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

TL;DR

This paper investigates how inhomogeneous dipole-field coupling in a superconducting qubit chain affects its excitation spectrum, revealing a crossover between Frenkel- and Wannier-type excitons as qubit spacing varies.

Contribution

It derives an exact diagonalization of the N-qubit Hamiltonian considering inhomogeneous coupling, highlighting the impact on spectral density and exciton nature.

Findings

Inhomogeneous coupling creates l-dependent ladder operators.

Varying qubit spacing l alters transition amplitudes.

Transition from Frenkel- to Wannier-type excitons observed.

Abstract

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.