Probing Quantum Speed Limits with Ultracold Gases

Quantum speed limits (QSLs) rule the minimum time for a quantum state to evolve into a distinguishable state in an arbitrary physical process. These fundamental results constrain a notion of distance traveled by the quantum state, known as the Bums angle, in terms of the speed of evolution set by nonadiabatic energy fluctuations. I theoretically propose how to measure QSLs in an ultracold quantum gas confined in a time-dependent harmonic trap. In this highly-dimensional system of continuous variables, quantum tomography is prohibited. Yet, QSLs can be probed whenever the dynamics is self-similar by measuring as a function of time the cloud size of the ultracold gas. This makes it possible to determine the Bures angle and energy fluctuations, as I discuss for various ultracold atomic systems.