Optical phase conjugation of nonclassical fields

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.