### Abstract

We consider theoretically a superconducting qubit-nanomechanical resonator (NR) system, which was realized by LaHaye. First, we study the problem where the state of the strongly driven qubit is probed through a 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-Stückelberg 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.

Original language | English |
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Article number | 094502 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 85 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2 Mar 2012 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*85*(9), [094502]. https://doi.org/10.1103/PhysRevB.85.094502