Dynamics of a mobile impurity in a two-leg bosonic ladder

Abstract

We have analyzed the behavior of a mobile quantum impurity in a bath formed by a two-leg bosonic ladder by a combination of field theory (Tomonaga-Luttinger liquid) and numerical (Density Matrix Renormalization Group) techniques. Computing the Green's function of the impurity as a function of time at different momenta, we find a power law decay at zero momentum, which signals the breakdown of any quasi-particle description of the impurity motion. We compute the exponent both for the limits of weak and strong impurity-bath interactions. At small impurity-bath interaction, we find that the impurity experiences the ladder as a single channel one-dimensional bath, but effective coupling is reduced by a factor of √ 2, thus the impurity is less mobile in the ladder compared to a one dimensional bath. We compared the numerical results for the exponent at zero momentum with a semi-analytical expression that was initially established for the chain and find excellent agreement without adjustable parameters. We analyze the dependence of the exponent in the transverse hopping in the bath and find surprisingly an increase of the exponent at variance with the naive extrapolation of the single channel regime. We study the momentum dependence of the impurity Green's function and find that, as for the single chain, two different regime of motion exist, one dominated by infrared metatrophy and a more conventional polaronic behavior. We compute the critical momentum between these two regimes and compare with prediction based on the structure factor of the bath. In the polaronic regime we also compute numerically the lifetime of the polaron. Finally we discuss how our results could be measured in cold atomic experiments.

Entanglement-assisted tunneling dynamics of impurities in a double well immersed in a bath of lattice trapped bosons

“…Indeed, in these systems correlation effects, such as entanglement, are expected to be a crucial ingredient since the impurities form a few-body subsystem [47]. Moreover, the underlying trapping potential plays an important role for the behavior of the impurity species, which has been analyzed for homogeneous systems [48][49][50], harmonic confinements [51][52][53][54][55] as well as lattice potentials [33,56,57]. The majority of the above-mentioned investigations have been focusing on the case where both species are trapped in the same geometry.…”

Many-body collisional dynamics of impurities injected into a double-well trapped Bose-Einstein condensate

“…Here, the concept of a polaron [18], which has been exhaustively studied in solid state physics, can be recovered where the impurity plays the role of an effective particle dressed by the excitations of its surrounding. In this context, the existence and characteristics of Fermi [19][20][21][22][23] and Bose polarons [24][25][26][27][28] have been unveiled, mainly focusing on their stationary properties [29][30][31][32] and more recently on the dynamics [33][34][35] of these quasi-particles. Another important aspect of such impurity settings concerns their transport properties through the environment.…”

Radiofrequency spectroscopy of one-dimensional trapped Bose polarons: crossover from the adiabatic to the diabatic regime

“…These methods initially aimed to address the equilibrium polaron properties, such as their effective mass [23,30], induced interactions [24,31], bound bipolaron [3,4,32] and trimeron [33] states. More recently, the nonequilibrium dynamics of polarons [25,26,29,[34][35][36][37][38] have attempted to address issues, such as the collisional properties with the host bath particles [18,[39][40][41][42][43][44], tunneling in optical lattices [45][46][47][48], dynamics of doped insulators [49][50][51], induced correlations [52,53], relaxation processes [36,54] and dynamical decay, i.e. the temporal orthogonality catastrophe (TOC) [25,52,55].…”