Exploring quantum critical phenomena in a nonlinear Dicke model through algebraic deformation

Abstract

In this work, we use a deformed version of the Heisenberg–Weyl algebra in the Dicke Model to incorporate a Kerr medium and nonlinear interaction between matter and radiation fields. The deformed algebra allows us to define two distinct nonlinear coherent states for the radiation field. These coherent states, along with the conventional Heisenberg–Weyl coherent states and their symmetry-adapted versions, are employed as trial variational states in the energy-surface minimisation method. The obtained results reveal that the Kerr medium introduces a delay in reaching the super-radiant region, with the delay becoming more pronounced as the nonlinear parameter increases. To evaluate the different approaches, we analyse the behaviour of the critical coupling, ground-state energy, entropy of entanglement between matter and radiation, and fidelity between the numerical solution and the symmetry-adapted solution. We find that one particular deformed coherent state outperforms the other trial states in approximating the ground state of the system, providing an accurate description of the critical behaviour in the proposed nonlinear model.