Maximum Energy Growth Rate in Dilute Quantum Gases

In this Letter we study how fast the energy density of a quantum gas can increase in time, when the interatomic interaction characterized by the s-wave scattering length as is increased from zero with arbitrary time dependence. We show that, at short time, the energy density can at most increase as t, which can be achieved when the time dependence of as is also proportional to t, and especially, a universal maximum energy growth rate can be reached when as varies as 2ℏt/(πm). If as varies faster or slower than t, it is, respectively, proximate to the quench process and the adiabatic process, and both result in a slower energy growth rate. These results are obtained by analyzing the short time dynamics of the short-range behavior of the many-body wave function characterized by the contact, and are also confirmed by numerically solving an example of interacting bosons with time-dependent Bogoliubov theory. These results can also be verified experimentally in ultracold atomic gases.