Dynamics of a Strongly Coupled Polaron

Sh. Mardonov, Eugene Ya. Sherman

Abstract We study various regimes of coherent coupled motion of a polaron and one-dimensional Bose–Einstein condensate in a harmonic potential. By using qualitative analysis, perturbation theory and direct numerical solution of the Gross–Pitaevskii equation, we show that the entire dynamics is strongly nonlinear and critically depends on the sign of the self-interaction in the condensate and the sign of the interaction between the polaron-forming embedded particle and the condensate. Strongly mutually related evolution of the condensate shape, its center of mass position, and polaron coordinate is studied for coupled nonlinear polaron-condensate oscillations and transmission/reflection of the polaron through/by the condensate.

Eduardo C. Marino

J. P. Hague, P. E. Kornilovitch, A. S. Alexandrov +1 more

We study the effects of lattice type on polaron dynamics using a continuous-time quantum Monte Carlo approach. Holstein and screened Fr\"ohlich polarons are simulated on a number of different Bravais lattices. The effective mass, isotope coefficients, ground-state energy and energy spectra, phonon numbers, and density of states are calculated. In addition, the results are compared with weak- and strong-coupling perturbation theory. For the Holstein polaron, it is found that the crossover between weak- and strong-coupling results becomes sharper as the coordination number is increased. In higher dimensions, polarons are much less mobile at strong coupling, with more phonons contributing to the polaron. The total energy decreases monotonically with coupling. Spectral properties of the polaron depend on the lattice type considered, with the dimensionality contributing to the shape and the coordination number to the bandwidth. As the range of the electron-phonon interaction is increased, the coordination number becomes less important, with the dimensionality taking the leading role.

Frédéric Chevy

Shijie Xie

Fabian Grusdt, Kushal Seetharam, Yulia E. Shchadilova +1 more

When a mobile impurity interacts with a surrounding bath of bosons, it forms a polaron. Numerous methods have been developed to calculate how the energy and the effective mass of the polaron are renormalized by the medium for equilibrium situations. Here, we address the much less studied nonequilibrium regime and investigate how polarons form dynamically in time. To this end, we develop a time-dependent renormalization-group approach which allows calculations of all dynamical properties of the system and takes into account the effects of quantum fluctuations in the polaron cloud. We apply this method to calculate trajectories of polarons following a sudden quench of the impurity-boson interaction strength, revealing how the polaronic cloud around the impurity forms in time. Such trajectories provide additional information about the polaron's properties which are challenging to extract directly from the spectral function measured experimentally using ultracold atoms. At strong couplings, our calculations predict the appearance of trajectories where the impurity wavers back at intermediate times as a result of quantum fluctuations. Our method is applicable to a broader class of nonequilibrium problems. As a check, we also apply it to calculate the spectral function and find good agreement with experimental results. At very strong couplings, we predict that quantum fluctuations lead to the appearance of a dark continuum with strongly suppressed spectral weight at low energies. While our calculations start from an effective Fr\"ohlich Hamiltonian describing impurities in a three-dimensional Bose-Einstein condensate, we also calculate the effects of additional terms in the Hamiltonian beyond the Fr\"ohlich paradigm. We demonstrate that the main effect of these additional terms on the attractive side of a Feshbach resonance is to renormalize the coupling strength of the effective Fr\"ohlich model.