Theoretical seminar | 24 March 2021
I am planning to discuss several recent findings (theoretical and experimental) in the dynamics of an impurity particle injected into a quantum liquid:
(i) The momentum distribution of the impurity in one dimension subject to a constant external force exhibits characteristic Bragg reflections at the edge of an emergent Brillouin zone. As a consequence, the impurity exhibits periodic dynamics that is interpreted as Bloch oscillations, which arise even though the quantum liquid is translationally invariant.
(ii) The impurity injected into a one-dimensional liquid with some initial momentum sheds only a part of it to the background gas, and forms a correlated state that no longer decays in time; furthermore, if the initial momentum is large enough, the impurity undergoes long-lived oscillations. The value of the impurity's velocity at infinite time lies between zero and the speed of sound in the gas, and is determined by the injection protocol. This way, the impurity's frictionless motion is a dynamically emergent phenomenon whose description goes beyond accounting for the kinematic constraints of Landau's approach to superfluidity.
(iii) The impurity traveling through a weakly interacting three-dimensional Bose-Einstein condensate (BEC) of ultra-cold atoms shows a phase transition in the ground state and far-from-equilibrium properties of the system as a function of the impurity's velocity. Above a critical initial velocity, the impurity's final velocity reaches a fundamental kinematic boundary, the BEC's speed of sound. For weak and intermediate impurity-BEC interactions, the critical line is determined by the effective mass of the polaron. This quantum transition can be interpreted as a dynamical Cherenkov effect; the impurity-BEC interaction causes the dynamics of the system to appear as if the bare impurity is propagating through a BEC whose speed of sound is altered by an effective refractive index.