Unveiling and veiling a Schr\"odinger cat state from the vacuum

Deep in the ultrastrong light-matter coupling regime, it has been predicted that the ground state of a two-level atom interacting with a cavity mode takes the form of a "virtual" Schr\"odinger cat entangled state between light and matter. We propose a method to convert this Schr\"odinger cat state from virtual to real, and back again, by driving the atom with optimally chosen pulses. Our system consists of a four-level atom, with two of these levels ultrastrongly coupled to a cavity mode. We show that the Schr\"odinger cat state can be converted between virtual and real by making use of either an ideal ultrafast pulse or a multi-tone {\pi}-pulse. In addition to allowing us to observe these unusual virtual states this method could also be used to generate entangled cat states on demand for quantum information processing.