  We study the circular shaking of a two dimensional optical lattice, which is
essentially a (2+1) dimensional space-time lattice exhibiting periodicities in
both spatial and temporal dimensions. The near-resonant optical shaking
considered here dynamically couples the low-lying $s$ band and the first
excited $p$ bands by transferring a photon of shaking frequency. The
intertwined space-time symmetries are further uncovered to elucidate the
degeneracy in the spectrum solved with the generalized Bloch-Floquet theorem.
Setting the chirality of circular shaking explicitly breaks time reversal
symmetry and lifts the degeneracy of $p_\pm = p_x \pm ip_y$ orbitals, leading
to the local circulation of orbital magnetism, i.e the imbalanced occupation in
$p_\pm$ orbitals. Moreover, the dynamics of Berry connection is revealed by the
time evolution of the Berry curvature and the polarization, which have physical
observable effects in experiments. Interestingly, the dynamics is found
characterized by a universal phase shift, governed by the time screw rotational
symmetry involving a fractional translation of time. These findings suggest
that the present lattice-shaking scheme provides a versatile platform for the
investigation of the orbital physics and the symmetry-protected dynamics.
