  A Quantum Point Contact (QPC) causes a one-dimensional constriction on the
spatial potential landscape of a two-dimensional electron system. By tuning the
voltage applied on a QPC at low temperatures the resulting regular step-like
electron conductance quantization can show an additional kink near pinch-off
around 0.7(2$e^2$/h), called 0.7-anomaly. In a recent publication, we presented
a combination of theoretical calculations and transport measurements that lead
to a detailed understanding of the microscopic origin of the 0.7-anomaly.
Functional Renormalization Group-based calculations were performed exhibiting
the 0.7-anomaly even when no symmetry-breaking external magnetic fields are
involved. According to the calculations the electron spin susceptibility is
enhanced within a QPC that is tuned in the region of the 0.7-anomaly. Moderate
externally applied magnetic fields impose a corresponding enhancement in the
spin magnetization. In principle, it should be possible to map out this spin
distribution optically by means of the Faraday rotation technique. Here we
report the initial steps of an experimental project aimed at realizing such
measurements. Simulations were performed on a particularly pre-designed
semiconductor heterostructure. Based on the simulation results a sample was
built and its basic transport and optical properties were investigated.
Finally, we introduce a sample gate design, suitable for combined transport and
optical studies.
