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Register a new userFeynman path-integral treatment of the Bose polaron beyond the Frohlich model
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Added by
Timour Ichmoukhamedov
Publication date
2019
fields
Physics
and research's language is
English
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An impurity immersed in a Bose-Einstein condensate is no longer accurately described by the Frohlich Hamiltonian as the coupling between the impurity and the boson bath gets stronger. We study the dominant effects of the two-phonon terms beyond the Frohlich model on the ground-state properties of the polaron using Feynmans variational path-integral approach. The previously reported discrepancy in the effective mass between the renormalization group approach and this theory is shown to be absent in the beyond-Frohlich model on the positive side of the Feshbach resonance. Self-trapping, characterized by a sharp and dramatic increase of the effective mass, is no longer observed for the repulsive polaron once the two-phonon interactions are included. For the attractive polaron we find a divergence of the ground-state energy and effective mass at weaker couplings than previously observed within the Frohlich model.
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We develop a renormalization group approach for analyzing Frohlich polarons and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations for a wide range of interaction strengths. We calculate the effective mass of polarons and find a smooth crossover from weak to strong coupling regimes. Possible experimental tests of our results in current experiments with ultra cold atoms are discussed.
Grusdt et al. [New J. Phys. 19, 103035 (2017)] recently made a renormalization group study of a one-dimensional Bose polaron in cold atoms. Their study went beyond the usual Frohlich description, which includes only single-phonon processes, by including two-phonon processes in which two phonons are simultaneously absorbed or emitted during impurity scattering [Shchadilova et al. Phys. Rev. Lett. 117, 113002 (2016)]. We study this same beyond-Frohlich model, but in the static impurity limit where the ground state is described by a multimode squeezed state instead of the multimode coherent state in the static Frohlich model. We solve the system exactly by applying the generalized Bogoliubov transformation, an approach that can be straightforwardly adapted to higher dimensions. Using our exact solution, we obtain a polaron energy free of infrared divergences and construct analytically the polaron phase diagram. We find that the repulsive polaron is stable on the positive side of the impurity-boson interaction but is always thermodynamically unstable on the negative side of the impurity-boson interaction, featuring a bound state, whose binding energy we obtain analytically. We find that the attractive polaron is always dynamically unstable, featuring a pair of imaginary energies which we obtain analytically. We expect the multimode squeezed state to help with studies that go not only beyond the Frohlich paradigm but also beyond Bogoliubov theory, just as the multimode coherent state has helped with the study of Frohlich polarons.
We present accurate results for optical conductivity of the three dimensional Frohlich polaron in all coupling regimes. The systematic-error free diagrammatic quantum Monte Carlo method is employed where the Feynman graphs for the momentum-momentum correlation function in imaginary time are summed up. The real-frequency optical conductivity is obtained by the analytic continuation with stochastic optimization. We compare numerical data with available perturbative and non-perturbative approaches to the optical conductivity and show that the picture of sharp resonances due to relaxed excited states in the strong coupling regime is ``washed outby large broadening of these states. As a result, the spectrum contains only a single-maximum broad peak with peculiar shape and a shoulder.
We propose a generalization of the Feynman path integral using squeezed coherent states. We apply this approach to the dynamics of Bose-Einstein condensates, which gives an effective low energy description that contains both a coherent field and a squeezing field. We derive the classical trajectory of this action, which constitutes a generalization of the Gross Pitaevskii equation, at linear order. We derive the low energy excitations, which provides a description of second sound in weakly interacting condensates as a squeezing oscillation of the order parameter. This interpretation is also supported by a comparison to a numerical c-field method.
Advancing our understanding of non-equilibrium phenomena in quantum many-body systems remains among the greatest challenges in physics. Here, we report on the experimental observation of a paradigmatic many-body problem, namely the non-equilibrium dynamics of a quantum impurity immersed in a bosonic environment. We use an interferometric technique to prepare coherent superposition states of atoms in a Bose-Einstein condensate with a small impurity-state component, and monitor the evolution of such quantum superpositions into polaronic quasiparticles. These results offer a systematic picture of polaron formation from weak to strong impurity interactions. They reveal three distinct regimes of evolution with dynamical transitions that provide a link between few-body processes and many-body dynamics. Our measurements reveal universal dynamical behavior in interacting many-body systems and demonstrate new pathways to study non-equilibrium quantum phenomena.
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