Dipolar quantum phase transition in the Dicke model with infinitely coordinated frustrating interaction.
We consider the Dicke Hamiltonian of a system of N $\rightarrow \infty$ half spins with infinitely coordinated antiferromagnetic interaction. This Hamiltonian arises when one considers a single-mode microwave cavity coupled to low-capacitance Josephson junctions via the gauge-invariant Josephson phases. We found analytically a critical coupling strength causing a first order quantum phase transition of the system into dipolar phase with symmetry breaking coherent electromagnetic field emerging in the cavity. A new analytic tool: self-consistently 'rotating' Holstein-Primakoff representation for the Cartesian components of the total spin, is proposed. Our approach enables, as a by-product, description of the second order quantum phase transition in the Dicke model without frustrating antiferromagnetic interaction, explored previously by other authors (Emary, Brandes 2003), but interpreted differently. Analytical time-dependent solutions for metastable 'bound luminosity' dynamic states lifting the double degeneracy of the dipolar ordered phases are found and expressed via Jacobi elliptic functions. Applicability of our theory to fabricated arrays is discussed.
Publisher URL: http://arxiv.org/abs/1711.00348