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arXiv:2409.09813 · Physical Review A

Mode hitching in traveling-wave optical parametric amplification

Joseph Kelly, Eleanor Fradgley, Lida Zhang, Vincent Boyer

Published Mar 21, 2025• 0 citations
arXivHTMLPDF

Abstract

Optical parametric amplifiers (OPAs) in traveling-wave configuration can generate localized spatial quantum correlations between a signal and an idler beam, a useful resource for quantum imaging. To characterize the spatial correspondence between the optical modes of the signal and those of the idler, we look at the classical transverse dynamics of these beams when they propagate in a generic thick OPA at a nominally small angle. In these conditions, the beams tend to copropagate while maintaining a fixed separation, a phenomenon that we term hitching. We develop a model for hitching, validated by a numerical simulation, and provide an experimental demonstration using four-wave mixing in a hot atomic vapor. They show that the OPA gain is the primary influence on the final hitching distance. These results have implications for the generation of multi-spatial-mode squeezed light for quantum imaging applications, where the exact spatial correlations between the quantum fluctuations of the signal and the idler are of prime importance.

DOI
10.1103/physreva.111.033523

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Optical parametric amplifiers (OPAs) in traveling-wave configuration can generate localized spatial quantum correlations between a signal and an idler beam, a useful resource for quantum imaging. To characterize the spatial correspondence between the optical modes of the signal and those of the idler, we look at the classical transverse dynamics of these beams when they propagate in a generic thick OPA at a nominally small angle. In these conditions, the beams tend to copropagate while maintaining a fixed separation, a phenomenon that we term hitching. We develop a model for hitching, validated by a numerical simulation, and provide an experimental demonstration using four-wave mixing in a hot atomic vapor. They show that the OPA gain is the primary influence on the final hitching distance. These results have implications for the generation of multi-spatial-mode squeezed light for quantum imaging applications, where the exact spatial correlations between the quantum fluctuations of the signal and the idler are of prime importance.
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Optical parametric amplifiers (OPA's) and optical parametric oscillators (OPO's) can exhibit squeezed amplification when an injected signal beam is used to elicit small-signal gain saturation. This paper extends previous work on OPA/OPO noise behavior under signal injection. Doubly resonant and triply resonant, single-ended cavities are considered in the good-cavity limit. Owing to the nonlinear coupling between the signal and idler beams within the cavity, both are sensitive to the detuning of each beam from its respective resonance. Signal and idler output noise spectra are found by linearizing the quantum coupled-mode equations about the classical mean-field solutions. Cavity detunings lead to frequency dependent phase shifts between the low-noise and high-noise quadratures of both the signal and idler beams. Moreover, the phase of the low-noise quadrature need not coincide with that of the corresponding mean field. The resulting large-signal, signal-to-noise ratio improvement afforded by squeezed amplification is therefore sensitive to the cavity detunings. The effects of classical excess noise on the pump beam and the injected signal beam are also considered.
We investigate amplification of optical images by means of a traveling-wave optical parametric amplifier. As shown recently by Kolobov and Lugiato [Phys. Rev. A 52, 4930 (1995)] for a cavity-based geometry, such a scheme can amplify images, without deteriorating their sign-to-noise ratio, thus working as a noiseless amplifier. Here we consider a configuration without cavity, which is more realistic for a possible experimental realization. We investigate in detail the quantum fluctuations of the amplifier and formulate criteria for its noiseless performance. The spatial resolution power, which guarantees noiseless amplification is estimated. We demonstrate how the optimum phase matching of a phase-sensitive wavefront of the image can improve the noise performance of the amplifier and bring it to the ultimate value achievable under given physical conditions. We discuss the effect of improvement of the signal-to-noise ratio in the case of observation of both the input and the amplified image, with an ideal photodetector of small area (i.e., much less than the coherence area of the amplifier). This improvement is due to the fact that the signal-to-noise ratio in the input is deteriorated by the observation with the photodetector of small area.
Abstract: We have performed a quantum mechanical analysis of travelling-wave parametric amplifiers (TWPAs) in order to investigate five experimental phenomena related to their operations, namely the effect of impedance mismatch, the presence of upper idler modes, the presence of quantum and thermal noise, the generation of squeezed states, and the preservation of pre-squeezed states during amplification. Our analysis uses momentum operators to describe the spatial evolution of quantised modes along a TWPA. We calculate the restriction placed on pump amplitude as well as amplifier gain as a result of impedance mismatch between a TWPA and its external system. We apply our analysis to upper idler modes and demonstrate that they will result in suppressed gain. We show that an ideal TWPA is indeed quantum-limited—i.e. it introduces a half-quantum of zero-point fluctuation which is the minimum possible noise contribution for a phase-preserving linear amplifier. We analyse the thermal noise associated with a TWPA by considering the effect of distributed sources along an amplifier transmission line. Our analysis predicts a doubling of thermal noise in the high gain limit as a result of wave-mixing between signal and idler modes. We study the operation of a TWPA in the presence of a DC bias current, and have shown that highly squeezed states can in principle be generated. However, amplifying a pre-squeezed state using a non-degenerate TWPA generally reduces the squeezing advantage.