Excitation spectrum for an inhomogeneously dipole-field-coupled superconducting qubit chain
Hou Ian, Yu-xi Liu, Franco Nori
DOI 10.1103/PhysRevA.85.053833 · Physical Review A
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Abstract
When a chain of N superconducting qubits couples to a coplanar resonator, each of the qubits experiences a different dipole-field coupling strength due to the wave form of the cavity field. We find that this inhomogeneous coupling leads to a dependence of the collective ladder operators of the qubit chain on the qubit-interspacing l. Varying the spacing l changes the transition amplitudes between the angular momentum levels. We derive an exact diagonalization of the general N-qubit Hamiltonian and, through the N=4 case, demonstrate how the l-dependent operators lead to a denser one-excitation spectrum and a probability redistribution of the eigenstates. Moreover, we show that the variation of l between its two limiting values coincides with the crossover between Frenkel- and Wannier-type excitons in the superconducting qubit chain.
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