Bloch steps in vortex interference in the presence of classical and nonclassical electromagnetic fields

Abstract

Interference of vortices winding around a time-dependent electric charge ${It+Q}_{0}\mathrm{sin}(\ensuremath{\omega}t)$ is considered. It is shown that the time-averaged intensity of vortices shows interference only if ${\ensuremath{\Phi}}_{0}I=N\ensuremath{\omega}$ (integral Bloch steps). The same phenomenon is studied for the electric charge ${Q(t)=Q}_{1}\mathrm{sin}({\ensuremath{\omega}}_{1}{t)+Q}_{0}\mathrm{sin}(\ensuremath{\omega}t)$ and it is shown that the time-averaged intensity of vortices shows interference only for rational values of the ratio ${\ensuremath{\omega}}_{1}/\ensuremath{\omega}$ (fractional Bloch steps). The case in which the electric charge is induced by nonclassical microwaves is also considered. Results for various examples of nonclassical microwaves (e.g., coherent states, squeezed states, etc.) are presented and a comparison with the corresponding classical case is made. It is shown that the quantum noise in the nonclassical microwaves causes partial destruction of the interference.