Ground-state properties of interacting Bose polarons

Abstract

We theoretically investigate the role of multiple impurity atoms on the ground-state properties of Bose polarons. The Bogoliubov approximation is applied for the description of the condensate resulting in a Hamiltonian containing terms beyond the Fröhlich approximation. The many-body nature of the impurity atoms is taken into account by extending the many-body description for multiple Fröhlich polarons, revealing the static structure factor of the impurities as the key quantity. Within this formalism various experimentally accessible polaronic properties are calculated such as the energy and the effective mass. These results are examined for system parameters corresponding to two recent experimental realizations of the Bose polaron, one with fermionic impurities and one with bosonic impurities.

Fate of the Bose polaron at finite temperature

“…One can see this by expanding Eq. (35) to lowest order in the fugacity e µ/T . With increasing temperature, we approach the classical scenario of a non-interacting impurity, which corresponds to a sharp peak in the spectrum at E = 0.…”

“…When χ(E) corresponds to the T matrix, the condition G −1 (E) = 0 is equivalent to Eq. ( 35) in the limit where f q → 0 such that we can set the hole momentum to zero in the kinetic terms and we are left with n ex = q f q . An equation similar to Eq.…”

“…The Bose polaron problem at strong coupling has been tackled with a variety of theoretical techniques, including quantum Monte Carlo (QMC) [26,27], fieldtheoretical diagrammatic approaches [28], renormalization group theory [29], and variational wave functions involving highly correlated [30][31][32] and coherent-state [33][34][35] ansatzes. However, the majority of the theoreti-cal work so far has been restricted to zero temperature, where the impurity-medium system is in a pure state and is thus easier to treat.…”

Feynman path-integral treatment of the Bose polaron beyond the Fröhlich model

“…The additional terms in (4) take into account the extended interactions beyond the Fröhlich model and consist of a part depending on the phonon coordinates Q k multiplied by V k , and a part depending on the phonon velocitiesQ k along with V −1 k . Within a mean-field approach where the excitation operators acquire a polaronic shiftα k →α k − f k , these velocity-dependent terms can be shown to arise due to a non-zero imaginary contribution from f k and vanish for the saddle-point solution [32,34], while the terms containing V k arise due to the real part of f k and have a non-negligible contribution to the ground state energy resulting in a resonance shift. In the RG approach [33] it is pointed out that the RG coupling constant corresponding to the V −1 k terms has a small effect on the polaron wavefunction, but is expected to be important when considering other qualitative properties such as the lifetime of the polaron due to the appearance of bound states at lower energies.…”

“…The effect of temperature is calculated trough the implicit temperature dependence of the variational parameters M and Ω, as has been done in [42]. Note that in the limit of weak coupling the effective mass (45) reduces to the mean-field result at zero polaron momentum [34].…”