The use of time-dependent flux is ubiquitous in the context of circuit quantum electrodynamics. It is critical to accurately model time-dependent flux in circuit Hamiltonians, which is what Xinyuan at al. did in our previous work. Working with Houck lab in Princeton, we provide experimental verification of what the flux allocation should be in the presence of rapid time-varying flux in superconducting circuits.

In particular, we design experiments by applying fast flux ramps to a fluxonium circuit. The circuit can be described by a Hamiltonian as a function of the external flux threading through the circuit loop. With a static magnetic flux, hamiltonians with external flux allocated either in the junction term or in the inductor term are equivalent. However, in the presence of time-dependent flux φ → φ(t), this equivalence no longer holds. We initially bias the circuit at or near the half-flux point, then rapidly tune the flux away to a common final value, and measure the qubit occupation probability. Our experimental results closely agree with the sudden-approximation predictions using the inductor allocation.

As flux modulation of multiloop circuits becomes more prevalent, careful use of irrotational variables is essential to obtain correct predictions of device behavior.

The paper can be found here.