Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light: Analytical formula

We develop a multimode theory to design the frequency mode matching in the photon-subtracting operation by an on/off-type photon detector on a wideband squeezed light. The output state thus generated is known to be the Schrodinger-cat-like state. Its Wigner function constructed by the homodyne tomography must have a negative dip around the phase space origin. In order to observe this nonclassical effect, however, one must achieve good mode matching between the fields observed by the on/off and homodyne detectors, those are quite different types from each other. The events are defined for finite measurement time duration T, and are measured by the homodyne detector with finite bandwidth B. We provide an explicit formulus to calculate the Wigner function of the state, taking into account multimode aspects of the squeezed light and the time and band limitation to the quantum states. A unified picture of the mode matching in terms of the single parameter BT is presented, covering the cw and pulsed schemes. The nonclassical effect can be realized and measured most remarkably when the modes excited in the detectors could be restricted to a single mode by taking BT as small as possible, and could reduce dark counts in the on/off detector and the vacuum noise invasion in the homodyne detector. Practical design of experimental setup is described based on presently available technologies.