Bose-Einstein-condensate polaron in harmonic trap potentials in the weak-coupling regime: Lee-Low-Pines–type approach

Abstract

We have calculated the zero-temperature binding energy of a single impurity atom immersed in a Bose-Einstein condensate (BEC) of ultracold atoms. The impurity and the condensed atoms are trapped in the respective axially symmetric harmonic potentials, where the impurity interacts with bosonic atoms in the condensate via low-energy s-wave scattering. In this case, bosons are excited around the impurity to form a quasiparticle, namely, a BEC polaron. We have developed a variational method, a la Lee-Low-Pines (LLP), for description of the polaron that has a conserved angular momentum around the symmetric axis. We find from numerical results that the binding between the impurity and the excited bosons breaks the degeneracy of the impurity energy with respect to the total angular momentum of the polaron. The angular momentum is partially shared by the excited bosons in a manner that is similar to the drag effect on the polaron momentum by a phonon cloud in the LLP theory for the electron-phonon system. * Electronic address: e.nakano@kochi-u.ac.jp

Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium

“…The corresponding impact on the medium atoms due to the presence of strong impurity-bath correlations is under active investigation [51]. In the case of Bose polarons [7][8][9][10][11][12][58][59][60], the influence of the impurities on their environment (BEC) is more pronounced when compared to Fermi polarons due to the absence of the Pauli blocking effect. Characteristic examples, here, constitute the self-localization [61][62][63][64][65] and temporal orthogonality catastrophe [21] phenomena as well as complex tunneling [66][67][68][69] and emergent relaxation processes [56,70].…”

General memory kernels and further corrections to the variational path integral approach for the Bogoliubov-Fröhlich Hamiltonian

“…The Bogoliubov-Fröhlich model has been studied within this approach [17], where Feynman's original S 0 has been used [4]. Just as is the case for the solid state polaron, the variational upper bound reduces to the coherent state energy at weak coupling [28] and to a Landau-Pekar ansatz at strong coupling [29] and hence was expected to work well for this Hamiltonian. However, not long afterwards, very unexpectedly large discrepancies between the theory and rigorous DMC calculations [30] have been observed.…”

Lattice and quintic nonlinearity induced stripe phase in Bose–Einstein condensate under non-inertial and inertial motion

“…Bose-Einstein condensate (BEC) in a periodic potential has been an area of active research for more than two decades [1,2]. It is truly an interdisciplinary field, which has connections with many areas of physics: electrons in crystal lattices [3,4], polarons [5,6], photons in optical fibers [7], gauge theories [8] and exotic phase transitions [9][10][11][12], to mention a few. A major advantage of the Bose-condensed gas in a periodic potential is its tunability over a wide range of parameter domain.…”