Invariant operator theory for the single-photon energy in time-varying media

doi:10.1088/1674-1056/19/1/010306

摘要/Abstract

摘要： After the birth of quantum mechanics, the notion in physics that the frequency of light is the only factor that determines the energy of a single photon has played a fundamental role. However, under the assumption that the theory of Lewis--Riesenfeld invariants is applicable in quantum optics, it is shown in the present work that this widely accepted notion is valid only for light described by a time-independent Hamiltonian, i.e., for light in media satisfying the conditions,ε(t)=ε(0), μ(t)=μ(0), and σ(t)=0 simultaneously. The use of the Lewis--Riesenfeld invariant operator method in quantum optics leads to a marvelous result:the energy of a single photon propagating through time-varying linear media exhibits nontrivial time dependence without a change of frequency.

Abstract: After the birth of quantum mechanics, the notion in physics that the frequency of light is the only factor that determines the energy of a single photon has played a fundamental role. However, under the assumption that the theory of Lewis--Riesenfeld invariants is applicable in quantum optics, it is shown in the present work that this widely accepted notion is valid only for light described by a time-independent Hamiltonian, i.e., for light in media satisfying the conditions, $\varepsilon(t)=\varepsilon(0)$, $\mu(t)=\mu(0)$, and $\sigma(t)=0$ simultaneously. The use of the Lewis--Riesenfeld invariant operator method in quantum optics leads to a marvelous result:the energy of a single photon propagating through time-varying linear media exhibits nontrivial time dependence without a change of frequency.

Key words: single-photon energy, invariant operator theory, time-varying media

中图分类号: (Quantum optics)

42.50.-p

02.30.Tb (Operator theory) 32.80.-t (Photoionization and excitation)

ChoiJeong-Ryeol. Invariant operator theory for the single-photon energy in time-varying media[J]. 中国物理B, 2010, 19(1): 10306-010306.

Choi Jeong-Ryeol. Invariant operator theory for the single-photon energy in time-varying media[J]. Chin. Phys. B, 2010, 19(1): 10306-010306.

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