Quantum phase transition in a driven Tavis-Cummings model

Quantum phase transitions (QPTs) describe when a many-body quantum system displays non-analytic behavior associated with a discontinuous change in a property of the ground state as a parameter is varied. The QPT in prototypical Dicke model is difficult to reach experimentally as the spin-field coupling strength must be quite large. In this work we describe a new model-the off-resonant Tavis-Cummings model where we drive the common mode, and discover a new type of QPT at quite low coupling strengths which are comparable with the geometric mean of the atomic and field detunings lambda similar to lambda(c) equivalent to root Delta(a)Delta(c). Through analytic methods we demonstrate this QPT for both finite and infinite numbers of spins and show that vertical bar < J(x)(J(z))>vertical bar/(N/2) similar to vertical bar lambda/lambda(c) - 1 vertical bar(gamma x(gamma z)) and < a(dagger)a >/N similar to vertical bar lambda/lambda(c) - 1 vertical bar(gamma a) for lambda >= lambda(c), with critical exponents gamma(x) approximate to 1/2, gamma(z) approximate to 1 and gamma(a) approximate to 1. We show that this QPT can be immediately observed by laboratory cavity-QED setups such as Bose-Einstein condensate in optical cavity and superconducting circuit-QED as well as a line of trapped ultracold ions.