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We determine the exact dynamics of an initial Bardeen-Cooper-Schrieffer (BCS)state of ultra-cold atoms in a deep hexagonal optical lattice. The dynamicalevolution is triggered by a quench of the lattice potential, such that theinteraction strength $U_f$ is much larger than the hopping amplitude $J_f$. Thequench initiates collective oscillations with frequency $|U_f|/(2\pi)$ in themomentum occupation numbers and imprints an oscillating phase with the samefrequency on the BCS order parameter $\Delta$. The oscillation frequency of$\Delta$ is not reproduced by treating the time evolution in mean-field theory.In our theory, the momentum noise (i.e. density-density) correlation functionsoscillate at frequency $|U_f|/2\pi$ as well as at its second harmonic. For avery deep lattice, with zero tunneling energy, the oscillations of momentumoccupation numbers are undamped. Non-zero tunneling after the quench leads todephasing of the different momentum modes and a subsequent damping of theoscillations. The damping occurs even for a finite-temperature initial BCSstate, but not for a non-interacting Fermi gas. Furthermore, damping isstronger for larger order parameter and may therefore be used as a signature ofthe BCS state. Finally, our theory shows that the noise correlation functionsin a honeycomb lattice will develop strong anti-correlations near the Diracpoint.

Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices