Quantum electrodynamics near a photonic bandgap

Photonic crystals areapowerful tool for themanipulationofoptical dispersion and density of states, and have thus been used in applications from photon generation to quantum sensing with nitrogen vacancy centres and atoms. The unique control providedby thesemediamakes themabeautiful, if unexplored, playground for strong-coupling quantum electrodynamics, where a single, highly nonlinear emitter hybridizes with the band structure of the crystal. Here we demonstrate that such a hybridization can create localized cavity modes that live within the photonic bandgap, whose localization and spectral properties we explore in detail. We then demonstrate that the coloured vacuum of the photonic crystal can be employed for e cient dissipative state preparation. This work opens exciting prospects for engineering long-range spinmodels in the circuit quantum electrodynamics architecture, as well as new opportunities for dissipative quantum state engineering. The perturbative effect of a structured vacuum is the renowned Purcell effect, which states that the lifetime of an atom in such a space will be proportional to the local photonic density of states (DOS) near the atomic transition frequency. In practice, the birth of the photonic crystal, which greatly modifies the vacuum fluctuations, has enabled the control of spontaneous emission of various emitters, such as quantum dots, magnons and superconducting qubits. However, when an atom is strongly coupled to a photonic crystal, non-perturbative effects become important, and significantly enrich the physics. For instance, a single-photon bound state has been predicted to emerge within the gap, and spontaneous emission of the atom will thus exhibit Rabi oscillation and light-trapping behaviour. In contrast to electronic bandgap systems, even multiple photons can be simultaneously localized by a single atom, and the coherent photonic transport within the otherwise forbidden bandgap can have a strongly correlated nature. In contrast to a system with discrete cavity modes, which is well described by the single-mode or multimode Jaynes–Cummings Hamiltonian, a continuous density of states enables the formation of a localized state in the bandgap. While other spin-boson problems with continuous DOS have also been studied experimentally or theoretically with superconducting circuits, this work explores physics near the band edge, where localized states emerge and reservoir engineering becomes possible. Light–matter interactions are being actively pursued using cold atoms coupled to optical photonic crystals, where the study of photonic band edge effects requires a combination of challenging nanostructure fabrication and optical laser trapping. Although impressive progress has been made, atoms are only weakly coupled to photonic crystal waveguides, potentially limiting the physics to the perturbative regime. In this letter, using a microwave photonic crystal and a superconducting transmon qubit, we are able to reach the strong-coupling regime of quantum electrodynamics near a photonic bandgap. This regime is characterized by the emergence of spectrally resolvable new polariton states, similar to the wellknown vacuum Rabi splitting in cavity quantum electrodynamics. We will give a more quantitative definition of strong coupling in the following discussion. Our device consists of 14 unit cells, each of which contains two coplanar waveguide (CPW) sections with different lengths ` and impedances Z (`lo = 0.45 mm, `hi = 8mm and Zlo=28,Zhi=125). These parameters are chosen so that the band edge is within our measurement window (4–10GHz) and that the bare photonic crystal has a smooth spectrum. The dispersion relation can be calculated using transfer matrices and is given by