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Chinese Physics Letters

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

高孝纯

Published Jan 1, 2002• 0 citations
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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 th make three interesting predictions related to the geometric phases for photons.

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

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arXiv:quant-ph/0304172•Apr 28, 2003•0 citations
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.
An experimental arrangement is proposed which combines the idea of two-photon interferometry with that of geometric phases. A pair of photons generated by parametric down-conversion is fed into a pair of Mach-Zehnder interferometers, in each of which there is phase shift produced by the helically wound optical fibre in the manner of Tomita and Chiao(1986). If the winding angle is a multiple of 2 pi there is a closed path in parameter space, in accordance with the pioneering analysis of Berry(1984). More general windings are also considered in which the path in parameter space is not closed, and the geometric phase for such open paths is calculated in accordance with the gauge-invariant prescription of Aitchison and Wanelik. If the proposed experiment is realized, it will provide a test for the noncyclic geometric phase for photons and for the set of prescriptions equivalent to that of Aitchison and Wanelik(1992). Furthermore, the geometric phase in this arrangement will be unequivocally quantum mechanical because of the non-classical character of two-photon interferometry.
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 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.