Critical exponent of a quantum-noise-driven phase transition: The open-system Dicke model

The quantum phase transition of the Dicke model has been observed recently in a system formed by motional excitations of a laser-driven Bose-Einstein condensate coupled to an optical cavity [Baumann et al., Nature (London) 464, 1301 (2010)]. The cavity-based system is intrinsically open: photons leak out of the cavity where they are detected. Even at zero temperature, the continuous weak measurement of the photon number leads to an irreversible dynamics toward a steady state. In the framework of a generalized Bogoliubov theory, we show that the steady state exhibits a dynamical quantum phase transition. We find that the critical point and the mean field are only slightly modified with respect to the phase transition in the ground state. However, the critical exponents of the singular quantum correlations are significantly different in the two cases. There is also a drastic modification of the atom-field entanglement, since the divergence of the logarithmic negativity of the ground state at the critical point is suppressed and a finite entanglement is found in the steady state.