Majorana-like Modes of Light in a One-Dimensional Array of Nonlinear Cavities

The search for Majorana fermions in $p$-wave paired fermionic systems has recently moved to the forefront of condensed matter research. Here we propose an alternative route and show theoretically that Majorana-like modes can be realized and probed in a driven-dissipative system of strongly correlated photons consisting of a chain of tunnel-coupled cavities, where $p$-wave pairing effectively arises from the interplay between strong on-site interactions and two-photon parametric driving. The nonlocal nature of these exotic modes could be demonstrated through cross-correlation measurements carried out at the ends of the chain—revealing a strong photon-bunching signature—and their non-Abelian properties could be simulated through tunnel-braid operations.

Figure 1

Driven-dissipative chain of coupled cavities. Each cavity exhibits a large optical nonlinearity and sustains a single Wannier mode which weakly overlaps with its nearest neighbors, thus allowing for photon hopping between sites. Parametric pumps (depicted by arrows) couple to the weak intercavity field and inject photon pairs which, owing to strong photon-photon repulsion, split up into different cavities, effectively giving rise to $p$-wave pairing.

Figure 2

Numerical results showing the second-order cross-correlation function $g_{LR}^{(2)}$ as a function of the detuning $\mu$ for $N=12$ (including probe cavities), $\Delta /J=1$, $J_{L,R}/J=0.02$, and for different values of $\Gamma /J={\Gamma }_{L,R}/J$. MLMs (with energy splitting ${\delta }_M$ determined by $\mu$) are expected in the region $0\le \mu /J<2$ (delimited by a dashed vertical line), which corresponds to a topologically nontrivial phase (in the limit $N\to \infty$). As expected, a strong bunching signature is observed for large $\mu$ inside the topologically nontrivial region, while $g_{LR}^{(2)}\approx 1$ beyond the critical point $\mu /J=2$, clearly signaling the absence of MLMs. All results were obtained using a Monte Carlo wave function approach (see, e.g., Ref. 37) with 400 trajectories.