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. In the chiral limit, in particular, the QCD vacuum is found unstable by the laser with an arbitrary small intensity. Our work would pave the way for novel Floquet vacuum engineering.
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