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Physical Review Letters

Interferometric measurement of quantum noise in a Raman amplifier

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

Published Jul 1, 1991• 15 citations
Publisher

Abstract

How large must the input signal to an amplifier be to dominate the quantum noise introduced during amplification? We attempt to answer this question for a Raman amplifier with an experiment that utilizes a modified Mach-Zender interferometer with an amplifier placed in each leg. The quantum noise added by the amplifiers manifests itself by degrading the visibility of the output fringes from the interferometer. Only an average of a few photons per mode were necessary to achieve good visibility.

DOI
10.1103/physrevlett.67.38

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Physical Review A•Aug 1, 1991•13 citations
How large must the input signal to an amplifier be to dominate the quantum noise introduced during amplification? We attempt to answer this question for a Raman amplifier with an experiment that utilizes a modified Mach-Zender interferometer with an amplifier placed in each leg. The quantum noise added by the amplifiers manifests itself by degrading the visibility of the output fringes from the interferometer. Only an average of a few photons per mode were necessary to achieve good visibility.
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.
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.
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.
Any amplifier requires coupling to its internal degrees of freedom for energy gain. This coupling introduces extra quantum noise to the output. On the other hand, if the internal degree of the amplifier can be accessed and manipulated, we can manage and even reduce the quantum noise of the amplifier's output. In this Letter, we present an experiment to reduce the quantum noise of a Raman amplifier by preparing the atomic medium in a correlated state with the Stokes light field. We report an observation of quantum noise reduction of more than 3.5 dB in the atomic Raman amplification process. From another perspective, the Raman amplifier at high gain in turn serves as a measurement tool for the quantum correlation between the atom and light. Furthermore, such a scheme, when viewed as a whole, also forms a quantum-entangled atom-light hybrid interferometer that can lead to quantum-enhanced sensors.
Probing the quantum noise level with respect to a coherent input has recently received much attention. Several researchers have probed this question by examining the level of external optical input needed to influence the output field of a quantum noise amplifier. For example, it has been found that it takes, on average, about one photon per (temporal) mode to control the phase of the output field of a Raman amplifier.1 A similar result has been seen in optical parametric amplification.2 In contrast to using light to seed the amplification, we have investigated the level of initial molecular coherence needed to control the phase of the output field of a Raman amplifier. Two laser pulses, separated in time, were used to pump a common set of hydrogen molecules producing two Stokes pulses via stimulated Raman scattering. The relative phase of the two Stokes pulses was measured interferometrically. The variance of this relative phase is a direct measure of the memory of the molecular coherence that was induced by the first scattering process. Correlations between the two Stokes phases were observed even after nine molecular dephasing times, when the level of coherence had decayed by a factor of e−9. We show that this extraordinarily long-lived phase memory comes about because a molecular coherence corresponding to order ten vibrational photons per mode is sufficient to influence the phase of the output field.
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.