Quenching a Bose-condensate to unitarity: transients, steady states, and novel singularities

Motivated by recent experiments [1], we study the dynamics of a three-dimensional Bose gas following a sudden quench of the scattering length from zero to unitarity. We show that essential features of the time-evolution of the momentum distribution $n(k)$ can be captured with two simple approaches: an analytic two-body calculation and a numerical time-dependent variational ansatz for the many-body state. Although both approaches can capture the growth and oscillations of $n(k)$ as a function of time for short times and large $k$, only the variational approach predicts the formation of a steady state for large-momentum observables, where $n(k)$ approaches a time-independent function. We report the appearance of a short-distance (large-momentum) singularity that is absent in equilibrium. We incorporate the physics governing particle loss through a three-body calculation. Consistent with experiments, we predict lifetimes which are long compared to the dynamics of large momentum modes. \\[4pt] [1] Makotyn \textit{et al.}, Nature Physics \textbf{10}, 116-119 (2014)