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

We study spatial correlations in the ground state of a one-dimensional electron gas coupled to a dynamic quantum impurity. The system displays a non-trivial many-body effect known as the Fermi edge singularity: transitions between discrete internal states of the impurity have a power-law dependence on the internal energies of the impurity states. We present compact formulas for the static current-current correlator and the pair correlation function. These reveal that spatial ...

Single- and two-particle spectra of a single immobile impurity immersed in a fermionic bath can be computed exactly and are characterized by divergent power laws (edge singularities). Here, we present the leading lattice correction to this canonical problem, by embedding both impurity and bath fermions in bands with non-vanishing Bloch band geometry, with the impurity band being flat. By analyzing generic Feynman diagrams, we pinpoint how the band geometry reduces the effecti...

We present exact numerical data for the lowest-energy momentum eigenstates (yrast states) of a repulsive spin impurity in a one-dimensional Bose gas using full configuration interaction quantum Monte Carlo (FCIQMC). As a stochastic extension to exact diagonalization it is well suited for the study of yrast states of a lattice-renormalized model for a quantum gas. Yrast states carry valuable information about the dynamic properties of slow-moving mobile impurities immersed in ...

We consider the motion of an impurity particle in a general one-dimensional quantum fluid at zero temperature. The dispersion relation $\Omega(P)$ of the impurity is strongly affected by interactions with the fluid as the momentum approaches $\pm\pi\hbar n, \pm 3\pi\hbar n, ...$, where $n$ is the density. This behavior is caused by singular $\pm 2\pi\hbar n$ scattering processes and can be understood by analogy to the Kondo effect, both at strong and weak coupling, with the p...

We study the problem of a mobile impurity of mass $M$ interacting {\sl via} a s-wave broad or narrow Feshbach resonance with a Fermi sea of particles of mass $m$. Truncating the Hilbert space to at most one pair of particle-hole excitations of the Fermi sea, we determine ground state properties of the polaronic branch other than its energy, namely the polaron quasiparticle residue $Z$, and the impurity-to-fermion pair correlation function $G(x)$. We show that $G(x)$ deviates ...

We consider the quench dynamics of non-interacting fermions in one dimension in the presence of a finite-size impurity at the origin. This impurity is characterized by general momentum-dependent reflection and transmission coefficients which are changed from ${\sf r}_0(k), {\sf t}_0(k)$ to ${\sf r}(k), {\sf t}(k)$ at time $t=0$. The initial state is at equilibrium with ${\sf t}_0(k)=0$ such that the system is cut in two independent halves with ${\sf r}_0^R(k)$, ${\sf r}_0^L(k...

Using exact Bethe ansatz (BA) solutions, we show that a spin-down fermion immersed into a fully polarized spin-up Fermi sea with a weak attraction is dressed by the surrounding spin-up fermions to form the one-dimensional analog of a polaron. As the attraction becomes strong, the spin-down fermion binds with one spin-up fermion to form a tightly bound molecule. Throughout the whole interaction regime, a crossover from the polaron to a molecule state is fully demonstrated thro...

Mobile impurity atoms immersed in Bose-Einstein condensates provide a new platform for exploring Bose polarons. Recent experimental advances in the field of ultracold atoms make it possible to realize such systems with highly tunable microscopic parameters and to explore equilibrium and dynamical properties of polarons using a rich toolbox of atomic physics. In this paper we present a detailed theoretical analysis of Bose polarons in one dimensional systems of ultracold atoms...

The properties of a Bose polaron immersed in a dilute two-dimensional medium at finite temperatures are discussed. Assuming that the impurity is weakly-coupled to the bath particles we have perturbatively calculated the polaron energy, effective mass, quasiparticle residue and damping rate. The parameters of impurity spectrum are found to be well-defined in the whole temperature region whereas the pole structure of the impurity Green's function is visible only at absolute zer...

We present a semiclassical treatment of a fermionic impurity coupled to Bogolyubov modes of a BEC. In the lowest order approximation we find a full solution of an initial value problem, which turns out to behave differently in the sub- and supersonic regimes. While in the former case no impurity deceleration is observed, in the latter case non-Markovian dissipation effects kick in resulting in slowing down of the fermion. Although this scenario is compatible with the one offe...