The Dynamics of Polarons

Rupert L. Frank, Benjamin Schlein

Hiroyuki Tajima, Junichi Takahashi, Eiji Nakano +1 more

We propose a protocol to examine many-polaron properties in a cold atom experiment. Initially, polaronic clouds are prepared around the opposite edges of a majority gas cloud. After time evolution, the collision of two clouds exhibits various polaronic effects. To see how collective properties of many polarons with mediated interactions appear in the case in which the impurity and majority gases are composed of mass-balanced fermions with different spin components, we perform a nonlinear hydrodynamic simulation for collisional dynamics of two Fermi polaronic clouds. We found that the dynamics is governed by the impurity Fermi pressure, polaron energy, and multipolaron correlations. In particular, shock waves occur in such a way as to reflect the many-body properties of polarons through the first sound of minority clouds. Our idea is applicable to other systems such as Bose polarons as well as mass-imbalanced mixtures.

Eduardo C. Marino

It is shown that the Hamiltonian describing the acoustic many-polaron dynamics in one spatial dimension is identical, except for the cutoff procedure, to that of an exactly solvable field theory. Cutoff independent quantities, such as the spectrum of excitations and dynamical correlation functions, are computed. A critical coupling is found above which there is a condensation of polaron pairs and the system exhibits a polaronic superconductivity. Below the critical coupling, the spectrum contains only collective excitations of polarons and the system has a metallic behavior.

E. V. L. de Mello, J. Ranninger

On the basis of the two-site polaron problem, which we solve by exact diagonalization, we analyze the spectral properties of polaronic systems in view of discerning localized from itinerant polarons and bound polaron pairs from an ensemble of single polarons. The corresponding experimental techniques for that concern photoemission and inverse photoemission spectroscopy. The evolution of the density of states as a function of concentration of charge carriers and strength of the electron-phonon interaction clearly shows the opening up of a gap between single-polaronic and bipolaronic states, in analogy to the Hubbard problem for strongly correlated electron systems. In studying the details of the intricately linked dynamics of the charge carriers and of the molecular deformations which surround them, we find that in general the dynamical delocalization of the charge carriers helps to strengthen the phase coherence for itinerant polaronic states, except for the crossover regime between adiabatic and antiadiabatic small polarons. The crossover between these two regimes is triggered by two characteristic time scales: the renormalized electron hopping rate and the renormalized vibrational frequency becoming equal. This crossover regime is then characterized by temporarily alternating self-localization and delocalization of the charge carriers which is accompanied by phase slips in the charge and molecular deformation oscillations and ultimately leads to a dephasing between these two dynamical components of the polaron problem. We visualize these features by a study of the temporal evolution of the charge redistribution and the change in molecular deformations. The spectral and dynamical properties of polarons discussed here are beyond the applicability of the standard Lang-Firsov approach to the polaron problem.

Nikolay N. Bogolubov, Nikolay N. Bogolubov