Coupling Circuit Resonators Among Themselves and To Nitrogen-Vacancy Centers in Diamond

We propose a scheme to couple NV centers in diamond through coplanar waveguide resonators. The central conductor of the resonator is split into several pieces which are coupled strongly with each other via simple capacitive junctions or superconducting Josephson junctions. The NV centers are then put at the junctions. The discontinuity at the junctions induces a large local magnetic field, with which the NV centers are strongly coupled to the circuit resonator. The coupling strength $g$ between the resonator and the NV center is of order of $g/2\pi\sim 1$--30\unit{MHz}.Comment: 4 pages; 3 figures; several typos corrected; figure 1 regenerate

Anomalous multicritical phenomena and frustration induced by synthetic magnetic fields

We consider a one-dimensional Dicke lattice with complex photon hopping amplitudes and investigate the influence of time-reversal symmetry breaking due to synthetic magnetic fields. We show that, by tuning the total flux threading the loop, the universality class of superradiant phase transition (SPT) changes from that of the mean-field fully-connected systems to one that features anomalous critical phenomena. The anomalous SPT exhibits a closing of the energy gap with different critical exponents on both sides of transition and a discontinuity of correlations and fluctuation despite it being a continuous phase transition. In the anomalous normal phase, we find that a non-mean-field critical exponent for the closing energy gap and non-divergent fluctuations and correlations appear, which we attribute to the asymmetric dispersion relation. Moreover, we show that the nearest neighborhood complex hopping induces effective long-range interactions for position quadratures of the cavity fields, whose competition leads to a series of first-order phase transitions among superradiant phases with varying degrees of frustration. The resulting multicritical points also show anomalous features such as two coexisting critical scalings on both sides of the transition. Our work shows that the interplay between the broken time-reversal symmetry and frustration on bosonic lattice systems can give rise to anomalous critical phenomena that have no counterpart in fermionic or spin systems or time-reversal symmetric quantum optical systems.Comment: 5+9 pages, 8 figure