Anomalous superradiant phases in a quantum Rabi zigzag chain under a synthetic gauge field

Abstract

We present the phase diagram of a one-dimensional quantum Rabi zigzag chain under an artificial gauge field, which is implemented via phase-modulated next-nearest-neighbor (NNN) hopping. For a system size of $N=8$, we analytically determine the order parameters and critical thresholds, identifying five distinct superradiant phases. For strong nearest-neighbor (NN) coupling, the system exhibits either a ferro-superradiant (FSR) or an antiferro-superradiant (AFSR) phase depending on its sign. Increasing NNN coupling induces a stripe antiferro-superradiant (sAFSR) phase with antiparallel NNN and parallel NN displacements, which is distinct from the conventional AFSR phase. Tuning the magnetic flux drives the system into chiral or antichiral superradiant phases with opposite ground-state photon currents, which are different from the conventional superradiant phases. Remarkably, geometric frustration within each triangular plaquette stabilizes chiral phases even at small magnetic flux while suppressing the sAFSR phase, which vanishes for $N=6$. Mapping the system onto an effective magnetic Hamiltonian yields an analogous phase diagram featuring distinct magnetic phases, offering insight into the anomalous superradiant phases. This equivalence establishes a quantum optical platform for simulating chiral magnetism.

The paper studies how synthetic flux and competing nearest-neighbor (NN) and next-nearest-neighbor (NNN) photon hopping affect superradiant ordering in a periodic quantum Rabi zigzag chain. It proposes phase-modulated NNN coupling in circuit QED to implement a hopping phase $\theta$, interpreted as flux through triangular plaquettes. A Schrieffer–Wolff transformation and quadratic bosonic diagonalization give the normal-phase excitation spectrum and momentum-dependent instability thresholds $\tilde g_c(k)$, where $\tilde g=g/\sqrt{\omega\Delta}$. For $N=8$, the analysis identifies five superradiant configurations: ferro, antiferro, stripe antiferro, chiral, and antichiral. The stripe configuration has opposite displacements on NNN sites; the chiral configurations have complex, spatially varying cavity displacements and opposite signs of the reported chain-current observable. Nonlinear displacement equations determine the superradiant order parameters. Normal-to-superradiant transitions are identified as second order, while transitions between superradiant configurations are reported as first order. Comparison with $N=6$ shows that odd-length, three-site sublattices frustrate stripe ordering: the stripe phase disappears, and chiral configurations occur at small flux. A classical-spin mapping produces NN and NNN $XY$ interactions together with an NNN Dzyaloshinskii–Moriya term proportional to $J_2\sin\theta$; mean-field minimization yields analogous magnetic configurations. The treatment relies on the frequency-ratio limit $\Delta/\omega\to\infty$, neglecting higher-order terms, and examines phase diagrams for $N=6$ and $8$. Displayed calculations use $\Delta/\omega=50$ and $J_2/\omega=0.12$. The circuit implementation is proposed rather than experimentally demonstrated.