A Physically Meaningful Relativistic Description of the Spin State of an Electron

We introduced a new model to present the states of a two-state quantum system. The space is the complexified Minkowski space. The Lorentz group acts by the linear extension of its action on the four-vectors. We applied this model to represent the spin state of an electron or any relativistic spin 1/2 particle. The spin state of such particle is of the form U+iS, where U is the four-velocity of the particle in the lab frame, and S is the 4D spin in this frame. Under this description, the transition probability between two pure spin states ϱ1 and ϱ2 of particles moving with the same velocity are defined by use of Minkowski dot product as 12<ϱ2|ϱ1>. This transition probability is Lorentz invariant, coincide with the quantum mechanics prediction and thus agree with the experimental results testing quantum mechanics predictions based on Bell’s inequality. For a a particle of mass m and charge q with the spin state ϱ, the total momentum is mcϱ and the electromagnetic momentum is qϱ. This imply that the Landé g factor for such particles must be g=2. We obtain an evolution equation of the spin state in an electromagnetic field which defines correctly the anomalous Zeeman effect and the fine structure splitting.

Polarization Anisotropies in Strain-Free, Asymmetric, and Symmetric Quantum Dots Grown by Droplet Epitaxy

We provide an extensive and systematic investigation of exciton dynamics in droplet epitaxial quantum dots comparing the cases of (311)A, (001), and (111)A surfaces. Despite a similar s-shell exciton structure common to the three cases, the absence of a wetting layer for (311)A and (111)A samples leads to a larger carrier confinement compared to (001), where a wetting layer is present. This leads to a more pronounced dependence of the binding energies of s-shell excitons on the quantum dot size and to the strong anti-binding character of the positive-charged exciton for smaller quantum dots. In-plane geometrical anisotropies of (311)A and (001) quantum dots lead to a large electron-hole fine interaction (fine structure splitting (FSS) ∼100 μeV), whereas for the three-fold symmetric (111)A counterpart, this figure of merit is reduced by about one order of magnitude. In all these cases, we do not observe any size dependence of the fine structure splitting. Heavy-hole/light-hole mixing is present in all the studied cases, leading to a broad spread of linear polarization anisotropy (from 0 up to about 50%) irrespective of surface orientation (symmetry of the confinement), fine structure splitting, and nanostructure size. These results are important for the further development of ideal single and entangled photon sources based on semiconductor quantum dots.