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Journal of Modern Optics

Theory of the Double-amplifier Interferometer

N. Hussain, R. Loudon

Published Dec 1, 1989• 2 citations
Publisher

Abstract

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.

DOI
10.1080/09500348914551781

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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.
This paper investigates the gain characteristics of coherent optical amplifiers that amplify only one of two quadrature phase components in an input signal light according to the phase of pump light. It is constructed around a Mach-Zehnder interferometer with Kerr media. To heuristically obtain the design parameters of the coherent optical amplifier, small-signal analysis is adapted to the Mach-Zehnder interferometer with Kerr media. The theoretical results are then compared to experimental results and shown to agree well, which confirms the validity of this design approach. By utilizing low-loss and high-nonlinearity silica fiber as the Kerr medium and optimizing its length, a coherent optical amplifier is constructed that yields high-gain (up to 26 dB) operation.
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.
The characteristics of the quantum optical complementarity principle and the coherence of the photons generated in a Mach-Zehnder interferometer with two degenerate optical parametric amplifiers are analysed. The photon statistics and the phase fluctuation of the combined states are analysed in a homodyning Mach-Zehnder interferometer with two degenerate optical parametric amplifiers. By analysing the photon statistics, the mean-square phase fluctuation and the fringe visibility, the complementarity is considered as a function of the gain and input phase, when the amplified input is a coherent state containing one photon, on average. It is also considered when the input is a number state with one photon.
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.
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.