Double symmetry breaking and 2D quantum phase diagram in spin-boson systems

When the collective coupling between a chain of spins (two-levels systems) and a bosonic mode becomes comparable with the two-level transition frequency, superradiant quantum phase transitions for the cavity vacuum can occur, for instance within the Dicke model [1]. Here, the quantum ground state properties of two independent chains of pseudo-spins interacting with the same bosonic field are investigated [2] . Each chain is coupled to a different quadrature of the field, leading to two independent symmetry breakings for increasing values of the two spin-boson interaction constants. A 2D phase diagram is provided with 4 different phases that can be characterized by the complex bosonic coherence of the ground states and can be manipulated via non-abelian Berry effects. Possible realizations of such model in circuit QED are discussed, generalizing the previous proposals to implement the standard Dicke model [3,4]. \\[4pt] [1] C. Emary, and T. Brandes, Phys. Rev. Lett. 90, 044101 (2003).\\[0pt] [2] P. Nataf, A. Baksic and C. Ciuti, arXiv:1111.1617 (2011).\\[0pt] [3] P. Nataf and C. Ciuti, Nat. Commun. 1 :72 (2010).\\[0pt] [4] P. Nataf and C. Ciuti, Phys. Rev. Lett. 104, 023601 (2010).