  High resolution spin- and angle-resolved photoemission spectroscopy
(spin-ARPES) was performed on the three-dimensional topological insulator
Bi$_2$Se$_3$ using a recently developed high-efficiency spectrometer. The
topological surface state's helical spin structure is observed, in agreement
with theoretical prediction. Spin textures of both chiralities, at energies
above and below the Dirac point, are observed, and the spin structure is found
to persist at room temperature. The measurements reveal additional unexpected
spin polarization effects, which also originate from the spin-orbit
interaction, but are well differentiated from topological physics by
contrasting momentum and photon energy and polarization dependencies. These
observations demonstrate significant deviations of photoelectron and
quasiparticle spin polarizations. Our findings illustrate the inherent
complexity of spin-resolved ARPES and demonstrate key considerations for
interpreting experimental results.
