Berry Phase of Two Impurity Qubits as a Signature of Dicke Quantum Phase Transition

In this paper, we investigate the effect of the Dicke quantum phase transition on the Berry phase of the two impurity qubits. The two impurity qubits only have dispersive interactions with the optical field of the Dicke quantum system. Therefore, the two impurity qubits do not affect the ground state energy of the Dicke Hamiltonian. We find that the Berry phase of the two impurity qubits has a sudden change at the Dicke quantum phase transition point. Therefore, the Berry phase of the two impurity qubits can be used as a phase transition signal for the Dicke quantum phase transition. In addition, the two impurity qubits change differently near the phase transition point at different times. We explain the reason for the different variations by studying the variation of the Berry phase of the two impurity qubits with the phase transition parameters and time. Finally, we investigated the variation of the Berry phases of the two impurity qubits with their initial conditions, and we found that their Berry phases also have abrupt changes with the initial conditions. Since the Dicke quantum phase transition is already experimentally executable, the research in this paper helps to provide a means for manipulating the Berry phase of the two impurity qubits.