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Annual Meeting Optical Society of America

Raman amplifiers in a two-leg interferometer: quantum noise versus fringe visibility

R. C. Swanson, Philip R. Battle, John L. Carlsten

Published Jan 1, 1990• 0 citations

Abstract

Quantum mechanics fundamentally requires any linear amplifier to introduce quantum noise onto the amplified signal.1 In the case of the linear Raman amplifier, the fully quantum-mechanical Raman equations give a precise prediction of how much noise is introduced.2 Understanding and testing this prediction is important not only from a practical point of view, where one might be interested in the conditions for which a signal can be amplified without distortion, but also from the fundamental point of view of understanding the quantum-mechanical Raman process. To test these predictions, we consider the specific case of a Mach-Zehnder interferometer with a Raman amplifier in each leg of the interferometer. The input signal is provided by a separate Raman generator. As the input signal is varied from a small input to a large input, the fringe visibility varies from essentially zero, indicating that the noise dominates the output pulse, to nearly unity, as the amplified input signal dominates the noise. Using the Raman equations, we find that surprisingly few photons are predicted to be necessary for the signal to dominate the noise. The present work is devoted to measuring these fringes experimentally.

DOI: 10.1364/oam.1990.tunn1

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Quantum mechanics fundamentally requires any linear amplifier to introduce quantum noise onto the amplified signal.1 In the case of the linear Raman amplifier, the fully quantum-mechanical Raman equations give a precise prediction of how much noise is introduced.2 Understanding and testing this prediction is important not only from a practical point of view, where one might be interested in the conditions for which a signal can be amplified without distortion, but also from the fundamental point of view of understanding the quantum-mechanical Raman process. To test these predictions, we consider the specific case of a Mach-Zehnder interferometer with a Raman amplifier in each leg of the interferometer. The input signal is provided by a separate Raman generator. As the input signal is varied from a small input to a large input, the fringe visibility varies from essentially zero, indicating that the noise dominates the output pulse, to nearly unity, as the amplified input signal dominates the noise. Using the Raman equations, we find that surprisingly few photons are predicted to be necessary for the signal to dominate the noise. The present work is devoted to measuring these fringes experimentally.

We have measured the quantum noise added to a signal by a Raman amplifier. This was done using a modified Mach-Zender interferometer with an amplifier placed in each leg. Quantum noise added by the amplifiers manifests itself by degrading the visibility of the ensemble-average output fringe patterns. The amount of noise added by the amplifiers is deduced from the degradation of the visibility. The experimental results are compared with both ideal, single-mode amplifier theory and Raman theory. We find that the Raman amplifier operates near the quantum limit with only a few input photons per mode required to dominate the noise added by the amplifiers.

By utilizing amplifiers in a modified interferometer, both particlelike and wavelike characteristics of single input photons are analyzed theoretically. Quantum theory predicts that proposed measurements on the amplified field will indicate that the single input photon exhibits extremes of both wavelike and particlelike characteristics. The evidence for wavelike behavior is fringe visibility at the output of the interferometer. Anticorrelation between the outputs of the two legs of the interferometer provides the evidence for particlelike behavior. Although quantum noise degrades both the particle-sensitive and the wave-sensitive measurement, no trade-off between the wavelike and the particlelike characteristics takes place. Complementarity, however, is maintained by the quantum noise added during amplification.

Using Caves's theory on the quantum-noise limit in an amplifier, we consider the quantum limit on noise in a Raman amplifier. We show explicitly that the full quantum equations for the Raman interaction can be transformed into the general form for a quantum amplifier. In addition, we show that in the steady-state limit the Raman amplifier becomes a phase-insensitive amplifier. At this limit we find that the output signal-to-noise ratio is unity when one photon per mode is input. Thus we conclude that the Raman amplifier, in the phase-insensitive limit, will operate at the quantum-noise limit.

We present an extension of Glauber's theory of the Mach-Zehnder interferometer with optical amplifiers placed in each of its internal paths. Conditions are derived for the achievement of maximum fringe visibility with amplifiers of general linear characteristics. The effects of the phase-conjugated and the phase-preserved components of the amplified light are elucidated for the contrasting cases of coherent and number-state inputs. Particular attention is paid to the minimization of amplifier noise in the limit of high gain.

How much noise does quantum mechanics require a linear amplifier to add to a signal it processes? An analysis of narrow-band amplifiers (single-mode input and output) yields a fundamental theorem for phase-insensitive linear amplifiers; it requires such an amplifier, in the limit of high gain, to add noise which, referred to the input, is at least as large as the half-quantum of zero-point fluctuations. For phase-sensitive linear amplifiers, which can respond differently to the two quadrature phases ("$cos\ensuremath{\omega}t$" and "$sin\ensuremath{\omega}t$"), the single-mode analysis yields an amplifier uncertainty principle---a lower limit on the product of the noises added to the two phases. A multimode treatment of linear amplifiers generalizes the single-mode analysis to amplifiers with nonzero bandwidth. The results for phase-insensitive amplifiers remain the same, but for phase-sensitive amplifiers there emerge bandwidth-dependent corrections to the single-mode results. Specifically, there is a bandwidth-dependent lower limit on the noise carried by one quadrature phase of a signal and a corresponding lower limit on the noise a high-gain linear amplifier must add to one quadrature phase. Particular attention is focused on developing a multimode description of signals with unequal noise in the two quadrature phases.