Comment on "Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons [Phys. Rev. A 79, 033610 (2009)]"

The transition from "few to many" has recently been probed experimentally in an ultra cold harmonically confined one-dimensional lithium gas, in which a single impurity atom interacts with a background gas consisting of one, two, or more identical fermions [A. N. Wenz {\em{et al.}}, Science {\bf{342}}, 457 (2013)]. For repulsive interactions between the background or majority atoms and the impurity, the interaction energy for relatively moderate system sizes was analyzed and ...

A kinetic theory describing the motion of an impurity particle in a degenerate Tonks-Girardeau gas is presented. The theory is based on the one-dimensional Boltzmann equation. An iterative procedure for solving this equation is proposed, leading to the exact solution in number of special cases and to an approximate solution with the explicitly specified precision in a general case. Previously we have reported that the impurity reaches a non-thermal steady state, characterized...

We study the quantum dynamics of the two impurities in a trapped quasi-one-dimensional Bose-Einstein condensate (BEC). We explore the effect of impurity-BEC and impurity-impurity interaction strengths on the dynamics of impurities inside the Bose-Einstein condensate. By studying the auto-correlation function of impurities and the BEC, we analyze and quantify the trapping of impurities inside the BEC. We find out that for the small value of inter-species coupling strength the ...

We unravel the nonequilibrium dynamics of two fermionic impurities immersed in a one-dimensional 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...

The impurities, introduced intentionally or accidentally into certain materials, can significantly modify their characteristics or reveal their intrinsic physical properties, and thus play an important role in solid-state physics. Different from those static impurities in a solid, the impurities realized in cold atomic systems are naturally mobile. Here we propose an effective theory for treating some unique behaviors exhibited by ultracold mobile impurities. Our theory revea...

We develop a systematic perturbation theory for the quasiparticle properties of a single impurity immersed in a Bose-Einstein condensate. Analytical results are derived for the impurity energy, the effective mass, and residue to third order in the impurity-boson scattering length. The energy is shown to depend logarithmically on the scattering length to third order, whereas the residue and effective mass are given by analytical power series. When the boson-boson scattering le...

We study the motion of a slow quantum impurity in one-dimensional environments focusing on systems of strongly interacting bosons and weakly interacting fermions. While at zero temperature the impurity motion is frictionless, at low temperatures finite friction appears. The dominant process is the scattering of the impurity off two fermionic quasiparticles. We evaluate the friction force and show that, at low temperatures, it scales either as the fourth or the sixth power of ...

We study the static properties of a mobile impurity interacting with a bath with a few distinguishable particles trapped in a one-dimensional harmonic trap. We focus on the limiting case where the bath is non-interacting. We provide numerical results for the energy spectra and density profiles by means of the exact diagonalization of the Hamiltonian and find that these systems show non-trivial solutions, even in the limit of infinite repulsion. A detailed physical interpretat...

We investigate the problem of $N$ identical bosons that are coupled to an impurity particle with infinite mass. For non-interacting bosons, we show that a dynamical impurity-boson interaction, mediated by a closed-channel dimer, can induce an effective boson-boson repulsion which strongly modifies the bound states consisting of the impurity and $N$ bosons. In particular, we demonstrate the existence of two universal 'multi-body' resonances, where all multi-body bound states i...

We present a theoretical study based upon quantum Monte Carlo methods of the Bose polaron in one-dimensional systems with contact interactions. In this instance of the problem of a single impurity immersed in a quantum bath, the medium is a Lieb-Liniger gas of bosons ranging from the weakly interacting to the Tonks-Girardeau regime, whereas the impurity is coupled to the bath via a different contact potential producing both repulsive and attractive interactions. Both the case...