Quantum phase transitions in coupled two-level atoms in a single-mode cavity

The dipole-coupled two-level atoms(qubits) in a single-mode resonant cavity is studied by extended bosonic coherent states. The numerically exact solution is presented. For finite systems, the first-order quantum phase transitions occur at the strong interatomic interaction. Similar to the original Dicke model, this system exhibits a second-order quantum phase transition from the normal to the superradiant phases. Finite-size scaling for several observables, such as the average fidelity susceptibility, the order parameter, and concurrence are performed for different interatomic interactions. The obtained scaling exponents suggest that interatomic interactions do not change the universality class.