WKB analysis of relativistic Stern-Gerlach measurements

Spin is an important quantum degree of freedom in relativistic quantum information theory. This paper provides a first-principles derivation of the observable corresponding to a Stern-Gerlach measurement with relativistic particle velocity. The specific mathematical form of the Stern-Gerlach operator is established using the transformation properties of the electromagnetic field. To confirm that this is indeed the correct operator we provide a detailed analysis of the Stern-Gerlach measurement process. We do this by applying a WKB approximation to the minimally coupled Dirac equation describing an interaction between a massive fermion and an electromagnetic field. Making use of the superposition principle we show that the +1 and -1 spin eigenstates of the proposed spin operator are split into separate packets due to the inhomogeneity of the Stern-Gerlach magnetic field. The operator we obtain is dependent on the momentum between particle and Stern-Gerlach apparatus, and is mathematically distinct from two other commonly used operators. The consequences for quantum tomography are considered.Comment: 13 pages, no figures. Comments welcom

Magneto-Optical Stern-Gerlach Effect in Atomic Ensemble

We study the birefringence of the quantized polarized light in a magneto-optically manipulated atomic ensemble as a generalized Stern-Gerlach Effect of light. To explain this engineered birefringence microscopically, we derive an effective Shr\"odinger equation for the spatial motion of two orthogonally polarized components, which behave as a spin with an effective magnetic moment leading to a Stern-Gerlach split in an nonuniform magnetic field. We show that electromagnetic induced transparency (EIT) mechanism can enhance the magneto-optical Stern-Gerlach effect of light in the presence of a control field with a transverse spatial profile and a inhomogeneous magnetic field.Comment: 7 pages, 5 figure

Optical evidence for adsorption of charged inverse micelles in a Stern layer

Understanding the properties and behavior of nonpolar liquids containing surfactant and colloidal particles is essential for applications such as electrophoretic ink displays and liquid toner printing. Charged inverse micelles, formed from aggregated surfactant molecules, and their effect on the electrophoretic motion of colloidal particles have been investigated in quite some detail over the past years. However, the interactions of charged inverse micelles at the electrode interfaces are still not well understood. In some surfactant systems the charged inverse micelles bounce off the electrodes, while in other systems they are quickly adsorbed to the electrodes upon contact. In this work a fluorocarbon solvent doped with a fluorosurfactant is investigated in which the adsorption of charged inverse micelles to the electrode occurs slowly, leading to long-term charging phenomena. We propose a physical model and an equivalent electrical model based on adsorption and desorption of inverse micelles into a Stern layer with finite thickness. We compare two limiting cases of this model: the 'adsorption/desorption' limit and the 'Stern layer adsorption' limit. Both limits are compatible with electrical measurements. The 'Stern layer adsorption' limit additionally explains the optical measurements, because these measurements indicate that the diffuse double layer vanishes over time when a polarizing voltage step is applied. The obtained value for the Stern layer thickness and the proportionality between the charging time constant and the surfactant concentration are also compatible with the 'Stern layer adsorption' limit

Arithmetic properties of the sequence of degrees of Stern polynomials and related results

Let $B_{n}(t)$ be a $n$-th Stern polynomial and let e(n)=\op{deg}B_{n}(t) be its degree. In this note we continue our study started in \cite{Ul} of the arithmetic properties of the sequence of Stern polynomials and the sequence $\{e(n)\}_{n=1}^{\infty}$. We also study the sequence d(n)=\op{ord}_{t=0}B_{n}(t). Among other things we prove that $d(n)=\nu(n)$, where $\nu(n)$ is the maximal power of 2 which dividies the number $n$. We also count the number of the solutions of the equations $e(m)=i$ and $e(m)-d(m)=i$ in the interval $[1,2^{n}]$. We also obtain an interesting closed expression for a certain sum involving Stern polynomials.Comment: 16 page