Description
In the two-excitation sector of waveguide QED, the collective emission from subwavelength atom arrays universally hosts two distinct classes of subradiant eigenstates: free-Fermion states (FSs) and bound photon pairs (bound states, BSs). FSs emerge from the quadratic band extrema of the single-excitation polaritonic dispersion, displaying a universal $N^{-3}$ decay rate scaling with respect to the atom number $N$; BSs are subradiant bound atomic excitations that reside within the bandgaps of the scattering continuum. In conventional non-chiral systems, FSs are typically the longest-lived two-excitation states. However, the competition between FSs and BSs in dictating the most subradiant states in chiral waveguide QED, as well as a rigorous analytical derivation for the scaling of BS decay rates, remain largely unexplored.
We address this gap by investigating the subradiant decay rates of BSs in the presence of interaction chirality. We demonstrate that chiral interactions can drive BSs to become the most subradiant two-excitation states across a wide range of lattice spacings. This phenomenon originates from the modulation of BS dispersion by chirality. Specifically, we rigorously prove that the BS decay rate follows the scaling $\Gamma\sim|\alpha_{2}|/N^{3}$ if the BS dispersion is $\mathcal{E}_{K}\approx\alpha_{2}(K-K_\mathrm{ex})^{2}$ near a band extremum $K_\mathrm{ex}$, revealing that by increasing chirality, the BS band curvature $|\alpha_{2}|$ can be suppressed, which is the key to achieving extreme subradiance. Aided by an additional toy model, we clarify the general role of chirality for shaping polaritonic dispersion relations toward subradiance, and for engineering exotic photon-photon correlations in nanophotonic systems. Finally, we show that these subradiant chiral BSs can be prepared in a realistic optical nanofiber interface.
