Phase-sensitive amplification (PSA) based on nonlinear parametric interaction provides low-noise amplification such that the noise figure can be 0 dB in principle. However, when an optical fiber is used as a nonlinear medium for PSA, multiple four-wave-mixing (FWM) processes other than the PSA process are induced, which can degrade the PSA noise performance, especially in dual-pump PSA with a narrow signal-pump wavelength separation. This paper investigates the influence of multiple FWM processes on quantum noise of dual-pump PSA in an optical fiber. The noise figure is calculated using quantum-mechanical operators, considering multiple FWM processes with the PSA process. Calculation examples are also presented, which indicate that the noise figure is degraded by 0.2–0.4 dB from the ideal 0 dB, depending on the signal-pump wavelength separation and fiber parameters.
Phase-sensitive amplification (PSA) based on nonlinear parametric interaction provides low-noise amplification such that the noise figure can be 0 dB in principle. However, when an optical fiber is used as a nonlinear medium for PSA, multiple four-wave-mixing (FWM) processes other than the PSA process are induced, which can degrade the PSA noise performance, especially in dual-pump PSA with a narrow signal-pump wavelength separation. This paper investigates the influence of multiple FWM processes on quantum noise of dual-pump PSA in an optical fiber. The noise figure is calculated using quantum-mechanical operators, considering multiple FWM processes with the PSA process. Calculation examples are also presented, which indicate that the noise figure is degraded by 0.2–0.4 dB from the ideal 0 dB, depending on the signal-pump wavelength separation and fiber parameters.
Phase-sensitive amplification (PSA) can provide low-noise signal amplification, and a quantum-limited noise figure of 0 dB, that is, additional noise-free amplification, is theoretically achievable. However, in fiber-based single-pumped PSA systems, it has been reported that Raman scattering in the fiber degrades the noise figure from the ideal 0 dB. In the present study, the influence of Raman scattering on quantum noise in dual-pumped degenerate PSA in a fiber is investigated. A quantum mechanical treatment starting from the Heisenberg equation of motion is developed, considering the parametric interaction and Raman interaction simultaneously, and an analytical expression for the noise figure is derived. An example of calculation is also presented, which quantitatively indicates the degradation in the noise figure due to Raman scattering.
Phase-sensitive amplification (PSA) is a unique optical amplification scheme, featuring a low-noise property (i.e., quantum limited noise figure of 0 dB) and a phase clamping effect available for phase noise suppression [1]. It is based on optical parametric interaction between signal and pump lights. It is known that the interaction efficiency and then the signal gain depend on the phase matching between those interacting lights. There are typically two frequency arrangements for PSA in an optical fiber: (i) one pump (frequency: fp) with signal (frequency: fs) and conjugated idler (frequency: fi) satisfying fs+ fi= 2fp[Fig. 1(a)], and (ii) two pumps (frequencies: fp1, fp2) with signal (frequency: fs) satisfying fp1+ fp2= 2fs[Fig. 1(b)]. The phase matching condition for the former is well known, which is equivalent to that of phase-insensitive amplification where the signal light is amplified without an idler incident, such that the phase matching is satisfied when the center wavelength of interacting lights is in the normal dispersion region, i.e., a wavelength longer than the zero-dispersion wavelength of a fiber, as indicated in Fig. 1(a) [2]. On the other hand, the phase-matching condition for the latter has not been explicitly investigated, to the author's knowledge. Although several experimental demonstrations of dual-pump fiber PSA have been reported, many of them employed the wavelength allocation of the center wavelength being in the normal dispersion region, without detailed considerations on the phase matching [3-6]. Thereupon, this paper studies the phase matching condition of dual-pump PSA in an optical fiber.
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.
Quantum noise fundamentally limits the performance of fiber-optic systems beyond the standard quantum limit (SQL), restricting long-distance quantum key distribution, quantum communication, and precision quantum sensing. To overcome these limitations, quantum-squeezed states enable quadrature-dependent noise suppression, yet their benefits rapidly degrade under fiber attenuation, necessitating low-noise amplification. Since conventional phase-insensitive amplifiers (PIAs) impose a minimum 3 dB noise figure (NF) penalty and disrupt quantum correlations, phase-sensitive amplification (PSA) becomes essential. In this work, we propose a PSA based on dual-pump frequency-degenerate four-wave mixing (FWM) to amplify weak coherent squeezed states. Here, the PSA is seeded by an information-carrying single-mode squeezed state, where the information is encoded in the displacement degree of freedom, rather than in the squeezing itself. By optimizing the relative phases among the squeezed state, pump fields, and weak signal, the scheme maintains proper squeezing alignment and preserves the encoded quantum correlations during propagation. Under low-loss conditions, it is shown that the effective NF reaches −7.787 dB, demonstrating that the scheme enables quantum-limited amplification suitable for long-haul transmission and offering a viable path toward scalable fiber-based quantum technologies.
A semi-classical seven-wave model is developed to investigate the noise performances of a degenerate dual-pump phase-sensitive amplifier. This approach takes into account the transfer to the signal, through multiple four-wave mixing processes, of the vacuum fluctuations injected into high-order waves. This effect leads to a degradation of the noise figure of the amplifier with respect to the 0 dB value predicted by the usual three-wave model. However, it is proved that a careful choice of the fiber dispersion allows us to use high-order waves to enhance the signal gain without degrading the noise figure above 1 dB.
Optical phase-sensitive amplifiers (PSAs) leverage nonlinear interactions to achieve noise figures below the conventional quantum limit. Dual-pump phase-insensitive amplification has been studied in wavelength conversion, phase conjugation and spectral inversion, but phase-sensitive amplification remains challenging due to stimulated Brillouin scattering (SBS) in optical fibers. While pump-phase modulation helps mitigate SBS, it broadens the idler spectrum, complicating practical implementation. We demonstrate a counter-phase pump modulation approach to suppress idler spectral broadening using optical coherent combining and delayed self-heterodyne techniques to achieve excellent noise figure (NF) performance in dual-pump PSAs. Our methods achieve over 30 dB suppression of residual phase modulation tones and significantly improve the idler spectrum. We obtained a 20 dB gain with an NF of 1.45 dB and a minimal NF penalty of 0.2 dB due to pump-phase modulation. This achievement enables PSAs to support optical communication, wavelength conversion, and deep-space communication applications.