Effect of filtering on the generation of Schrödinger cat-like states from a pulsed multimode squeezing

Light is a perfect candidate to carry out quantum information for applications to quantum computation, communication and metrology. Information can be encoded using observables with discrete spectrum (or DV for discrete variable encoding) as well as with continuous spectrum observables (or CV for continuous variable encoding). One of the most used states to encode a CV qubit is the so called optical Schrödinger cat state, i.e. a superposition of two coherent states with the same amplitude and opposite phases. Approximation of these states, named Schrödinger kittens, have been generated in an heralded fashion by subtraction of one or two photons from a degenerate single mode squeezed vacuum states. Experiments have been conducted in continuous wave regime generally using optical parametric oscillators as well as in the pulsed regime. The quality of Schrödinger kittens generated with this strategy, however, suffers from the impurity of the squeezing in the wave-packet of the heralded state. In the CW regime, it is shown theoretically and experimentally that a narrowband filtering of the heralding photon increase the purity of thegenerated state. We extend this study so as to describe also the pulsed regime where the squeezed vacuum state is in general spectrally multimode. We calculate and numerically simulate the state generated when subtracting a photon from an arbitrary multimode pulsed squeezed vacuum state. Inaddition, we investigate its homodyne detection by considering an arbitrary pulsed local oscillator. The fidelity between the heralded state and a perfect single mode photon subtracted squeezed state decreases when the number of modes excited in the multimode squeezed vacuum increases. We show how to increase this fidelity by using a narrowband filter in the heralding path. This study quantifies the effect of spectral filtering on the quality of the generated state using a multimode approach that can be applied to a wide variety of situations. We believe that it will have a major impact on realisation of non-Gaussian states in an heralded fashion.