Purification of photon subtraction from continuous squeezed light by filtering

Photon subtraction from squeezed states is a powerful scheme to create good approximation of so-called Schr\"odinger cat states. However, conventional continuous-wave-based methods actually involve some impurity in squeezing of localized wavepackets, even in the ideal case of no optical losses. Here we theoretically discuss this impurity, by introducing mode-match of squeezing. Furthermore, here we propose a method to remove this impurity by filtering the photon-subtraction field. Our method in principle enables creation of pure photon-subtracted squeezed states, which was not possible with conventional methods.