Impact of phonon-meditated back-action in SiGe spin qubits

Phonons emitted by semiconducting spin qubit read out devices, such as quantum point contacts or single electron transistors, can be coherently absorbed by the qubit leading to back-action effects. For example, it was experimentally demonstrated that phonons emitted by a quantum point contact can modify the charge stability diagram of a GaAs spin qubit [1]. More specifically, the absorption of the phonons lead to oscillations in the probability of being in different charge states, which produced observable ripples in the charge stability diagram. In this work, we theoretically extend the work of Ref. [1] to a SiGe spin qubit which is readout by a single electron transistor. Using various analytical methods, including Keldysh field theory, we discuss how the charge stability diagram is impacted by the coherent absorption of phonons emitted by the single electron transistor and similarities and differences with the results presented in Ref. [1] for GaAs. We then move beyond a single qubit and investigate how two-qubit gate fidelity is impacted by this phonon-mediated back-action process.

 

[1] G. Granger, et al. Nature Physics 8, 522 (2012)