Von Neumann spin measurements with Rashba fields

We show that dynamics in spin-orbit coupling field simulates 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. First example is a simultaneous measurement of spin components, $\sigma _{x}$ and $\sigma _{y}$, 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 $\sigma _{x}$ and $\sigma _{y}$, which already can 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 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.Comment: 6 figure

Spin evolution of cold atomic gases in SU(2)⊗\otimes U(1) fields

We consider response function and spin evolution in spin-orbit coupled cold atomic gases in a synthetic gauge magnetic field influencing solely the orbital motion of atoms. We demonstrate that various regimes of spin-orbit coupling strength, magnetic field, and disorder can be treated within a single approach based on the representation of atomic motion in terms of auxiliary collective classical trajectories. Our approach allows for a unified description of fermionic and bosonic gases.Comment: 8 pages, 2 figure

Duality of the spin and density dynamics for two-dimensional electrons with a spin-orbit coupling

We study spin dynamics in a two-dimensional electron gas with a pure gauge non-Abelian spin-orbit field, for which systems with balanced Rashba and Dresselhaus spin-orbit couplings, and the (110)-axis grown GaAs quantum wells are typical examples. We demonstrate the duality of the spin evolution and the electron-density dynamics in a system without spin-orbit coupling, which considerably simplifies and deepens the analysis of spin-dependent processes. This duality opens a venue for the understanding of this class of systems, highly interesting for their applications in spintronics, through known properties of the systems without spin-orbit coupling.Comment: version accepted to PRB, revtex4, 4+ pages, 1 figur

Diffusive and precessional spin dynamics in a two-dimensional electron gas with disorder: a gauge theory view

We develop a gauge theory for diffusive and precessional spin dynamics in two-dimensional electron gas with disorder. Our approach reveals a direct connections between the absence of the equilibrium spin current and strong anisotropy in the spin relaxation: both effects arise if the spin-orbit coupling is reduced to a pure gauge SU(2) field. In this case, by a gauge transformation in the form of a local SU(2) rotation in the spin subspace the spin-orbit coupling can be removed. The resulting spin dynamics is exactly described in terms of two kinetic coefficients: the spin diffusion and electron mobility. After the inverse transformation, full diffusive and precessional spin density dynamics, including the anisotropic spin relaxation, formation of stable spin structures, and spin precession induced by a macroscopic current, is restored. Explicit solutions of the spin evolution equations are found for the initially uniform spin density and for stable nonuniform structures. Our analysis demonstrates a universal relation between the spin relaxation rate and spin diffusion coefficient.Comment: published version, minor correction