  What happens to the QCD vacuum when a time-periodic circularly polarized
laser field with a sufficiently large intensity and frequency is applied? Based
on the Floquet formalism for periodically driven systems and the systematic
low-energy effective theory of QCD, we show that for a sufficiently large
frequency and above a critical intensity, the QCD vacuum is unstable against
the chiral soliton lattice of pions; a crystalline structure of topological
solitons that spontaneously breaks parity and continuous translational
symmetries. Our work would pave the way for novel "Floquet vacuum engineering."
