Quantum theory, as normally formulated, describes systems enclosed in an artificial box through its time evolution. In some systems, such as a laser, the box may be a physical element such as a cavity. In optical fibre communications the situation is somewhat different. The optical field is continuously generated by a source such as a laser. Once generated the field propagates along an optical fibre and is detected in some form of receiver at the far end. Quantum theory, with its reliance on Hamiltonian systems necessarily conserves the total energy in the system whereas fibre communication is better described as a balance between sources and sinks. Under these circumstances it may be more appropriate to describe the spatial evolution of the field [1], [2], [3]. In this paper we describe an approach to the study of quantum propagation in optical fibres. The discussion will be based on the description of single mode weakly guiding fibres so that a one dimensional scalar wave equation can be used to describe the electric field.
Quantum theory, as normally formulated, describes systems enclosed in an artificial box through its time evolution. In some systems, such as a laser, the box may be a physical element such as a cavity. In optical fibre communications the situation is somewhat different. The optical field is continuously generated by a source such as a laser. Once generated the field propagates along an optical fibre and is detected in some form of receiver at the far end. Quantum theory, with its reliance on Hamiltonian systems necessarily conserves the total energy in the system whereas fibre communication is better described as a balance between sources and sinks. Under these circumstances it may be more appropriate to describe the spatial evolution of the field [1], [2], [3]. In this paper we describe an approach to the study of quantum propagation in optical fibres. The discussion will be based on the description of single mode weakly guiding fibres so that a one dimensional scalar wave equation can be used to describe the electric field.
The transmission of light through optical fibre has traditionally been governed by classical electromagnetic theory. However, increasing interest in quantum communication, quantum-limited amplification, and photonic quantum technologies necessitates a quantum mechanical treatment of guided light. This study presents a theoretical investigation into the application of quantum field theory and quantum noise models to light propagation in optical fibres. We formulate a quantized waveguide model, examine decoherence and photon statistics, and analyse implications for quantum communication and sensing. The results demonstrate that quantum theoretical approaches provide deeper insights into noise limits, entanglement preservation, and nonlinear photon interactions, offering pathways for next-generation quantum-enabled fibre networks.
The electromagnetic fields of a single optic fibre mode are quantized based on the observation that these fields can be derived from a scalar harmonic oscillator function depending on only time and the axial wavenumber. Asymptotic results for both the one-photon probability density and two-photon correlation density functions within the forward light cone are presented, showing an algebraic decay for large times or distances. This algebraic decay, increasing the uncertainty in the arrival time of the photons, also remains in the presence of dispersion shift, in qualitative agreement with experimental results. Also presented are explicit formulae to be used in parameter studies to optimize quantum optic fibre communications.
We analyze the quantum dynamics of radiation propagating in a single-mode optical fibre 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 fibre-optics communications, networking, and sensor technology.
There are two optic fibre properties in particular that obstruct the transfer over long distances in quantum communications. One of them is dispersion, which reduces the maximum bit rate. In classical communication with modern highly purified fibres, dispersion is the major limiting factor. The other property is the material loss that causes fluctuations in addition to a general annihilation with distance of photons. It is believed that losses are the major limiting factor in quantum communication over long distances if the bit rate is not an issue. Of major interest in quantum communication is the photon source. It is therefore a high priority to develop methods for the determination of properties like initial temporal modes, repeatability, independence of sequentially emitted photons, etc., for a source emitting single photons in a given spatial mode. In the current paper we suggest that the source properties can be estimated using statistics of the run times of the photons. This requires that the fibre is modelled with sufficient accuracy. To simplify the analysis, it is assumed that the fibre losses can be neglected and that the photons are independent and identically generated. Energy detection in one spin state is employed, making the modelling scalar. The one photon initial temporal mode is found by maximizing a maximum–likelihood function based on running time statistics. Unfortunately, this optimization problem is, in general, not convex. However, for photon detection in the so-called asymptotic radiation zone, where the probability density can be determined to a sufficient degree with asymptotic methods, the optimization problem is convex. In the current paper, quantum tomography in fibres based on this convex optimization method is presented, and its generalization to more complicated situations like the introduction of losses in the modelling is discussed.
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.
Starting with the canonical quantization procedure for the electromagnetic field inside an effective (linear or nonlinear) medium, we present a direct-space formulation of the theory of quantum optics. This approach does not use the conventional modal decomposition of the field, but relies on the electromagnetic momentum operator defined in terms of local electric- and magnetic-field operators. The momentum operator contains all the information on the spatial characteristics of the field, and can describe the translation of a short light pulse in a nonlinear medium, without a modal analysis of the pulse. Propagation is described through an operatorial wave equation that relates the temporal evolution of an electromagnetic pulse to its spatial progression. Through this equation, the direct-space approach to quantum optics can treat traveling-wave nonlinear-optical phenomena and, at the same time, account for their quantum statistics. The theory is applied to squeezed-light generation by the parametric down-conversion of a short laser pulse, as an illustration.