  We present a novel approach to precisely synthesize arbitrary polarization
states of light with a high modulation bandwidth. Our approach consists of
superimposing two laser light fields with the same wavelength, but with
opposite circular polarizations, where the phase and the amplitude of each
light field are individually controlled. We find that the
polarization-synthesized beam reaches a degree of polarization of 99.99%, which
is mainly limited by static spatial variations of the polarization state over
the beam profile. We also find that the depolarization caused by temporal
fluctuations of the polarization state is about 2 orders of magnitude smaller.
In a recent work, Robens et al. [Phys. Rev. Lett. 118, 065302 (2017)]
demonstrated an application of the polarization synthesizer to create two
independently controllable optical lattices, which trap atoms depending on
their internal spin state. We here use ultracold atoms in
polarization-synthesized optical lattices to give an independent, in situ
demonstration of the performance of the polarization synthesizer.
