### 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 |
---|---|

Article number | 094502 |

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

Volume | 85 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2 Mar 2012 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

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

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

**Inverse Landau-Zener-Stückelberg problem for qubit-resonator systems.** / Shevchenko, S. N.; Ashhab, Sahel; Nori, Franco.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 85, no. 9, 094502. https://doi.org/10.1103/PhysRevB.85.094502

}

TY - JOUR

T1 - Inverse Landau-Zener-Stückelberg problem for qubit-resonator systems

AU - Shevchenko, S. N.

AU - Ashhab, Sahel

AU - Nori, Franco

PY - 2012/3/2

Y1 - 2012/3/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84858059208&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858059208&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.85.094502

DO - 10.1103/PhysRevB.85.094502

M3 - Article

VL - 85

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 9

M1 - 094502

ER -