  According to Noethers theorem, for every symmetry in nature there is a
corresponding conservation law. For example, invariance with respect to spatial
translation corresponds to conservation of momentum. In another well-known
example, invariance with respect to rotation of the electrons spin, or SU(2)
symmetry, leads to conservation of spin polarization. For electrons in a solid,
this symmetry is ordinarily broken by spin-orbit coupling, allowing spin
angular momentum to flow to orbital angular momentum. However, it has recently
been predicted that SU(2) can be achieved in a two-dimensional electron gas,
despite the presence of spin-orbit coupling. The corresponding conserved
quantities include the amplitude and phase of a helical spin density wave
termed the persistent spin helix. SU(2) is realized, in principle, when the
strength of two dominant spin-orbit interactions, the Rashba (strength
parameterized by \alpha) and linear Dresselhaus (\beta_1), are equal. This
symmetry is predicted to be robust against all forms of spin-independent
scattering, including electron-electron interactions, but is broken by the
cubic Dresselhaus term (\beta_3) and spin-dependent scattering. When these
terms are negligible, the distance over which spin information can propagate is
predicted to diverge as \alpha approaches \beta_1. Here we observe
experimentally the emergence of the persistent spin helix in GaAs quantum wells
by independently tuning \alpha and \beta_1. Using transient spin-grating
spectroscopy, we find a spin-lifetime enhancement of two orders of magnitude
near the symmetry point.........
