  The recent experimental implementation of condensed matter models in optical
lattices has motivated research on their nonequilibrium behavior. Predictions
on the dynamics of superconductors following a sudden quench of the pairing
interaction have been made based on the effective BCS Hamiltonian; however,
their experimental verification requires the preparation of a suitable excited
state of the Hubbard model along a twofold constraint: (i) a sufficiently
nonadiabatic ramping scheme is essential to excite the nonequilibrium dynamics,
and (ii) overheating beyond the critical temperature of superconductivity must
be avoided. For commonly discussed interaction ramps there is no clear
separation of the corresponding energy scales. Here we show that the matching
of both conditions is simplified by the intrinsic relaxation behavior of
ultracold fermionic systems: For the particular example of a linear ramp we
examine the transient regime of prethermalization [M. Moeckel and S. Kehrein,
Phys. Rev. Lett. 100, 175702 (2008)] under the crossover from sudden to
adiabatic switching using Keldysh perturbation theory. A real-time analysis of
the momentum distribution exhibits a temporal separation of an early energy
relaxation and its later thermalization by scattering events. For long but
finite ramping times this separation can be large. In the prethermalization
regime the momentum distribution resembles a zero temperature Fermi liquid as
the energy inserted by the ramp remains located in high energy modes. Thus
ultracold fermions prove robust to heating which simplifies the observation of
nonequilibrium BCS dynamics in optical lattices.
