Correlated quantum dynamics of two quenched fermionic impurities immersed in a Bose-Einstein condensate

Abstract

We unravel the nonequilibrium dynamics of two fermionic impurities immersed in a onedimensional bosonic gas following an interspecies interaction quench from weak to strong repulsions. Monitoring the temporal evolution of the single-particle density of each species we reveal the existence of four distinct dynamical regimes. For weak interspecies repulsions both species either perform a breathing motion or the impurity density splits into two parts which interact and disperse within the bosonic cloud. Turning to strong interactions we observe the formation of darkbright states within the mean-field approximation. However, the correlated dynamics shows that the fermionic density splits into two repelling density peaks which either travel towards the edges of the bosonic cloud where they equilibrate or they approach an almost steady state propagating robustly within the bosonic gas which forms density dips at the same location. For these strong interspecies interactions an energy transfer process from the impurities to their environment occurs at the many-body level, while a periodic energy exchange from the bright states (impurities) to the bosonic species is identified in the absence of correlations. Finally, inspecting the one-body coherence function for strong interactions enables us to conclude on the spatial localization of the quench-induced fermionic density humps.

Many-body quantum dynamics and induced correlations of Bose polarons

“…Moreover, at initial evolution times (t<60) the amplitude of the breathing is almost constant whilst later on (t>60) it shows a slightly decaying tendency, see for instance the smaller height of the density peak at t=70 compared to t=20 in figure 5(b). This decaying amplitude can be attributed to the build up of impurityimpurity correlations in the course of the evolution [42] due to the presence of induced interactions discussed later on, see also figure 7(a). The breathing motion of the impurities is directly captured by the periodic contraction and expansion in the shape of the instantaneous density profiles of ( ) ( ) r  x t ; 1 depicted in figure 6(b).…”

“…Evidently, for weak  g B belonging either to region R II with = figure 4(b)) at frequencies ω f ≈8. 42 and ω f ≈8.79 for both the N I =1 and N I =2 cases. Accordingly, these two peaks suggest the formation of a quasiparticle dressed, for higher frequencies, by higher-order excitations of the BEC background.…”

“…Moreover, it provides insights into the spatially resolved dynamics of the two impurities with respect to one another. Indeed, the impurities are dressed by the excitations of the bosonic gas forming quasiparticles which in turn can move independently or interact, and possibly form a bound state [8,10,42,94].…”

“…To capture the emerging effective interactions between the two bosonic impurities we monitor their relative distance [9,42] given by Here,N a with =   a , is the number operator that measures the number of bosons in the spin-a state. Experimentally, ( ) á ñ r t aa can be probed via in situ spin-resolved single-shot measurements on the spin-a state [91].…”

“…However, the non-equilibrium dynamics of impurities is far less explored and is expected to be dominated by correlation effects which build up in the course of the evolution [34-36, 39, 42-45]. Existing examples include the observation of self-trapping phenomena [46,47], formation of dark-bright solitons [6,42], impurity transport in optical lattices [48][49][50][51], orthogonality catastrophe events [35,52], injection of a moving impurity into a gas of Tonks-Girardeau bosons [53][54][55][56][57][58][59][60] and the relaxation dynamics of impurities [45,61,62]. Besides these investigations, which have enabled a basic description of the quasiparticle states in different interaction regimes, a number of important questions remain open and a full theoretical understanding of the dynamics specifically of Bose polarons is still far from complete.…”