Sensing Single Photon in a Cat State

TL;DR

This paper demonstrates how a cat state can store a single photon and explores how photon addition affects its quantum interference, phase space structure, and photon number distribution, revealing new quantum state manipulation techniques.

Contribution

It introduces a method to store a photon in a cat state and analyzes the effects of photon addition on its phase space and photon statistics, highlighting novel quantum state control.

Findings

Photon addition causes a π phase shift in the Wigner function interference.

Photon addition interchanges maxima and minima of sub-Planck tiles, leading to orthogonality.

Photon addition to Yurke-Stoler state results in sub-Poissonian photon statistics.

Abstract

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.