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Chinese Physics Letters

Geometric Phases for Photons in an Optical Fibre and Some Related Predictions

Gao Xiao-Chun

Published Apr 18, 2002• 16 citations
Publisher

Abstract

We propose a quantum electrodynamic model for the description of the time evolution of the quantum states of the photons in an optical fibre. By means of this model, we are able to make three interesting predictions related to the geometric phases for photons.
DOI
10.1088/0256-307x/19/5/302

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The propagation of monomode photons inside a coiled optical fibre was regarded as a time-dependent quantum evolution process, which gives rise to a geometric phase. It is well known that the investigation of non-adiabatic geometric phases ought to be performed only in the Schrödinger picture. So, the projections of photon spin operators onto the fixed frame of reference is discussed in this paper. In addition, we also treat the non-normal-order spin operators and consider the potential effects (e.g., quantum-vacuum geometric phases) of quantum fluctuation fields arising in a curved optical fibre. The quantum-vacuum geometric phase, which is of physical interest, can be deducted by using the operator normal product, and the doubt of validity and universality for the normal-normal procedure applied to time-dependent quantum systems is thus proposed. In the Appendix, the discussion of possible experimental realizations of quantum-vacuum geometric phases is briefly presented.
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.
High-dimensional quantum cryptography through optical fibres with several spatial modes requires an efficient quantum key distribution (QKD). However, optical modes acquire different phases and lags due to modal dispersion and random fluctuations, and a modal crosstalk appears under propagation. At present, special optical fibres for spatial multiplexing are being proposed in order to reduce notably the modal crosstalk, however, arbitrary relative phases and lags between modes are always present, which prevents getting an efficient phase encoding QKD. In this work, we take advantage of elliptical-core few-mode optical fibres presenting a very low modal crosstalk and propose an exact phase auto-compensating method by making photons travel several times the path between Alice and Bob (rounds) and by using appropriate modal inversions in each round trip. In order to make clear the proposed phase auto-compensating method, we study in detail a four-dimensional BB84 QKD case with single photon states excited in both polarization and spatial LP modes.