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.
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.
Intense light beams propagating in a lossless, dispersionless, single-mode optical fiber are subject to the Kerr effect, i.e., to the intensity-dependent refractive index of the fiber’s fused-silica core. Classically, Kerr-effect-induced self-phase modulation (SPM) can be used for spectral broadening of a picosecond pulse for grating-pair pulse compression down to femtosecond duration. Quantum mechanically, Kerr-effect-induced four-wave mixing (FWM) has been used to produce squeezed-state light. We present a quantum propagation theory for a lossless, dispersionless fiber with the Kerr nonlinearity. The theory includes classical SPM and quantum FWM within their regions of validity. It introduces a material time constant for the Kerr interaction, limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any input field, to develop a coarse-grained time multitemporal mode field analysis. Explicit expressions are obtained for the first and the second output-field moments when the fiber’s input field is in an arbitrary Gaussian state. These results are used to obtain homodyne-detection noise spectra, which are employed, in turn, to seek experimentally accessible manifestations of the Kerr time constant.
We analyze the quantum dynamics of radiation propagating in a single-mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum-noise sources, including linear gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This treatment allows quantum Langevin equations, which have a classical form except for additional quantum-noise terms, to be calculated. In practical calculations, it is more useful to transform to Wigner or +P quasi-probability operator representations. These transformations result in stochastic equations that can be analyzed by use of perturbation theory or exact numerical techniques. The results have applications to fiber-optics communications, networking, and sensor technology.
We analyze the quantum dynamics of radiation propagating in a single mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum noise sources, including linear gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This allows quantum Langevin equations to be calculated, which have a classical form except for additional quantum noise terms. In practical calculations, it is more useful to transform to Wigner or +P quasi-probability operator representations. These result in stochastic equations that can be analyzed using perturbation theory or exact numerical techniques. The results have applications to fiber optics communications, networking, and sensor technology.
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.
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.
Classical optical solitons propagate in optical fibers without temporal or spectral distortion as a result of a balance between phase shifts due to group velocity dispersion and those due to nonlinear self-phase modulation. This balance is achieved by the proper choice of pulse shape and duration for a given pulse energy. The quantum fluctuations associated with a coherent soliton do not undergo stationary propagation, however, and a number of effects are predicted, including the evolution of vacuum noise associated with the input coherent pulse into squeezed fluctuations and the temporal spreading of the soliton pulse because of dispersion acting on quantum fluctuations of the pulse frequency.