Abstract We discuss the dynamics of the formation of a Bose polaron when an impurity is injected into a weakly interacting one-dimensional Bose condensate. While for small impurity-boson couplings this process can be described within the Froehlich model as generation, emission and binding of Bogoliubov phonons, this is no longer adequate if the coupling becomes strong. To treat this regime we consider a mean-field approach beyond the Froehlich model which accounts for the backaction to the condensate, complemented with Truncated Wigner simulations to include quantum fluctuation. For the stationary polaron we find a periodic energy-momentum relation and non-monotonous relation between impurity velocity and polaron momentum including regions of negative impurity velocity. Studying the polaron formation after turning on the impurity-boson coupling quasi-adiabatically and in a sudden quench, we find a very rich scenario of dynamical regimes. Due to the build-up of an effective mass, the impurity is slowed down even if its initial velocity is below the Landau critical value. For larger initial velocities we find deceleration and even backscattering caused by emission of density waves or grey solitons and subsequent formation of stationary polaron states in different momentum sectors. In order to analyze the effect of quantum fluctuations we consider a trapped condensate to avoid 1D infrared divergencies. Using Truncated Wigner simulations in this case we show under what conditions the influence of quantum fluctuations is small.
We study the quantum dynamics of a single impurity following its sudden immersion into a Bose-Einstein condensate. The formation of the Bose polaron after such a quench stems from decoherence of the impurity, driven by collisions with the condensate. Using a master equation approach, we derive rigorous analytical results for the decoherence dynamics of the impurity, which reveals different stages of its evolution from a universal non-exponential initial relaxation to the final approach of the equilibrium state of the Bose polaron. The associated polaron formation time exhibit a strong dependence of the impurity momentum and is found to undergo a critical slowdown around the Landau critical velocity of the condensate. The rich non-equilibrium behavior of quantum impurities in a Bose gas revealed in this work is of direct relevance to recent cold-atom experiments, in which Bose polarons are created by a sudden quench of the impurity-bath interaction.
We discuss impurities in a one-dimensional Bose gas with arbitrary boson-boson and boson-impurity interactions. To fully account for quantum effects, we employ numerical simulations based on the density-matrix renormalization group (DMRG) and—in the regime of strong boson-boson interactions—the mapping to weakly interacting fermions. A mean-field description of the Bose polaron based on coupled Gross–Pitaevskii Schrödinger equations predicts the existence of a self-localized polaron. We here show that such a solution does not exist and is an artifact of the underlying decoupling approximation. To this end we consider a mobile impurity in a box potential. Our work demonstrates that correlations between the impurity position and the bosons are important even in the limit where mean-field approaches are expected to work well. Furthermore, we derive analytical approximations for the energy of a single polaron formed by a heavy impurity for arbitrary interaction strengths and large but finite boson-boson couplings which accurately reproduce DMRG results. This demonstrates that the polaron problem of a heavy impurity in a one-dimensional Bose gas can be accurately approximated by a proper mean-field description plus a linearized treatment of quantum fluctuations for arbitrary boson-boson and impurity-boson couplings. Finally, we determine the polaron-polaron interaction potential V ( r ) in the Born-Oppenheimer approximation for small and intermediate distances r , which in the Tonks gas limit is oscillatory due to Friedel oscillations in the Bose gas.
We study a weakly interacting one-dimensional Bose gas with two impurities coupled locally to the boson density. We derive analytical results for the induced interaction between the impurities at arbitrary positive coupling and separation
r. At $r\ensuremath{\lesssim}\ensuremath{\xi}$, where $\ensuremath{\xi}$ denotes the healing length of the Bose gas, the interaction is well described by the mean-field contribution. Its form changes as the coupling is increased, approaching a linear function of
r at short distances in the regime of strong coupling. The mean-field contribution decays exponentially at arbitrary coupling for $r\ensuremath{\gg}\ensuremath{\xi}$. At such long distances, however, the effect of quantum fluctuations becomes important, giving rise to a long-ranged quantum contribution to the induced interaction. At longest distances it behaves as
1/r3, while at strong coupling we find an intermediate distance regime with a slower decay,
1/r. The quantum contribution in the crossover regime is also calculated. The induced interaction between impurities (i.e., polarons) is attractive and leads to the formation of their bound state, known as bipolaron. We discuss its binding energy.
Two-dimensional quantum gases provide a distinctive setting in which enhanced thermal fluctuations, finite-size effects, and two-body bound-state formation are intrinsically intertwined. In this work, we study a single attractive impurity immersed in a finite, weakly interacting two-dimensional Bose gas, where finite size stabilizes a nonzero condensate fraction by introducing an infrared momentum scale, thereby enabling a Bogoliubov description of the bath. Using a hybrid approach that combines finite-temperature many-body scattering theory with input from path-integral Monte Carlo, we analyze the impurity quasiparticle energy across the condensate and normal regimes. The infrared scale generates a phonon-activation temperature below which the impurity energy remains nearly temperature independent. Once the resolved phonon modes become thermally populated, their contribution competes with condensate depletion, producing a nonmonotonic temperature dependence of the polaron energy. These results suggest that attractive Bose polarons may serve as sensitive probes of finite-size thermal fluctuations, phonon dressing, and bound-state physics in low-dimensional Bose gases.
We give a detailed account of a stationary impurity in an ideal Bose-Einstein condensate, which we call the ideal Bose polaron, at both zero and nonzero temperatures and arbitrary strength of the impurity-boson coupling. The time evolution is solved exactly and it is found that, surprisingly, many of the features that have been predicted for the real BEC are already present in this simpler setting and can be understood analytically therein. We obtain explicit formulas for the time evolution of the condensate wave function at
T=0 and of the one-particle density matrix at
T>0. For negative scattering length, the system is found to thermalize even though the dynamics are perfectly coherent. The time evolution and thermal values of the Tan contact are derived and compared to a recent experiment. We find that contrary to the Fermi polaron, the contact is not bounded at unitarity as long as a condensate exists. An explicit formula for the dynamical overlap at
T=0 allows us to compute the rf spectrum which can be understood in detail by relating it to the two-body problem of one boson and the impurity.