Prof. Evgeny Ya. Sherman - How Spin-Orbit Coupling Measures the Spin

We show that a linear in momentum spin-orbit coupling simulates a dynamical meas-urement of a spin 1/2. This procedure realizes the seminal proposal of von Neumann for mapping a quantum process onto a motion of a corresponding pointer. We demonstrate how the measurement influences the spin and coordinate evolution of a particle by ana-lyzing two examples. First example is a simultaneous measurement of spin projections at the x and y- axes.  These quantities cannot be accurately obtained together at a given time instant due to the Heisenberg uncertainty ratio. We find that such a procedure de-termines measurement-time averages of these projections, which can be precisely known [1]. Second example is a measurement of spin components of a one-dimensional particle in a magnetic field. We discuss a possibility to see the Zeno effect, that is a slow dynamics, with spin-orbit coupling. These results can be applied to electrons in semiconductor nanostructures and cold atoms.

[1] D. Sokolovski and E. Ya. Sherman, Phys. Rev. A 84, 030101(R) (2011)