Effective approach to impurity dynamics in one-dimensional trapped Bose gases

Abstract

We investigate a temporal evolution of an impurity atom in a one-dimensional trapped Bose gas following a sudden change of the boson-impurity interaction strength. Our focus is on the effects of inhomogeneity due to the harmonic confinement. These effects can be described by an effective one-body model where both the mass and the spring constant are renormalized. This is in contrast to the classic renormalization, which addresses only the mass. We propose an effective single-particle Hamiltonian and apply the multi-layer multi-configuration time-dependent Hartree method for bosons to explore its validity. Numerical results suggest that the effective mass is smaller than the impurity mass, which means that it cannot straightforwardly be extracted from translationally-invariant models.arXiv:1809.01889v3 [cond-mat.quant-gas]

Many-body quantum dynamics and induced correlations of Bose polarons

“…It is also important to mention that this effective potential approximation is adequate only for weak interspecies interactions where the impurity-BEC entanglement is small [35,75]. Note also that the inclusion of the Thomas-Fermi approximation in the effective potential of equation (15) can not adequately describe the impurities dynamics when they reach the edges of the bosonic cloud, see [36] for more details. However in this case ( ) [35,65].…”

“…Experimentally Bose [20][21][22][23][24] and Fermi [12,13,17] polarons have been observed and these experiments confirmed the importance of higher-order correlations for the description of the polaronic properties. The experiments in turn have spurred additional several theoretical investigations which have aimed at describing different polaronic aspects [25,26] by operating e.g.within the Fröhlich model [27][28][29][30][31], effective Hamiltonian approximations [8,[32][33][34], variational approaches [7,9,22,[35][36][37], renormalization group methods [25,38,39] and the path integral formalism [40,41].…”

Dissipative correlated dynamics of a moving impurity immersed in a Bose–Einstein condensate

“…Indeed, we can deduce that X t I á ñ ( ) oscillates with a decaying amplitude in time which is more pronounced deeper in the attractive regime of interactions, compare X t I á ñ ( ) for g BI =−0.5 and g BI =−2. This attenuation of the oscillation amplitude of X t I á ñ ( ) is a direct effect of the presence of interspecies interactions and the underlying energy transfer process from the impurity to the bath, see also the discussion below and[25,64]. Also, -like shape tends to be more localized for larger negative values…”

“…These experiments triggered an intense theoretical activity in order to describe the polaron characteristics by operating within different frameworks [31,32]. These include, but are not restricted to, the mean-field approximation [33][34][35][36], the Fröhlich model [37][38][39][40][41][42], variational methods [14,17,24,25,27], effective Hamiltonian approaches [16,21,43,44] and renormalization group techniques [20,31,45]. While the majority of these investigations have been mainly focused on the equilibrium properties of the emergent quasiparticles, the dynamics of impurities is far less explored.…”

Pulse- and continuously driven many-body quantum dynamics of bosonic impurities in a Bose-Einstein condensate

“…Having established an adequate understanding of the stationary properties of polarons, a natural next step which has been very recently put forward is to investigate their nonequilibrium dynamics [40,41] revealing peculiar correlation effects [36,[40][41][42][43][44][45][46]. Indeed, the crucial involve-ment of interparticle correlations can lead to non-linear structure formation [43,47], alterations of the breathing frequency [48], the manifestation of orthogonality catastrophe phenomena [41,49,50], dissipative motion of impurities in the many-body medium [51] and also their relaxation dynamics [46,52]. Other applications address impurity transport in optical lattices [53][54][55][56], their collisional dynamics when penetrating with a finite velocity a gas of Tonks-Girardeau bosons [57][58][59][60][61], the effective control of quantum coherence [62] and investigations of three-body Effimov physics [63,64].…”