Floquet-engineered tunable and nonreciprocal couplings in waveguide QED

We propose and analyze a general scheme to engineer programmable and nonreciprocal interactions in an array of atoms coupled to a photonic waveguide. By subjecting each atom to a local harmonic frequency modulation with a defined phase ${\ensuremath{\theta}}_{i}$, we demonstrate the emergence of effective long-range couplings whose parameters are dynamically controllable. For atoms coupled to a conventional waveguide, the modulation dresses the atomic operators, leading to effective interactions governed by the Bessel function ${\mathcal{J}}_{0}$ whose argument depends on the phase differences $\mathrm{\ensuremath{\Delta}}{\ensuremath{\theta}}_{ij}$. For atoms coupled to a photonic crystal waveguide near its band edge, where the density of states is sharply varying, the modulation can be tuned to selectively activate the ${\mathcal{J}}_{1}^{2}$ term, which simultaneously scales both the coherent and dissipative components of the complex coupling strength ${\mathrm{\ensuremath{\Gamma}}}_{ij}$. Crucially, the spatial profile of the local modulation phases imprints a factor $exp(\mathrm{i}\mathrm{\ensuremath{\Delta}}{\ensuremath{\theta}}_{ij})$ onto the waveguide-mediated coupling strength ${\mathrm{\ensuremath{\Gamma}}}_{ij}$, enabling the synthesis of nonreciprocal quantum interactions. Our approach thus provides a flexible toolbox for simulating a wide range of non-Hermitian Hamiltonians on waveguide-QED platforms.