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Physical Review A

Quantum noise reduction in two-photon oscillators

Paulo A. Maia Neto, L. Davidovich

Published Mar 1, 1992• 8 citations
Publisher

Abstract

We present an exact nonlinear derivation of the spectrum of fluctuations in the difference of output intensities for the signal and idler beams generated by intracavity two-photon gain, when the cavity decay rates are the same for the two modes, and taking into account the atomic fluctuations. For the field inside the cavity, we show that the variance in the difference of intensities may be up to 50% below the shot-noise value. We also consider the case of different decay rates, and show that the noise in the output-intensity difference vanishes at zero frequency, for single-ported cavities, and as long as the only source of field decay is the transmission through the mirror. Within this general approach, we show that for the two-photon laser there is a strong correlation between signal and idler output beams when the relay-level detuning is larger than the power broadening. We calculate, in lowest order, the correction to the noise spectrum of the difference of intensities due to the population of the relay level.

DOI
10.1103/physreva.45.3139

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We present an exact nonlinear derivation of the spectrum of fluctuations in the difference of output intensities for the signal and idler beams generated by intracavity two-photon gain, when the cavity decay rates are the same for the two modes, and taking into account the atomic fluctuations. For the field inside the cavity, we show that the variance in the difference of intensities may be up to 50% below the shot-noise value. We also consider the case of different decay rates, and show that the noise in the output-intensity difference vanishes at zero frequency, for single-ported cavities, and as long as the only source of field decay is the transmission through the mirror. Within this general approach, we show that for the two-photon laser there is a strong correlation between signal and idler output beams when the relay-level detuning is larger than the power broadening. We calculate, in lowest order, the correction to the noise spectrum of the difference of intensities due to the population of the relay level.
A quantum analysis of the intensity fluctuations is given for the nondegenerate parametric oscillator both above and below threshold. Theoretical analysis and experiments by Heidmann, Horowicz, Reynaud, Giacobino, and Fabre [Phys. Rev. Lett. 59, 2555 (1987)] have shown that a noise suppression below the vacuum level is possible in the difference of the intensities of the signal and idler modes. The effect of nonequal cavity decay rates and intracavity losses is shown to modify significantly the fluctuation spectra for the difference in the intensity of the signal and idler beams. The results of exact nonlinear solutions for the internal cavity modes are discussed. We demonstrate that a very sensitive absorption detector may be made by operating the oscillator near threshold.
We consider lasers with intracavity nonlinear elements, e.g., two-photon absorption, second-harmonic generation, as a possible means to reduce the amplitude fluctuations in a laser. While amplitude squeezing up to 37% may be obtained for the internal field, only a modest amount of noise reduction (10% for two-photon absorption, effectively zero for second-harmonic generation) is found in the output field at the laser frequency. In the second-harmonic field an amplitude-noise reduction of 50% below the shot-noise level may be achieved.
We consider here the problem of quantum noise in light produced by an optical parametric oscillator operating below threshold inside a singlesided cavity. By employing the correct boundary conditions on quantum fields at the output mirror, a procedure that is valid for arbitrary mirror transmission, we derive exact expressions for quantum noise reduction for arbitrary pump phase and mirror out-coupling. We find that for a given out-coupling, squeezing of quantum noise in the intracavity field increases to a final value of 50%, as the pump intensity is increased and the oscillation threshold is approached. The output field on the other hand exhibits perfect squeezing of noise in one quadrature of its central Fourier component at threshold regardless of the mirror out-coupling. The present approach, which is based on boundary conditions, is quite general and applicable to any matter-field interaction problem inside a cavity. In fact, we have previously employed this approach in the calculation of the intrinsic linewidth of a laser with arbitrary out-coupling.1
The authors consider the problem of second harmonic generation in an optical cavity which contains both the laser and the nonlinear crystal. They calculate the spectrum of the amplitude fluctuations in the output field, for the mode which is generated by the laser. They focus on the case that the damping constant of this mode is much larger than all the other relaxation rates of the system, and show that in this limit the spectrum is correctly described by the universal normal form for two-photon processes. Finally, they show in general that in the framework of linearised theories the spectrum of the intensity fluctuations in the output field reduces exactly to the spectrum of squeezing of the amplitude quadrature component.