Nonlinear spectroscopy of superconducting anharmonic resonators

TL;DR

This paper develops a quantum nonlinear oscillator model for superconducting resonators, revealing complex excitation responses, quantum interference effects, and Fano resonances, with implications for qubit readout techniques.

Contribution

It introduces a circuit-based quantum model for nonlinear resonators, analyzing both classical and quantum features of their steady-state response under various damping and excitation conditions.

Findings

Identification of a classical-like trough near Duffing bifurcation at high damping

Observation of discrete spectral features indicating quantum Fano resonances at low damping

Quantum effects modify classical interference patterns in the oscillator response

Abstract

We formulate a model for the steady state response of a nonlinear quantum oscillator structure, such as those used in a variety of superconducting qubit experiments, when excited by a steady, but not necessarily small, ac tone. We show that this model can be derived directly from a circuit description of some recent qubit experiments in which the state of the qubit is read out directly, without a SQUID magnetometer. The excitation profile has a rich structure depending on the detuning of the tone from the small-signal resonant frequency, on the degree of damping, and on the excitation amplitude. We explore two regions in detail: First, at high damping there is a trough in the excitation response as a function of detuning, near where the classical Duffing bifurcation occurs. This trough has been understood as a classical interference between two metastable responses with opposite phase. We use Wigner function studies to show that while this picture is roughly correct, there are also more quantum mechanical aspects to this feature. Second, at low damping we study the emergence of sharp, discrete spectral features from a continuum response. We show that these the structures, associated with discrete transitions between different excited-state eigenstates of the oscillator, provide an interesting example of a quantum Fano resonance. The trough in the Fano response evolves continuously from the "classical" trough at high damping.