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Optics Express

Phase-sensitive amplification via multi-phase-matched four-wave mixing

Erin M. Knutson, J. Sam Cross, Sara K. Wyllie, Ryan T. Glasser

Published Jun 24, 2020• 6 citations
Publisher

Abstract

Phase-sensitive nonlinear gain processes have been implemented as noise-reduced optical amplifiers, which have the potential to achieve signal-to-noise ratios beyond the classical limit. We experimentally demonstrate a novel phase-sensitive four-wave mixing amplification process in a single atomic vapor cell with only two input frequencies and two input vacuum modes. The amount of phase sensitivity depends on the power ratio between the inserted probes as well as on the input frequency of the probes. We find that, for certain phase values, the intensity noise of an output mode is lower than that of its phase-insensitive counterpart.

DOI
10.1364/oe.396234

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Phase-sensitive nonlinear gain processes have been implemented as noise-reduced optical amplifiers, which have the potential to achieve signal-to-noise ratios beyond the classical limit. We experimentally demonstrate a novel phase-sensitive four-wave mixing amplification process in a single atomic vapor cell with only two input frequencies and two input vacuum modes. The amount of phase sensitivity depends on the power ratio between the inserted probes as well as on the input frequency of the probes. We find that, for certain phase values, the intensity noise of an output mode is lower than that of its phase-insensitive counterpart.
We implement a noiseless optical amplifier using a phase-sensitive four-wave mixing process in rubidium vapor. We observe performance near the quantum limit for this type of amplifier over a range of experimental parameters and show that the noise figure is always better than would be obtained with a phase-insensitive amplifier with the same gain. Additionally, we observe that the amplifier supports hundreds of spatial modes, making it possible to amplify complex two-dimensional spatial patterns with less than a 10% degradation of the input signal-to-noise ratio for gains up to 4.6. To confirm the multimode character of the amplifier, we study the noise figure as a function of spatially-varying losses. Additionally, we investigate the spatial resolution of the amplifier and show that it supports a range of spatial frequencies from 1.3 to more than 35 line pairs per millimeter.
Abstract Phase sensitive amplifiers (PSA), contrary to usual phase insensitive amplifiers (PIA), are in principle capable to achieve noiseless amplification, i.e. exhibit a quantum-limited noise figure (NF) of 0 db. When implemented using four-wave mixing (FWM) in a non-linear fibre, extra waves can be generated by undesired FWM processes, which may introduce extra input ports for vacuum fluctuations, thus potentially degrading the NF. In this situation, we give here a general analytical quantum derivation of the PSA NF, valid for an arbitrary number of nonlinearly coupled modes. This expression is usable as soon as a linear input-output relation can be found for the annihilation and creation operators of the involved modes. It predicts that the noise level depends on the number of interacting waves. We illustrate the usefulness of this expression in the case of six waves, corresponding to four interacting quantum modes. In this example the signal NF is degraded by 0.4 db, compared to 10 db obtained for PIA operation of the same scheme.
Optical parametric amplifiers rely on second-order susceptibility (three-wave mixing) or third-order susceptibility (four-wave mixing) in a nonlinear process where the energy of incoming photons is not changed (elastic scattering). In the latter case, two pump photons are converted to a signal and to an idler photon. Under certain conditions, related to the phase evolution of the waves involved, this conversion can be very efficient, resulting in large amplification of an input signal. As the nonlinear process can be very fast, all-optical applications aside from pure amplification are also possible. If the amplifier is implemented in an optical input-phase-sensitive manner, it is possible to amplify a signal wave without excess noise, i.e., with a noise figure of 0 dB. In this paper, we will provide the fundamental concepts and theory of such amplifiers, with a focus on their implementation in highly nonlinear optical fibers relying on four-wave mixing. We will discuss the distinctions between phase-insensitive and phase-sensitive operation and include several experimental results to illustrate their capability. Different applications of parametric amplifiers are also discussed, including their use in optical communication links.
According to the fundamental laws of quantum optics, vacuum noise is inevitably added to the signal when one tries to amplify a signal. However, it has been recently shown that noiseless signal amplification can be realized when a phase-sensitive process is involved. Two phase-sensitive schemes, a correlation injection scheme and a two-beam phase-sensitive amplifier scheme, are both proposed to realize multi-way noiseless signal amplification in a symmetrical cascaded four-wave mixing process. We theoretically study the possibility of the realization of four-way noiseless signal amplification by using these two schemes. The results show that the correlation injection scheme can only realize one-way noiseless signal amplification, but that the two-beam phase-sensitive amplifier scheme can lead to four-way noise figure values below 1. Our results here may find potential applications in quantum information processing, e.g., the realization of quantum information tap and quantum non-demolition measurement, etc.
We propose a new architecture of phase sensitive optical frequency converter based on dual-pump phase sensitive amplification in a highly nonlinear fiber. This frequency converter allows generation of extra tones through nonlinear four-wave mixing between two strong pumps and an input tone. The frequency channel to which the input tone is converted can be chosen by adjusting the phase of the input signal. The conversion efficiency and extinction ratio of this frequency converter are predicted and optimized and its noise figure is calculated using a numerical approach based on the nonlinear Schrödinger equation. A semi-classical noise figure calculation for this approach was used and validated using an analytical fully quantum calculation based on the multi-wave model.