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In a circuit quantum eletrodynamic system, a chain of N qubitsinhomogeneously coupled to a cavity field forms a mesoscopic quasi-lattice,which is characterized by its degree of deformation from a normal lattice. Thisdeformation is a function of the relative spacing, that is the ratio of thequbit spacing to the cavity wavelength. A polariton mode arise in thequasi-lattice as the dressed mode of the lattice excitation by the cavityphoton. We show that the transition probability of the polariton mode is eitherenhanced or decreased compared to that of a single qubit by the deformation,giving a selective spontaneous radiation spectrum. Further, unlike amicroscopic lattice with large-N limit and nearly zero relative spacing, thepolariton in the quasi-lattice has uneven decay rate over the relative spacing.We show that this unevenness coincides with the cooperative emission effectexpected from the superradiance model, where alternative excitations in thequbits of the lattice result in maximum decay.

Cavity polariton in a quasi-lattice of qubits and its selective radiation