We investigate experimentally and theoretically the interference at avoided crossings which are repeatedly traversed as a consequence of an applied ac field. Our model system is a charge qubit in a serial double quantum dot connected to two leads. Our focus lies on effects caused by simultaneous driving with two different frequencies. We work out how the commensurability of the driving frequencies affects the symmetry of the interference patterns both in real space and in Fourier space. For commensurable frequencies, the symmetry depends sensitively on the relative phase between the two modes, whereas for incommensurable frequencies the symmetry of monochromatic driving is always recovered.

On-chip magnets can be used to implement relatively large local magnetic field gradients in nanoelectronic circuits. Such field gradients provide possibilities for all-electrical control of electron spin-qubits where important coupling constants depend crucially on the detailed field distribution. We present a double quantum dot (QD) hybrid device laterally defined in a GaAs / AlGaAs heterostructure which incorporates two single domain nanomagnets. They have appreciably different coercive fields which allows us to realize four distinct configurations of the local inhomogeneous field distribution. We perform dc transport spectroscopy in the Pauli-spin blockade regime as well as electric-dipole-induced spin resonance (EDSR) measurements to explore our hybrid nanodevice. Characterizing the two nanomagnets we find excellent agreement with numerical simulations. By comparing the EDSR measurements with a second double QD incorporating just one nanomagnet we reveal an important advantage of having one magnet per QD: It facilitates strong field gradients in each QD and allows to control the electron spins individually for instance in an EDSR experiment. With just one single domain nanomagnet and common QD geometries EDSR can likely be performed only in one QD.

The control of nuclear spins in quantum dots is essential to explore their many-body dynamics and exploit their prospects for quantum information processing. We present a unique combination of dynamic nuclear spin polarization and electric-dipole-induced spin resonance in an electrostatically defined double quantum dot (DQD) exposed to the strongly inhomogeneous field of two on-chip nanomagnets. Our experiments provide direct and unrivaled access to the nuclear spin polarization distribution and allow us to establish and characterize multiple fixed points. Further, we demonstrate polarization of the DQD environment by nuclear spin diffusion which significantly stabilizes the nuclear spins inside the DQD.