Photon catalysis and quantum state engineering

Abstract

Photon catalysis is a technique by which a readily available Gaussian state of light prepared in one mode is incident upon a beam splitter with a discrete number of photons, q, prepared in another mode; the resulting two-mode state is then subjected to single-photon resolving detection for q photons on one of the output modes. By employing beam splitters of different transmissivities and reflectivities, the subsequent single-mode state is shown to possess nonclassical properties such as quadrature squeezing and sub-Poissonian statistics. We consider the case in which the input state is the most general of pure single-mode Gaussian states: a squeezed coherent state. Noting the Gaussianity of the initial state, we demonstrate non-Gaussianity of the photon-catalyzed state by analyzing the quadrature uncertainty product and explicitly illustrate it through the Wigner quasi-probability distribution. We extend this technique to the two-mode squeezed states, whereby we perform photon catalysis on one mode of a two-mode squeezed vacuum state. The resulting correlated two-mode state may have applications in fundamental tests of quantum mechanics, such as violations of Bell’s inequalities, as the detection loophole can be closed due to the non-Gaussianity of the photon-catalyzed state. We also generalize our method to include state projective measurements for l≠q photons.