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Physical Review A

Theory of quantum-optical measurements with a phase-conjugate mirror

Mary Yvonne Lanzerotti, Alexander L. Gaeta

Published May 1, 1995• 9 citations
Publisher

Abstract

We show theoretically that optical phase conjugation via four-wave mixing can satisfy the quantitative criteria [Holland et al., Phys. Rev. A 42, 2995 (1990)] for performing quantum nondemolition measurements of a signal field despite the fact that this measurement scheme introduces noise into the signal field and thus does not perform a true quantum nondemolition measurement. The criteria can be satisfied under conditions in which the vacuum field injected in the rear of the phase-conjugate mirror is quadrature squeezed. Using this measurement scheme, it is possible to obtain values of the total information transfer coefficient that are as large as those that can be achieved using quantum nondemolition measurements.

DOI
10.1103/physreva.51.4057

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We show theoretically that optical phase conjugation via four-wave mixing can satisfy the quantitative criteria [Holland et al., Phys. Rev. A 42, 2995 (1990)] for performing quantum nondemolition measurements of a signal field despite the fact that this measurement scheme introduces noise into the signal field and thus does not perform a true quantum nondemolition measurement. The criteria can be satisfied under conditions in which the vacuum field injected in the rear of the phase-conjugate mirror is quadrature squeezed. Using this measurement scheme, it is possible to obtain values of the total information transfer coefficient that are as large as those that can be achieved using quantum nondemolition measurements.
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 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.
According to quantum mechanics, there exists a class of observables for which is possible to confine the perturbation produced by a continuous measurement to the conjugate variable. Therefore, it is possible to devise experimental schemes that allow estimating the observed variable with arbitrary accuracy, or preparing it in a well-known state. Such schemes are referred to as quantum non-demolition measurements (QND). Among these observables there is the amplitude of the light field. Indeed, it is possible to exploit a movable mirror to implement a QND scheme [1]. Intensity fluctuations of an optical field impinging on it are not affected by the interaction. However, the movable mirror is excited by the associated radiation pressure. This, in turn, affects the phase of the field.
The process of making a measurement on a quantum-mechanical system introduces quantum noise to that system. A quantum nondemolition measurement scheme seeks to make a measurement of an observable to better than this quantum limit, by feeding all the introduced noise into a conjugate variable to that under consideration. In this paper three quantitative criteria are suggested for the evaluation of nonideal quantum nondemolition measurements. The application of these criteria is illustrated using both a simple beam splitter and the ${\mathrm{\ensuremath{\chi}}}^{3}$ interaction in a Raman-active medium.
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.