Multi-frequency modes in superconducting resonators: Bridging frequency gaps in off-resonant couplings

TL;DR

This paper develops a theoretical framework for multi-frequency modes in superconducting resonators with periodically driven SQUIDs, enabling efficient quantum state transfer and entanglement in hybrid quantum systems.

Contribution

It introduces a novel quantization theory for multi-frequency modes induced by driven SQUIDs and demonstrates their application in quantum information processing.

Findings

Derived the eigenmodes of resonators with driven SQUIDs

Showed resonant coupling to qubits with different frequencies

Proposed a bi-chromatic scheme for entanglement and gates

Abstract

A Superconducting Quantum Interference Device (SQUID) inserted in a superconducting waveguide resonator imposes current and voltage boundary conditions that makes it suitable as a tuning element for the resonator modes. If such a SQUID element is subject to a periodically varying magnetic flux, the resonator modes acquire frequency side bands. In this work we calculate the multi-frequency eigenmodes of resonators coupled to periodically driven SQUIDs and we use the Lagrange formalism to propose a theory for their quantization. The elementary excitations of a multi-frequency mode can couple resonantly to physical systems with different transition frequencies and this makes the resonator an efficient quantum bus for state transfer and coherent quantum operations in hybrid quantum systems. As an example of the application of our multi-frequency modes, we determine their coupling to transmon qubits with different frequencies and we present a bi-chromatic scheme for entanglement and gate operations.