Abstract
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 -wave scattering length is increased from zero with arbitrary time dependence. We show that, at short time, the energy density can at most increase as , which can be achieved when the time dependence of is also proportional to , and especially, a universal maximum energy growth rate can be reached when varies as . If varies faster or slower than , 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.
- Received 9 March 2021
- Revised 19 April 2021
- Accepted 21 May 2021
DOI:https://doi.org/10.1103/PhysRevLett.126.240401
© 2021 American Physical Society