  Quantum spin liquids (QSLs) define an exotic class of quantum ground states
where spins are disordered down to zero temperature. We propose routes to QSLs
in kagome optical lattices using applied flux. An optical flux lattice can be
applied to induce a uniform flux and chiral three-spin interactions that drive
the formation of a gapped chiral spin liquid. A different approach based on
recent experiments using laser-assisted tunneling and lattice tilt implements a
staggered flux pattern which can drive a gapless spin liquid with symmetry
protected nodal lines. Our proposals, therefore, establish kagome optical
lattices with effective flux as a powerful platform for exploration of QSLs.
