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Physical Review A

Quantum statistics of the light generated by phase-conjugate resonators

G. S. Agarwal, Alexander L. Gaeta, Robert W. Boyd

Published Jan 1, 1993• 11 citations
Publisher

Abstract

We examine the quantum noise characteristics of the field produced by a phase-conjugate resonator formed from two mirrors, one of which is a phase-conjugate mirror. We show that the output field on the side of the phase-conjugate mirror can be completely squeezed. Numerical results for the quantum-statistical properties of the forward and backward output fields are given as functions of the reflectivities of the two mirrors.

DOI
10.1103/physreva.47.597

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Physical Review A•Dec 1, 1999•3 citations
We examine the quantum noise characteristics of the field produced by a phase-conjugate resonator formed from two mirrors, one of which is a phase-conjugate mirror. We show that the output field on the side of the phase-conjugate mirror can be completely squeezed. Numerical results for the quantum-statistical properties of the forward and backward output fields are given as functions of the reflectivities of the two mirrors.
We investigate theoretically the quantum-noise properties of optical phase conjugation via four-wave mixing of nonclassical signal fields. We show that while the field generated at a phase-conjugate mirror (PCM) can be in a nonclassical state, the generated field is not necessarily useful within the context of phase conjugation. For the case in which a quadrature-squeezed signal field is incident at a PCM, we determine that the signal-to-noise ratio of one of the quadrature components of the generated field can approach the signal-to-noise ratio of the corresponding quadrature component of the signal field as the amount of squeezing of the vacuum field injected at the rear of the PCM is increased. For the case in which the signal field is amplitude squeezed, we determine that the signal-to-noise ratio of the conjugate field is always much smaller than that of the signal field. These results demonstrate that the phase-conjugation process can preserve the desirable quantum-noise properties of quadrature-squeezed fields but not those of amplitude-squeezed fields.
We consider here the problem of quantum noise in light produced by an optical parametric oscillator operating below threshold inside a single-sided 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 output-mirror coupling. We find that for a given output-mirror power reflectance R, squeezing of quantum noise in the intracavity field increases to a final fractional value equal to R/(1+R) 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 output-mirror coupling. The present approach, which is based on boundary conditions, is quite general and applicable to any matter-field interaction problem inside a cavity.
A quantum theory of nearly degenerate backward four-wave mixing in a two-level atomic system is developed. The theory is used to calculate the quantum noise produced by a phase-conjugate mirror based on this system. The results indicate that in the case of pure radiative broadening the ideal quantum-noise limit is reached for relatively small pump-wave strengths and for relatively large probe-pump and pump-resonance detunings, so that the phase-conjugate reflectivity is far from its maximum value. Conversely, in the collisionally broadened case, operation closest to the quantum-noise limit occurs near the point of maximum reflectivity.
We present the results of a comprehensive investigation of the quantum-noise properties of a continuous-wave phase-conjugate mirror (PCM) formed using backward-four-wave mixing in potassium vapor. We characterize the quantum-noise properties of the PCM as functions of the vapor density, pump detuning from resonance, and relative frequency detuning of the signal beam from the probe beam. We compare the noise measurements of the PCM with the predicted noise of an ideal quantum-noise-limited PCM and determine the value of the minimum signal that can be used to perform phase conjugation with unity signal-to-noise ratio. For the range of vapor densities studied, we find that the PCM operates nearest the quantum-noise limit and that the value of the minimum signal is lowest under conditions in which the reflectivity is maximized. These results demonstrate that it is possible to perform phase conjugation with signals as weak as 14 fW with near-unity reflectivity. Our measurements are in qualitative agreement with the predictions of a quantum theory of phase conjugation via nearly degenerate four-wave mixing in a two-level system.