Non-Gaussianity of photon-added-then-subtracted squeezed vacuum state

In this paper, the photon-added-then-subtracted squeezed vacuum state (PASSVS), a non-Gaussian state, is presented by adding then subtracting photon to a squeezed vacuum state. It is found that PASSVS is just a superposition state between S(r) | 0〉 and S(r) | 2〉, where S(r) is the single-mode squeezing operator with the squeezing parameter r. Its non-Gaussianity is exhibited via its Wigner function and the Hilbert–Schmidt distance. In addition, a possible scheme is presented to produce the PASSVS by virtue of the cavity QED.