Inverse Landau-Zener-Stuckelberg problem for qubit-resonator systems

TL;DR

This paper theoretically analyzes a superconducting qubit-nanomechanical resonator system, demonstrating how the qubit's state influences the resonator's frequency and solving an inverse problem to determine qubit parameters from known states.

Contribution

It introduces a method to infer qubit Hamiltonian parameters from known states, linking the qubit's bias to the resonator's displacement, and aligns theoretical results with experimental observations.

Findings

Frequency shift changes sign under resonant driving

Theoretical results match experimental measurements

Inverse problem solution for qubit parameter estimation

Abstract

We consider theoretically a superconducting qubit - nanomechanical resonator (NR) system, which was realized by LaHaye et al. [Nature 459, 960 (2009)]. First, we study the problem where the state of the strongly driven qubit is probed through the frequency shift of the low-frequency NR. In the case where the coupling is capacitive, the measured quantity can be related to the so-called quantum capacitance. Our theoretical results agree with the experimentally observed result that, under resonant driving, the frequency shift repeatedly changes sign. We then formulate and solve the inverse Landau-Zener-Stuckelberg problem, where we assume the driven qubit's state to be known (i.e. measured by some other device) and aim to find the parameters of the qubit's Hamiltonian. In particular, for our system the qubit's bias is defined by the NR's displacement. This may provide a tool for monitoring of the NR's position.