Coupling a single electron spin to a microwave resonator: Controlling transverse and longitudinal couplings

Microwave-frequency superconducting resonators are ideally suited to perform dispersive qubit readout, to mediate two-qubit gates, and to shuttle states between distant quantum systems. A prerequisite for these applications is a strong qubit-resonator coupling. Strong coupling between an electron-spin qubit and a microwave resonator can be achieved by correlating spin- and orbital degrees of freedom. This correlation can be achieved through the Zeeman coupling of a single electron in a double quantum dot to a spatially inhomogeneous magnetic field generated by a nearby nanomagnet. In this paper, we consider such a device and estimate spin-resonator couplings of order ~ 1 MHz with realistic parameters. Further, through realistic simulations, we show that precise placement of the double dot relative to the nanomagnet allows to select between a purely longitudinal coupling (commuting with the bare spin Hamiltonian) and a purely transverse (spin non-conserving) coupling. Additionally, we suggest methods to mitigate dephasing and relaxation channels that are introduced in this coupling scheme. This analysis gives a clear route toward the realization of coherent state transfer between a microwave resonator and a single electron spin in a GaAs double quantum dot with a fidelity above 90%. Improved dynamical decoupling sequences, low-noise environments, and longer-lived microwave cavity modes may lead to substantially higher fidelities in the near future.