Quantum interference of force, Hanbury Brown and Twiss with electrons, and photon reflection by a quantum mirror

Abstract

This Thesis contains work developed in three subjects. In the first of them, we show that a quantum particle under the action of a positive force in one path of a Mach-Zehnderinterferometer and a null force in the other path may receive a negative average momentum transfer when it leaves the interferometer by a particular exit. In this scenario, an ensemble of particles may receive an average momentum in the opposite direction of the applied force due to quantum interference, a behavior with no classical analogue. We name this effect as ¿quantum interference of force¿, and discuss some experimental schemes that could verify the effect with current technology, with electrons or neutrons in Mach-Zehnder interferometers in free space and with atoms from a Bose-Einstein condensate. We then discuss the case of two electrons propagating in the same Mach Zehnder interferometer and show that, due to the same quantum interference of force effect, the two electrons can sometimes suffer an effective attraction. The second subject is the development of an experimental proposal to detect the Hanbury Brown and Twiss interference with electrons propagating in free space. In previously realized experiments, doubts were casted upon the results, which may be explained as caused by Coulomb repulsion of the electrons instead of a two-particle interference effect. In our proposal, the two effects can be clearly distinguished, opening the path for imaging with incoherent electron sources. Finally, the third subject concerns the derivation from first principles of the momentum exchange between a photon and a quantum mirror upon reflection, by considering the boundary conditions imposed by the mirror surface on the photon wave equation. We show that the system generally ends up in an entangled state, unless the mirror position uncertainty is much smaller than the photon wavelength, when the mirror behaves classically. Our treatment leads us directly to the conclusion that the photon momentum has the known value ~k, and this allows us to contribute to the longstanding Abraham¿Minkowski debate about the momentum of light in a medium. We show that in our setting the Minkowski momentum is revealed, in which the light momentum is proportional to the medium refractive index.