Floquet state spectroscopy of a semiconductor charge qubit with a microwave resonator

Applying a strong periodic drive to a qubit is a useful method to manipulate its state and gives rise to intricate physics, such as the ac Stark effect and Landau-Zener-Stückelberg interference [1], characterized by the emergence of Floquet states. Here, we measure a strongly driven GaAs double quantum dot charge qubit with a weakly coupled superconducting microwave resonator [2]. In contrast to earlier experiments [1, 3, 4], we probe the Floquet states by tracing the qubit - resonator resonance condition as a function of the drive amplitude and the detuning between the (2,1) and (1,2) charge configurations of the qubit. For large drive amplitudes, multiple resonances emerge corresponding to processes involving a single resonator photon and multiple drive field photons. Furthermore, we observe Landau-Zener-Stückelberg interference arising only for those resonances that involve at least a single photon absorbed from the drive.

[1] S.N. Shevchenko, S. Ashhab, and F. Nori, Phys. Rep. 492, 1 (2010)
[2] Manuscript in preparation
[3] F. Forster et al., Phys. Rev. Lett. 112, 116803 (2014)
[4] J. Stehlik et al., Phys. Rev. X 6, 041027 (2016)