Excitation spectrum for an inhomogeneously dipole-field-coupled superconducting qubit chain

Details Excitation spectrum for an inhomogeneously dipole-field-coupled superconducting qubit chain Excitation spectrum for an inhomogeneously dipole-field-coupled superconducting qubit chain

2011-01-20

arxiv.org/abs/1101.3893v2

Physics

Quantum Physics

9 pages, 3 figures, with 3 appendices

Scientific paper

When a chain of superconducting qubits couples to a coplanar resonator in a cavity, each of its N qubits (equally-spaced with distance l) experiences a different dipole-field coupling strength due to the waveform of the cavity field. We find that this inhomogeneous coupling leads to a pair of l-dependent ladder operators for the angular momentum of the spin chain. Varying the qubit 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, it will be shown that the variation of l between its two limiting values coincides with the crossover between Frenkel- and Wannier-type excitons in the superconducting spin chain.

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