Spectroscopy of Quantum-Dot Orbitals with In-Plane Magnetic Fields*

While spins in quantum dots have received a lot of attention for the development as a qubit, the orbitals which are hosting the qubit have largely been ignored. However, important processes such as electric-dipole spin resonance and spin relaxation depend sensitively on the dot shape due to the anisotropic nature of the spin-orbit interaction.
Here, we present a method which allows quantifying the in-plane orientation angle and the strength of the hard confinement perpendicular to the 2D gas in which the gate-defined single-electron GaAs dot is formed. Using a piezo electric rotator, we control the direction of the magnetic field in the 2D plane and measure the in-plane orbital energies using pulse gate spectroscopy. Based on a model of the orbitals, we extract the orientation angle of the dot in the 2D plane, quantify the strong confinement and characterize deviations from a harmonic oscillator potential. Our measurements demonstrate a versatile tool for quantum dots with one dominant axis of strong confinement.