Photon added state preparation via conditional measurement on a beam splitter

Abstract We show that conditional output measurement on a beam splitter may be used to produce photon-added states for a large class of signal-mode quantum states, such as thermal states, coherent states, squeezed states, and displaced photon-number states. Combining a mode prepared in such a state and a mode prepared in a photon-number state, the state of the mode in one of the output channels of the beam splitter “collapses” to a photon-added state, provided that no photons are detected in the other output channel. We present analytical and numerical results, with special emphasis on photon-added coherent and squeezed vacuum states. In particular, we show that adding photons to a squeezed vacuum yields Schrodinger-cat-like states in terms of superpositions of non-Gaussian squeezed coherent states. We finally show that the quantum features of the conditional output states are observed even when the reference mode is prepared in a sub-Poissonian statistical mixture of photon-number states.