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Journal of the Optical Society of America B

Enhanced squeezing in the transmitted fields in parametric oscillation with injected squeezed light at the pump frequency

Daniel B. Erenso

Published Mar 15, 2007• 4 citations
Publisher

Abstract

A degenerate parametric oscillator operating above threshold is studied when the cavity is injected by a broadband squeezed light at the pump frequency. Using the solution of the quantum Langevin equations for the signal and pump modes, we have studied the quantum fluctuations in the intracavity and transmitted field quadratures for the signal and pump modes. For the intracavity modes we studied the variance in the field quadratures, and for the transmitted modes we studied the spectra for the variance in the squeezed quadratures. Our results have revealed that the same relative cavity damping rates between the signal and the pump modes that predict enhanced squeezing in the intracavity do not necessarily predict enhanced squeezing in the transmitted modes.

DOI
10.1364/josab.24.000867

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A degenerate parametric oscillator operating above threshold is studied when the cavity is injected by a broadband squeezed light at the pump frequency. Using the solution of the quantum Langevin equations for the signal and pump modes, we have studied the quantum fluctuations in the intracavity and transmitted field quadratures for the signal and pump modes. For the intracavity modes we studied the variance in the field quadratures, and for the transmitted modes we studied the spectra for the variance in the squeezed quadratures. Our results have revealed that the same relative cavity damping rates between the signal and the pump modes that predict enhanced squeezing in the intracavity do not necessarily predict enhanced squeezing in the transmitted modes.
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.
The degenerate parametric oscillator above threshold is studied with phenomenological stochastic colored (nonwhite) pump noise for arbitrary pump to subharmonic relaxation rate. The current experimental limits of large intracavity threshold photon numbers (very small quantum noise) are considered, allowing for a semiclassical treatment of the system dynamics. A comparison between the effects of isotropic and squeezed pump noise on the internal transient and steady-state fluctuations is presented by simulation of the nonlinear semiclassical stochastic Langevin equations in the Wigner quadrature representation. It is found that the transient squeezing for the system starting in the unstable steady state (the vacuum) is not degraded by stochastic pump noise. A damped oscillatory behavior of the noise levels (periodic exchange of fluctuations between the squeezed quadrature of the signal and the pump) is observed for large damping of the signal in the turn on of pump depletion. Finally, it is shown that the limited squeezing above threshold in the steady state (50%) due to pump depletion can be enhanced if squeezed stochastic noise with sufficient significant spectral components (broadband squeezing) is fed to the pump. The above-threshold steady-state squeezing has been calculated analytically from the linearized stochastic equations and the effects of the time scale associated to the relaxation of the pump noise (the noise correlation time) compared to the dissipative time scale of the system and the pump to subharmonic loss ratio are presented.
This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light. i) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations — spatial Langevin equations — that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed. ii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large χ(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy. iii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier. iv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold — and possibly unrealizable — assumption, that the in-phase and quadrature Langevin sources which are responsible for the "noisiness" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.
Abstract In this paper we present a theoretical analysis of a scheme to enhance quantum statistical features of fluorescent light generated by a quantum well coupled to a degenerate optical parametric oscillator (DOPO) in a microcavity with an input squeezed field. We derive the quantum Langevin equations and solve them using Laplace transform method in the strong coupling regime. It is found that the intensity of the light is significantly enhanced while the normalized intensity spectrum remains largely unaffected by the external squeezed field. Additionally, the emitted light exhibits photon bunching, and the squeezing is notably improved, with the quadrature variance asymptotically approaching zero as the squeezing parameter increases. We also study the quadrature squeezing of the cavity mode and we show that a semiconductor microcavity can serve as a typical source of cavity mode squeezing, with the amount of squeezing significantly enhanced by the DOPO and the external squeezed field.
The authors present a quantum analysis of four-wave mixing in a non-resonant nonlinear medium inside a cavity which is driven by two driving fields. In this process a nonlinear medium couples two pump modes with a signal mode of the frequency equal to the half-sum of the two pump field frequencies. Three types of stable steady-state solutions of the deterministic problem, describing three regimes of oscillation, are found: one below threshold and two different above-threshold regimes. The spectra of fluctuations of the quadrature-phase amplitudes for all three modes are calculated. It is found that in the above-threshold regime each of three modes may display a squeezed noise reduction. Below threshold a squeezing is realized for the central mode.