Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states

We consider a system composed of a two-level system (i.e., a qubit) and a harmonic oscillator in the ultrastrongcoupling regime, where the coupling strength is comparable to the qubit and oscillator energy scales. Special emphasis is placed on the possibility of preparing nonclassical states in this system. These nonclassical states include squeezed states, Schrödinger-cat states, and entangled states. We start by comparing the predictions of a number of analytical methods that can be used to describe the system under different assumptions, thus analyzing the properties of the system in various parameter regimes. We then examine the ground state of the system and analyze its nonclassical properties. We finally discuss some questions related to the possible experimental observation of the nonclassical states and the effect of decoherence.