Meissner-Like Currents of Photons in Anomalous Superradiant Phases

Abstract

We present Meissner-like photon currents in a quantum Rabi zigzag chain under staggered synthetic magnetic fields. The ground state of the Meissner superradiant phase hosts persistent chiral edge currents in a sequence of cancellation of antiparallel vortex pairs, akin to surface currents of the Meissner effect in superconductors. The Meissner phase displays distinct vortex structures and anomalous scaling exponents, arising from geometric frustration effects. Modifying the staggered flux triggers transitions to even- or odd-vortex superradiant phases, where the chiral edge currents flow exclusively in even or odd cavities with localized vortices, respectively. Enhanced interspecies interactions induce the vanishing of currents in a ferromagnetic superradiant phase. Our results enable observation of stabilized photon vortices and edge currents with analogy to quantum Hall-like robustness in light-matter coupling systems.

Figures (5)

• Figure 1: (a) Constructing a quantum Rabi zigzag chain exposed to a staggered flux $\theta$ by rearranging a $1$D representation. (b) Phase diagram in ($J_1/J_2$, $g_1$) for $N=6$ cavities with $\theta=\pi/2$. Critical boundary $g_{1c}(k=\pm\pi/3)$ (red solid) and $g_{1c}(k=0)$ (black dash) in Eq. (\ref{['gc']}) mark the NP-MSR and NP-FSR transitions of second order. First-order line (blue dash dot) converges with the second-order line at a triple point (TP). In all calculations, we set $\omega=1$ as the unit for frequency, and $\Delta/\omega= 50, J_2/\omega= 0.05$.
• Figure 2: (a) Phase diagram in the superradiant regime ($g_1=0.7>g_{1c}$) for $N=10$ cavities. Phase boundary in solid line separates the MSR, FSR and E(O)VSR phases. Configurations of $\alpha_n$ are marked with red (blue) arrows in ($A_n$,$-B_n$) plane. (b) Average photon number $\langle a_n^{\dagger}a_n\rangle$ for each phase marked in (a) (1-3). Three distinct vortex pairs are indicated by gray shading, and the arrow thickness indicates the magnitude of the current. (c) Chiral current $I_C$ (red dashed line) and ground-state energy $E_g/\omega$ (black solid line) versus $\theta$ for $J_1/J_2=0.05$. (d) Excitation energies in Eq.(\ref{['excitation']}) versus $\theta$ for $g_1=0.1<g_{1c}$ and $J_1/J_2=0.1$.
• Figure 3: (a) Phase diagram in the superradiant regime for $N=8$ cavities. (b) Currents and average photon number $\langle a_n^{\dagger}a_n\rangle$ for each phase marked in (a) (1-4). Two distinct pairs of vortex currents are represented by shades of gray. Symbols and parameters align with those in Fig. \ref{['phasediagram']}.
• Figure 4: Edge currents in odd (even) cavities $I_{O\texttt{(E)}}$ (black dashed (red dotted) lines) and current along the chain $I_\texttt{T}$ (blue solid line ) against $J_1/J_2$ for the MSR-FSR transition with $N=8$ (a) and $N=10$ (b), and for OVSR-FSR (c) and EVSR-FSR transitions (d) with $g_1=0.7$. $I_{\circlearrowright1(2)}$ and $I_{\circlearrowleft1(2)}$ in triangle symbols mark distinct vortex currents in triangle plaquettes, with arrows showing circulation direction.
• Figure 5: Critical excitation energies follow $\epsilon$ versus $g_1/g_{1c}$ for the NP-MSR (a) and NP-FSR (b) transitions ($N=6$), and for the NP-MSR transition ($N=8$) (c) with distinct power laws with exponents $\gamma_\texttt{M}=1/2$ , $\gamma_\texttt{F}=1$ and $\gamma_\texttt{NF}=3/2$. Shapes represent numerical results, which fit well with to analytical $\epsilon(k)$ ( lines) from Eq.(\ref{['excitation']}) for $g_1<g_{\texttt{1c}}$. (d) Excitation energy scaling exponents for $N=10,12,14,16$ in the NP-MSR transition, with lines showing a power law.