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

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-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.

Multiphoton transitions in Josephson-junction qubits (Review Article)

“…As it was demonstrated in Ref. [88], two different approaches, called direct and inverse LZS interferometry, are of interest. In the direct interferometry the qubit state is probed via the NR's frequency shift, as in Ref.…”

“…In the case of inductive/capacitive coupling, the qubit's impact on the resonator can be described by introducing the qubit'sstate-dependent effective inductance/capacitance, while the losses can be described by the effective resistance. For concreteness, we will consider two realistic systems: the flux qubit inductively coupled to the tank circuit [87] and the charge qubit capacitively coupled to the nanomechanical resonator [88]. The resonator is demonstrated as the spring oscillator with the elasticity coefficient k0.…”

“…In contrast to the inductive coupling, considered in the previous subsection, here we mean capacitive coupling. Then it is straightforward to obtain the expression for the measurable value, the tank circuit phase shift at resonance frequency, ξ 0 = 0, [88] …”

“…[88] as the resonator's frequency shift ∆ω NR versus the energy bias n g and the driving amplitude n µ . The agreement with the experimental result of Ref.…”

“…The voltage-biased NR is measured through its resonance frequency shift ∆ωNR. [88] the NR is biased by dc and rf voltages V GNR and V RF through the capacitance C GNR .…”