Manifestation of classical phase in a single spontaneously emitted photon

Martin Ligare, J. Mod

Dielectric materials in which both the relative permittivity, , and the relative permeability, µ, are negative exhibit striking optical properties, which are the consequence of the fact that the effective index of refraction in such materials is negative.Most studies of the propagation of electromagnetic fields in these media have concentrated on classical fields with well-defined phases.In contrast, I use simple fully-quantized models to illustrate how some of the striking properties of negative-index media are manifested in the propagation of single, spontaneously emitted, photons.Single-photon quantum fields do not have an absolute phase, but the examples in this paper demonstrate a quantum analog of the negative phase accumulated by classical fields as photons propagate through negative-index media.The single photons also exhibit classical reflection and transmission coefficients, as well as the expected group velocity.

P. E. Gordon, N. M. Chase

Martin Ligare

Dielectric materials in which both the relative permittivity, ε, and the relative permeability, μ, are negative exhibit striking optical properties, which are a consequence of the fact that the effective index of refraction in such materials is negative. Most studies of the propagation of electromagnetic fields in these media have concentrated on classical fields with well-defined phases. In contrast, I use simple fully-quantized models to illustrate how some of the striking properties of negative-index media are manifested in the propagation of single, spontaneously emitted, photons. Single-photon quantum fields do not have an absolute phase, but the examples in this paper demonstrate a quantum analog of the negative phase accumulated by classical fields as photons propagate through negative-index media. The single photons also exhibit classical reflection and transmission coefficients, as well as the expected group velocity.

W. L. Lama, L. Mandeļ

Joerg Bochmann, Holger Specht, Martin Muecke +5 more

Thomas Purdy, Daniel R Taylor, Martin Ligare

We consider a fully quantized model of spontaneous emission, scattering and absorption, and study propagation of a single photon from an emitting atom to a detector atom both with and without an intervening scatterer. We find an exact quantum analogue to the classical complex analytic signal describing an electromagnetic wave scattered by a medium of charged oscillators. This quantum signal exhibits classical phase delays. We define a time of detection which, in the appropriate limits, exactly matches the predictions of a classically defined delay for light propagating through a medium of charged oscillators. The fully quantized model provides a simple, unambiguous and causal interpretation of delays that seemingly imply speeds greater than c in the region of anomalous dispersion.