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Optics Letters

Excess-noise-enhanced photon-pair generation in unstable resonators

Claus Lamprecht, Helmut Ritsch

Published May 1, 2002• 1 citation
Publisher

Abstract

We investigate a degenerate optical parametric device with a transversely finite unstable cavity configuration operated below threshold. Using an approximate quantum description in terms of a biorthogonal set of effective cavity-matched modes and their adjoint modes, we predict an intracavity field intensity enhancement by the Petermann excess-noise factor, K . This enhancement is accompanied by a reduction of photon bunching and quadrature squeezing.

DOI
10.1364/ol.27.000757

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We investigate a degenerate optical parametric device with a transversely finite unstable cavity configuration operated below threshold. Using an approximate quantum description in terms of a biorthogonal set of effective cavity-matched modes and their adjoint modes, we predict an intracavity field intensity enhancement by the Petermann excess-noise factor, K . This enhancement is accompanied by a reduction of photon bunching and quadrature squeezing.
We calculate the influence of excess noise on parametric down conversion in an unstable optical parametric oscillator (OPO), using a quantum quasimode description. We find a strongly enhanced pair photon generation rate below threshold as compared to a conventional stable cavity setup of comparable gain and loss. In addition, the oscillation threshold is lowered due to the influence of the excess noise and the squeezing properties of the emitted light are significantly changed. In general, the maximal quantum-noise suppression in one quadrature component is reduced, which poses strong limitations for the practical usefulness of a geometrically unstable OPO source. The analytical results from our quasimode description are in good agreement with numerical simulations using a positive-P representation of the field in mode space and in position space.
A single inverted two-level atom is used as a theoretical model for a quantum noise detector to investigate fundamental properties of excess noise in an unstable optical resonator. For a symmetric unstable spherical mirror cavity, we develop an analytic quantum description of the field in terms of a complete set of normalizable biorthogonal quasimodes and adjoint modes. Including the interaction with a single two-level atom leads to a description analogous to the Jaynes-Cummings model with modified coupling constants. One finds a strong position and geometry-dependent atomic decay probability proportional to the square root K\sqrt{K}K​ of the excess noise factor K at the cavity center. Introducing an additional homogeneous gain one recovers the K-fold emission enhancement that has been predicted before for the linewidth of an unstable cavity laser. We find that excess noise may be viewed as a spatial redistribution of the field quantum noise inside the resonator. Taking a position average of the atomic decay rate over the cavity volume leads to a cancellation of the excess noise enhancement.
We theoretically investigate the quantum dynamics of an unstable resonator laser. Compared to a stable cavity laser of equal gain and loss it exhibits a K-fold enhanced linewidth. This excess noise factor K is a measure of the nonorthogonality of the resonator eigenmodes and amounts to an enlargement of the quantum vacuum fluctuations. Using a quantum treatment starting from first principles based on the nonorthogonal eigenmodes, we put previous theoretical predictions onto a more firm ground. While we find a position-dependent enhancement of the spontaneous emission rate into an empty mode of only K,\sqrt{K},K​, the constructive quantum interference of the spontaneous emission with a single oscillating mode lets the Petermann excess noise factor K reappear in the phase diffusion (laser linewidth). Hence locally enhanced spontaneous emission as well as noise enhanced by interference (amplified spontaneous emission) play an equal role in the origin of excess noise.
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.
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.