We put forth an approach to obtain a quantum master equation for the propagation of light in nonlinear fiber optics by relying on simple quantum pictures of the processes (linear and nonlinear) occurring along propagation in an optical fiber. This equation is shown to be in excellent agreement with the classical Generalized Nonlinear Schrodinger Equation and predicts the effects of self-steepening and spontaneous Raman scattering. Last, we apply these results to the analysis of two cases of relevance in quantum technologies: single-photon frequency translation and spontaneous four-wave mixing.
We put forth an approach to obtain a quantum master equation for the propagation of light in nonlinear fiber optics by relying on simple quantum pictures of the processes (linear and nonlinear) occurring along propagation in an optical fiber. This equation is shown to be in excellent agreement with the classical Generalized Nonlinear Schrodinger Equation and predicts the effects of self-steepening and spontaneous Raman scattering. Last, we apply these results to the analysis of two cases of relevance in quantum technologies: single-photon frequency translation and spontaneous four-wave mixing.
In this Letter, we revisit the quantum theory of propagation in nonlinear fibers. Unlike previous works, we present an effective propagation equation for the reduced density matrix of the complex envelope of the electric field. This original proposal is shown to be in agreement with the theory of quantum noise in fibers and puts forth a powerful tool for the study of fiber-based quantum devices. To underscore its applicability, we analyze the performance of a heralded single-photon scheme in terms of probabilities, an approach that conveniently lends itself to the optimization of such sources.
In this Letter we introduce a novel equation addressing the effect of quantum noise in optical fibers with arbitrary frequency-dependent nonlinear profiles. To the best of our knowledge, such an endeavor has not been undertaken before despite the growing relevance of fiber optics in the design of new quantum devices. We show that the stochastic generalized nonlinear Schrödinger equation, derived from a quantum theory of optical fibers, leads to unphysical results such as a negative photon number and the appearance of a dominant anti-Stokes sideband when applied to this kind of waveguides. Starting from a recently introduced master-equation approach to propagation in fibers, we derive a novel stochastic photon-conserving nonlinear Schrödinger equation suitable for modeling arbitrary nonlinear profiles, thus greatly enhancing the study of fiber-based quantum devices.
We present a quantum theory for generating two-photon states by means of four-wave mixing in optical fiber. We start with an interaction Hamiltonian that can correctly describe all nonlinear interactions among the four waves present in the fiber, namely, the frequency non-degenerate pumps, signal, and idler, including the terms responsible for self-phase modulation (SPM), cross-phase modulation (XPM), and four-photon scattering (FPS). The exact form of this Hamiltonian is obtained through comparison between the classical and quantum equations of motion. The two-photon state is then calculated by means of first-order perturbation theory. It turns out that only the FPM and the pump SPM terms contribute to the formation of the two-photon state. The entangled nature of this state is verified in a coincidence counting experiment. The results of the theoretical calculation agree well with experimental data.
We theoretically reveal the potential of the parallelism of squeezed state generation by nonlinear pulse propagation in an optical fiber. Starting from a nonlinear Schr\"odinger equation coupling with phonon modes that cause Raman noise, we develop a multimode quantum theory of nonlinear propagation in an optical fiber. Based on our proposed method, we numerically simulate fiber nonlinear propagation in two conditions: solitonlike and zero-group-delay-dispersion (zero-GVD) propagation. As a result, we find that zero-GVD propagation enables the large-scale parallel generation of squeezed states relative to solitonlike propagation owing to the broadband phase matching of the four-wave mixing process.
As is well known, quantum optics has developed significantly in recent years and advanced several hot research topics, such as quantum communications, quantum sensing, quantum calculations, etc. Among these researches, it is important to understand the quantum information transmitting in optical fiber. For realizing longer transmission distance and better transmission quality, great effort has devoted to the researches of encoding and decoding at the transmitter and the receiver end. However, less attention was paid to the fading of signal in the transmission channel. In this work, we mainly focus on the transmission model of optical quantum transmission and the influences of loss, dispersion and nonlinear effect on fiber transmission of optical quantum information are also discussed.Quantum information transmission can be influenced by loss, dispersion and nonlinear effect in optical fiber, leading to transmission state evolution and energy transfer. Based on the transmission equation of single mode fiber and quantum theory of electromagnetic field, the fundamental mode field of single mode fiber is quantized. A quantum transmission equation is deduced from the classical optical transmission equation through quantizing the amplitude of electromagnetic field. Compared with classic wave theory, the photon transmission equation quantizing the slowly-varying amplitude in the coupled nonlinear Schrdinger equation is obtained. In the classic wave equation, light is interpreted as energy which propagates as waves. The photon transmission equation is obtained by quantizing the slowly-varying amplitude of light, that is, the particle nature of light. The energy propagates through alternative interaction between creation and annihilation operator on photons. The transmission equations show that photons will interact with the transmission medium during propagation and be influenced by dispersion, nonlinear effect, loss, etc. By giving a trail solution and introducing a perturbation term, the transmission equation is solved for the complicated case where the dispersion, loss and nonlinear effect are all involved. A dispersion equation that should be satisfied for nontrivial solution is then obtained. From this dispersion equation, the relation between photon power and perturbation frequency is calculated and analyzed. The change of photon power in generalized field with perturbation frequency is discussed, and the influences of fiber dispersion and nonlinearity on the solution are analyzed.Some conclusions are obtained by perturbed solution and analyses of single photon transmission equation in optical fiber. It is found that photon power decreases with the increase of perturbation frequency and reaches its maximum value for zero perturbation frequency. At the same time, the optical power is affected by the dispersion of the optical fiber. Photon power decreases with the GVD coefficient far from the zero dispersion point. It is also found that photon power decreases with the increase of nonlinear coefficient. This work may contribute to the research of the properties of quantum fiber transmission system.
This paper presents a theory for quantum light propagation in a single-mode fiber which includes the effects of the Kerr nonlinearity, group-velocity dispersion, and linear loss. The theory reproduces the results of classical self-phase modulation, quantum four-wave mixing, and classical solution physics, within their respective regions of validity. It demonstrates the crucial role played by the Kerr-effect material time constant, in limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any quantized input field. Operator moment equations - approximated, numerically, via a terminated cumulant expansion - are used to obtain results for homodyne-measurement noise spectra when dispersion is negligible. More complicated forms of these equations can be used to incorporate dispersion into the noise calculations.