Cotunneling in pairs of coupled flux qubits

Superconducting circuits have played an essential role in realizing quantum mechanical phenomena in macroscopic systems. One such example is the observation of macroscopic resonant tunneling (MRT) of magnetic flux between the lowest energy states of single rf-SQUID flux qubits, as demonstrated by several groups [1–4]. These measurements provide both a clear signature of quantum mechanics in a macroscopic circuit at a finite temperature and in the presence of noise and a direct means of determining the tunneling energy between states. Theoretical descriptions of the MRT rate have been presented [5, 6] and indicate a direct connection between the profile of the MRT rate peaks and properties of the environment. Analogous measurements of the tunneling of magnetization in nanomagnets [7, 8] suggest that MRT is responsible for dynamics in these materials as well. In this work, we extend measurements of MRT to inductively coupled pairs of flux qubits. We present experimental observations of tunneling between the two lowest energy states of the coupled system for several coupling strengths. These data yield two-qubit energy gaps that match those predicted by the independently calibrated Hamiltonian of the coupled system. Moreover, measurements of the two-qubit energy gap are used to infer sin