have different coupling strengths. The dressed states are closely related to the two-mode squeezed number states. We find that two-mode squeezing and nontrivial phase correlation occur in the model. The effects of weak cavity damping are also discussed.
The theory of a two-mode nondegenerate parametric amplifier in a cavity is reformulated in terms of quadrature-phase-amplitude variables. The corrrespondence with a genuine classical stochastic linear process is found (non-negative-definite diffusion matrices) for the case of a cavity device immersed in thermal or ordinary (nonsqueezed) vacuum sources. A special kind of squeezing, i.e., quadrature squeezing [B. L. Schumaker, Phys. Rep. 135, 318 (1986)], is found to be characteristic of the internal steady state for the case of a cavity model subjected to an additional phase-sensitive noise source coupled to one of the two internal modes. Finally, the usual squeezing spectrum of the output field is calculated in both cases by means of an input-output formalism based upon a symmetric ordering scheme of noncommuting operators, well adapted for the quadrature-phase description of the fields involved in the interaction.