Excited stationary states of small polarons

Ora Entin-wohlman A, David J. Bergman

Holger Fehske, Gerhard Wellein, A. R. Bishop

We study the quantum dynamics of small polaron formation and polaron transport through finite quantum structures in the framework of the one-dimensional Holstein model with site-dependent potentials and interactions. Combining Lanczos diagonalization with Chebyshev moment expansion of the time evolution operator, we determine how different initial states, representing stationary ground states or injected wave packets, after an electron-phonon interaction quench, develop in real space and time. Thereby, the full quantum nature and dynamics of electrons and phonons is preserved. We find that the decay out of the initial state sensitively depends on the energy and momentum of the incoming particle, the electron-phonon coupling strength, and the phonon frequency, whereupon bound polaron-phonon excited states may emerge in the strong-coupling regime. The tunneling of a Holstein polaron through a quantum wall or dot is generally accompanied by strong phonon number fluctuations due to phonon emission and reabsorption processes.

J. T. Devreese, R. Evrard

N. V. Tkach, Julia O. Seti, Voitsekhivska +1 more

Partial summing of infinite range of diagrams for the two-phonon mass operator of polaron described by Fröhlich Hamiltonian is performed using the Feynman-Pines diagram technique.Renormalized spectral parameters of ground and first excited (phonon repeat) polaron state are accurately calculated for a weak electron-phonon coupling at T = 0 K.It is shown that the stronger electron-phonon interaction shifts the energy of both states into low-energy region of the spectra.The ground state stays stationary and the excited one decays at a bigger coupling constant.

J. T. Devreese, R. Evrard, E. Kartheuser

Georgios M. Koutentakis, S. I. Mistakidis, Peter Schmelcher

Recent studies have demonstrated that higher than two-body bath-impurity correlations are not important for quantitatively describing the ground state of the Bose polaron. Motivated by the above, we employ the so-called Gross Ansatz (GA) approach to unravel the stationary and dynamical properties of the homogeneous one-dimensional Bose-polaron for different impurity momenta and bath-impurity couplings. We explicate that the character of the equilibrium state crossovers from the quasi-particle Bose polaron regime to the collective-excitation stationary dark-bright soliton for varying impurity momentum and interactions. Following an interspecies interaction quench the temporal orthogonality catastrophe is identified, provided that bath-impurity interactions are sufficiently stronger than the intraspecies bath ones, thus generalizing the results of the confined case. This catastrophe originates from the formation of dispersive shock wave structures associated with the zero-range character of the bath-impurity potential. For initially moving impurities, a momentum transfer process from the impurity to the dispersive shock waves via the exerted drag force is demonstrated, resulting in a final polaronic state with reduced velocity. Our results clearly demonstrate the crucial role of non-linear excitations for determining the behavior of the one-dimensional Bose polaron.