One-dimensional Fermi polaron after a kick: two-sided singularity of the momentum distribution, Bragg reflection and other exact results

We perform a diagrammatic analysis of the energy of a mobile impurity immersed in a strongly interacting two component Fermi gas to second order in the impurity-bath interaction. These corrections demonstrate divergent behavior in the limit of large impurity momentum. We show the fundamental processes responsible for these logarithmically divergent terms. We study the problem in the general case without any assumptions regarding the fermion-fermion interactions in the bath....

We study a highly imbalanced Fermi gas in a one-dimensional optical lattice from the polaronic point of view. The time-evolving block decimationg algorithm is used to calculate the ground state and dynamics of the system. We find qualitatively similar polaronic behaviour as in the recent experiment by Schirotzek et al. \cite{Schirotzek2009a} where radio-frequency spectroscopy was used to observe polarons in three-dimensional space. In the weakly interacting limit our exact re...

I study a model for a massive one-dimensional particle in a singular periodic potential that is receiving kicks from a gas. The model is described by a Lindblad equation in which the Hamiltonian is a Schr\"odinger operator with a periodic $\delta$-potential and the noise has a frictionless form arising in a Brownian limit. I prove that an emergent Markov process in a semi-classical limit governs the momentum distribution in the extended-zone scheme. The main result is a centr...

We study the motion of a heavy impurity in a one-dimensional Bose gas. The impurity experiences the friction force due to scattering off thermally excited quasiparticles. We present detailed analysis of an arbitrarily strong impurity-boson coupling in a wide range of temperatures within a microscopic theory. Focusing mostly on weakly interacting bosons, we derive an analytical result for the friction force and uncover new regimes of the impurity dynamics. Particularly interes...

We use analytic techniques and the dynamical mean field method to study the crossover from fermi liquid to polaron behavior in models of electrons interacting with dispersionless classical phonons.

We consider a mobile impurity immersed in a Bose gas at finite temperature. Using perturbation theory valid for weak coupling between the impurity and the bosons, we derive analytical results for the energy and damping of the impurity for low and high temperatures, as well as for temperatures close to the critical temperature $T_c$ for Bose-Einstein condensation. These results show that the properties of the impurity vary strongly with temperature. In particular, the energy e...

We present a precise solution of the polaron problem by a novel Monte Carlo method. Basing on conventional diagrammatic expansion for the Green function of the polaron, $G({\bf k}, \tau)$, we construct a process of generating continuous random variables ${\bf k}$ and $\tau$, with the distribution function exactly coinciding with $G({\bf k}, \tau)$. The polaron spectrum is extracted from the asymptotic behavior of the Green function. We compare our results for the polaron ener...

We investigate a single impurity interacting with a free two-dimensional atomic Fermi gas. The interaction between the impurity and the gas is characterized by an arbitrary attractive short-range potential, which, in two dimensions, always admits a two-particle bound state. We provide analytical expressions for the energy and the effective mass of the dressed impurity by including the two-body bound state, which is crucial for strong interactions, in the integral equation for...

The detailed study of the low-energy spectrum for a mobile impurity in the one-dimensional bosonic enviroment is performed. Particularly we have considered only two analytically accessible limits, namely, the case of an impurity immersed in a dilute Bose gas, where one can use many-body perturbation techniques for low-dimensional bosonic systemsm and the case of the Tonks-Girardeau gas, for which the usual fermionic diagrammatic expansion up to the second order is applied.

We study a one-dimensional Bose gas with two internal states described by the Yang-Gaudin model and calculate analytically the dispersion relation of a polaron quasiparticle, which is the lowest excitation branch. We study the dispersion in the thermodynamic limit in the regimes of weak and strong interaction without limitations on the momentum. At weak interaction the polaron dispersion is in the vicinity of the dark soliton one; we calculate the leading deviation in the par...