Ground state of an ultrastrongly coupled qubit-oscillator system with broken inversion symmetry

We study the effect of inversion symmetry breaking on properties of the ground state of a qubit-oscillator system within the ultrastrong-coupling regime. We obtain the solution of the ground state through the approximate analytical approach, which, under the near-resonance condition, agrees well with the numerical simulation. We demonstrate that, due to the inversion symmetry breaking, the ground state becomes asymmetric and the qubit-oscillator entanglement entropy strongly depends on the mean dipole moments. Furthermore, we find that the attainable maximum entanglement entropy undergoes a sharp change across a critical point and the minimum value of the Wigner function has a quadratic dependence on the mean dipole moments.