Controlling the Effective Hamiltonian of a Driven Quantum Superconducting Circuit

Abstract

Can we observe and control the quantum manifestations of an effective Hamiltonian in a superconducting circuit submitted to a fast-oscillating driving force?

We have implemented the effective Hamiltonian of a Kerr oscillator submitted to a squeezing drive in a Josephson tunnel junction-based quantum superconducting circuit submitted to a microwave sinusoidal driving excitation. We experimentally measure pairwise simultaneous degeneracies in the spectrum of this effective Hamiltonian, which models a quantum double well. What underlies these simultaneous degeneracies is the unusual destructive interference of tunnel paths in the classically forbidden region, an effect revealing a hidden symmetry of the system. Not only can these degeneracies be turned on-and-off on demand, but their number is tunable: when the detuning ∆ of the drive’s second subharmonic from the oscillator frequency equals an even multiple of the Kerr coefficient K, ∆/K = 2m, the oscillator experiences m+1 exact spectral degeneracies. Importantly, these degeneracies are robust as they are completely independent of the drive amplitude. They also lead to a drastic reduction of the incoherent well-switching rate leading to our realization of a super-protected cat qubit. Our work indicates the circumstances by which the control of parametric processes via the drive frequency can provide a practical new tool for quantum technologies. Underlying this experiment is a calculation tool to transform—beyond the rotating-wave approximation—a time-dependent Hamiltonian describing a superconducting nonlinear circuit submitted to a fast-oscillating driving force to a time-independent effective Hamiltonian governing the dynamics of our quantum double-well system.