Sensing Single Photon in a Cat State

The cat state is shown to `store' a single photon through the superposition of its orthogonal counterpart with itself, and an excited oscillator state. Photon addition leads to a $\pi$ phase shift at origin in the observed phase space interference of the Wigner function, which also displays negativity, controlled by the average photon number ($|\alpha|^2$) of coherent states comprising the cat state. The maxima and minima of the sub-Planck tiles in the phase space of the kitten state are interchanged after photon addition, leading to their orthogonality. Interestingly, photon addition to Yurke-Stoler state characterized by Poissonian statistics leads to a sub-Poissonian distribution.