von Neumann spin measurements with Rashba fields

• Published in: New journal of physics Vol. 16; no. 1; pp. 15013 - 17
• Main Authors: Ya Sherman, E, Sokolovski, D
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.01.2014
• Subjects: Cold atoms; Cold spinning; Electron spin; Evolution; Magnetic fields; Mapping; Orbital mechanics; Particle spin; Particles (of physics); Physics; Simulation; Spin dynamics; Spin-orbit interactions; Time measurement
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/16/1/015013

We show that dynamics in the spin-orbit coupling field simulate the von Neumann measurement of a particle spin. We demonstrate how the measurement influences the spin and coordinate evolution of a particle by comparing two examples of such a procedure. The first example is a simultaneous measurement of spin components, σx and σy, corresponding to non-commuting operators, which cannot be accurately obtained together at a given time instant due to the Heisenberg uncertainty ratio. By mapping spin dynamics onto a spatial walk, such a procedure determines measurement-time averages of σx and σy, which can already be precisely evaluated in a single short-time measurement. The other, qualitatively different, example is the spin of a one-dimensional particle in a magnetic field. Here, the measurement outcome depends on the angle between the spin-orbit coupling and magnetic fields. These results can be applied to studies of spin-orbit coupled cold atoms and electrons in solids.