Waveguide bandgap N-qubit array with a tunable transparency resonance

TL;DR

This paper analyzes single photon transmission through a 1D N-qubit chain in a waveguide, revealing tunable bandgap structures and narrow resonances controllable via a central qubit’s excitation frequency.

Contribution

It provides a simple analytical framework for large N qubit chains using Chebyshev polynomials and demonstrates tunable transparency resonances within bandgaps.

Findings

Flat bandgap structure with steep walls at half-wavelength spacing

Narrow transmission resonance appears for odd N with central qubit tuning

Resonance position and width are controllable by the central qubit's frequency

Abstract

We study a single photon transmission through 1D N- qubit chain. The qubits are supposed to be identical with equal distance between neighbors. We express the transfer matrix of N- qubit chain in terms of Chebyshev polynomials, which allows us to obtain simple expressions for the transmission and reflection amplitudes for arbitrarily large N. If the distance between neighbor qubits is equal to half wavelength, the transmission spectrum exhibits a flat bandgap structure with very steep walls. We show that for odd N the tuning of the excitation frequency of a central qubit gives rise to the appearance within a bandgap of a narrow resonance with a full transmission. The position of the resonance and its width can be controlled by the frequency of a central qubit. We show that the formation of the bandgap and of the transmission resonance is conditioned by the overlapping the widths of individual qubits which results from the strong coupling between qubits and waveguide photons.