Phase transitions in an Ising chain interacting with a single mode cavity field

Abstract: We investigate the thermodynamics of a combined Dicke- and Ising-model which exhibits a rich phenomenology arising from the second order and quantum phase transitions from the respective models. The partition function is calculated using mean field theory, and the free energy is analyzed in detail to determine the complete phase diagram for the system. The analysis reveals both first- and second-order Dicke phase transitions into a super-radiant state, and the cavity mean-field in this regime acts as an effective magnetic field, which restricts the Ising chain dynamics to parameter ranges away from the Ising phase transition. Physical systems with a first order phase transitions are natural candidates for metrology and calibration purposes, and we apply filter theory to show that the sensitivity of the physical system to temperature and external fields reaches the 1/N Heisenberg limit.