Adding or Subtracting a Single Photon is the Same for Pure Squeezed Vacuum States

Abstract

The addition of a single photon to a light field can lead to exactly the same outcome as the subtraction of a single photon. We prove that this identity-of-outcome is true for pure squeezed vacuum states of light, and in some sense only for those. We show that mixed states can show this identity-of-outcome for addition or subtraction of a photon if they are generated from incoherent sums of pure squeezed vacuum states with the same squeezing. Our results gives a reinterpretation to the fact that pure squeezed vacuum states are formally annihilated by Bogoliubov-transformed annihilation operators: âz=â cosh(z)-↠sinh(z).