Ole Keller | Searcharxiv

arXiv2009

Photon Wave Mechanics

In contrast to wave functions in nonrelativistic quantum mechanics interpreted as probability amplitudes, wave functions in relativistic quantum mechanics have generalized meanings such as charge-density amplitudes, energy-density amplitudes as well as particle-number density amplitudes, etc. Applying electromagnetic field intensities we construct a photon wave function, it corresponds to the (1,0)+(0,1) spinor representation of the electromagnetic field, and can be interpreted as the energy-density amplitude of photons outside a source. In terms of photon wave functions we develop photon wave mechanics, which provides us with a new quantum-mechanical description for photons outside a source.

quant-ph↗

arXiv2005

Photon Position Operator and Localization of Photons inside a Waveguide

In this article, we show that in the level of quantum mechanics, a photon position operator with commuting components can be obtained in a more natural way; in the level of quantum field theory, the photon position operator corresponds to the center of the photon number. It is most interesting for us to show that, a photon inside a waveguide can be localized in the same sense that a massive particle can be localized in free space, and just as that it is impossible to localize a massive particle with a greater precision than its Compton wavelength, one can also arrival at a similar conclusion: it is impossible to localize a photon inside a waveguide with a greater precision than its equivalent Compton wavelength, which owing to evanescent-wave or photon-tunneling phenomena.

quant-ph↗

arXiv1999

Local-field study of phase conjugation in metallic quantum wells with probe fields of both propagating and evanescent character

The phase conjugated response from nonmagnetic multi-level metallic quantum wells is analyzed and an essentially complete analytical solution is presented and discussed. The description is based on a semi-classical local-field theory for degenerate four-wave mixing in mesoscopic interaction volumes of condensed media developed by the present authors [T. Andersen and O. Keller, Phys. Scripta 58, 132 (1998)]. The analytical solution is supplemented by a numerical analysis of the phase conjugated response from a two-level quantum well in the case where one level is below the Fermi level and the other level is above. This is the simplest configuration of a quantum well phase conjugator in which the light-matter interaction can be tuned to resonance. The phase conjugated response is examined in the case where all the scattering takes place in one plane, and linearly polarized light is used in the mixing. In the numerical work we study a two-monolayer thick copper quantum well using the infinite barrier model potential. Our results show that the phase conjugated response from such a quantum-well system is highly dependent on the spatial dispersion of the matter response. The resonances showing up in the numerical results are analytically identified from the expressions for the linear and nonlinear response tensors. In addition to the general discussion of the phase conjugated response with varying frequency and parallel component of the wavevector, we present the phase conjugated response in the special case where the light is in resonance with the interband transition.

cond-mat.mes-hall↗