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Quantum Electronics and Laser Science Conference

Quantum noise properties of phase conjugate mirrors

Alexander L. Gaeta, Robert W. Boyd

Published Apr 24, 1989• 0 citations
OpenAlex

Abstract

We investigate theoretically the quantum electrodynamic properties of the phase conjugation process. Based on the requirement that the reflected (conjugate) field must obey proper communication relations,1 we find that the reflected field contains a noise contribution due to the phase conjugate mirror (PCM). To calculate the statistical properties of the field leaving the PCM, we use the diagonal coherent state representation for the density operator of the reflected field.

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The vacuum field’s role in the radiative properties of two-level atoms located externally to a phase-conjugate mirror (PCM) is investigated. The basic result of Gaeta and Boyd [ Phys. Rev. Lett.60, 2618 ( 1988)], that the PCM emits an average of R (where R is reflectivity) noise photons per mode of the radiation field, is modified. Stimulated emission of the combined PCM–atom system takes place when the atom is in its ground state; this emission is caused by a scattering–conjugation process of virtual photons. The expression for the power emitted by a system of N (N > 1) two-level atoms also contains terms that are the expectation values of products of two atomic raising or lowering operators in addition to the usual superradiant terms. The case N = 2 is solved exactly in the limit of a vanishing separation-to-wavelength ratio. The expectation values of individual and pair-product operators are derived from the Heisenberg equations of motion, and the solutions are classified according to the value of an integral of motion. When R < 1, the time evolution is characterized by four real-time constants, of which two are a complex-conjugate pair for R > 1, indicating relaxation by damped oscillations.

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We consider the spontaneous emission by an atom near a phase-conjugating mirror (PCM). The effect of the PCM on the decay rate may be understood equivalently in terms of vacuum-field modes reflected and conjugated by the PCM, or in terms of vacuum modes transmitted and amplified without conjugation by the PCM.

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Quantum theory of spontaneous emission and excitation near a phase-conjugating mirror

Peter W. Milonni, Erik J. Bochove, Richard J. Cook

We present a quantum-electrodynamic theory of spontaneous emission in the presence of a phase-conjugating mirror (PCM) and show that the radiative relaxation rate is increased owing to the amplification of quantum noise by the PCM. For any finite value of the PCM reflectivity an atom in any initial state will relax to a steady state with a finite probability of being excited. In particular, there is a finite probability of spontaneous excitation of a ground-state atom placed near the PCM. The fluorescence spectrum of an atom near a PCM is generally described by two Lorentzian functions.

Journal of the Optical Society of America B•Oct 1, 1989•15 citations
We investigate theoretically the quantum electrodynamic properties of the phase conjugation process. Based on the requirement that the reflected (conjugate) field must obey proper communication relations,1 we find that the reflected field contains a noise contribution due to the phase conjugate mirror (PCM). To calculate the statistical properties of the field leaving the PCM, we use the diagonal coherent state representation for the density operator of the reflected field.
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 show by means of a quantum electrodynamic calculation that excess noise is inherent in the process of optical phase conjugation, both in that the state of the field leaving a phase-conjugate mirror can always be described classically (i.e., its phase-space density is positive semidefinite) and in that the fluctuations in the generated field are always greater than those predicted by Poisson statistics. Except in special cases, quantum noise imposes a limitation on the ability of phase conjugation to remove the effects of aberrations.
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.
The vacuum field’s role in the radiative properties of two-level atoms located externally to a phase-conjugate mirror (PCM) is investigated. The basic result of Gaeta and Boyd [ Phys. Rev. Lett.60, 2618 ( 1988)], that the PCM emits an average of R (where R is reflectivity) noise photons per mode of the radiation field, is modified. Stimulated emission of the combined PCM–atom system takes place when the atom is in its ground state; this emission is caused by a scattering–conjugation process of virtual photons. The expression for the power emitted by a system of N (N > 1) two-level atoms also contains terms that are the expectation values of products of two atomic raising or lowering operators in addition to the usual superradiant terms. The case N = 2 is solved exactly in the limit of a vanishing separation-to-wavelength ratio. The expectation values of individual and pair-product operators are derived from the Heisenberg equations of motion, and the solutions are classified according to the value of an integral of motion. When R < 1, the time evolution is characterized by four real-time constants, of which two are a complex-conjugate pair for R > 1, indicating relaxation by damped oscillations.
We present a quantum-electrodynamic theory of spontaneous emission in the presence of a phase-conjugating mirror (PCM) and show that the radiative relaxation rate is increased owing to the amplification of quantum noise by the PCM. For any finite value of the PCM reflectivity an atom in any initial state will relax to a steady state with a finite probability of being excited. In particular, there is a finite probability of spontaneous excitation of a ground-state atom placed near the PCM. The fluorescence spectrum of an atom near a PCM is generally described by two Lorentzian functions.