We analyze the dynamics of Bose polarons in the vicinity of a Feshbach resonance between the impurity and host atoms. We compute the radio-frequency absorption spectra for the case when the initial state of the impurity is non-interacting and the final state is strongly interacting. We compare results of different theoretical approaches including a single excitation expansion, a self-consistent T-matrix method, and a time-dependent coherent state approach. Our analysis reveals sharp spectral features arising from metastable states with several Bogoliubov excitations bound to the impurity atom. This surprising result of the interplay of many-body and few-body Efimov type bound state physics can only be obtained by going beyond the commonly used Fröhlich model and including quasiparticle scattering processes. Close to the resonance we find that strong fluctuations lead to a broad, incoherent absorption spectrum where no quasi-particle peak can be assigned.Introduction. -Understanding the role of few-body correlations in many-body systems is a challenging problem that arises in many areas of physics. Few particle systems in isolation can be studied using powerful techniques of scattering theory such as Faddeev equations, the hyperspherical formalism, or effective field theory [1][2][3][4][5]. These approaches have been successfully applied to investigate collisions of neutrons and protons [6,7] and Efimov resonances in ultracold atoms [8,9]. On the other hand the common approach to interacting many-body systems is to use the mean-field approximation, which reduces a many-body problem to an effective single particle Hamiltonian with self-consistently determined fields. While this approach provides a good description of many fundamental states, including magnetic, superconducting, and superfluid phases [10], in many cases it is important to go beyond the mean-field paradigm and include correlations at a few particle level. Recent notable examples include 4e pairing in high Tc superconductors [11], spin nematic states [12], chains and clusters of molecules in ultracold atoms [13][14][15][16], and the QCD phase diagram in high-energy physics [17,18]. A particularly important class of problems where few-body correlations play a crucial role is the formation of quasiparticles and polarons. The key feature of both is the dramatic change in the particle dynamics due to the interaction with collective excitations of the many-body system. Famous examples include lattice polarons in semiconductors [19,20], magnetic polarons in strongly correlated electron systems [21][22][23], and 3 He atoms in superfluid 4 He [24].

When a mobile impurity interacts with a many-body system, such as a phonon bath, a polaron is formed. Despite the importance of the polaron problem for a wide range of physical systems, a unified theoretical description valid for arbitrary coupling strengths is still lacking. Here we develop a renormalization group approach for analyzing a paradigmatic model of polarons, the so-called Fröhlich model, 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. They are found to be logarithmically divergent with the ultra-violet cut-off, but physically meaningful regularized polaron energies are also presented. Moreover, 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.

We use a non-perturbative renormalization group approach to develop a unified picture of the Bose polaron problem, where a mobile impurity is strongly interacting with a surrounding Bose-Einstein condensate (BEC). A detailed theoretical analysis of the phase diagram is presented and the polaron-to-molecule transition is discussed. For attractive polarons we argue that a description in terms of an effective Fröhlich Hamiltonian with renormalized parameters is possible. Its strong coupling regime is realized close to a Feshbach resonance, where we predict a sharp increase of the effective mass. Already for weaker interactions, before the polaron mass diverges, we predict a transition to a regime where states exist below the polaron energy and the attractive polaron is no longer the ground state. On the repulsive side of the Feshbach resonance we recover the repulsive polaron, which has a finite lifetime because it can decay into low-lying molecular states. We show for the entire range of couplings that the polaron energy has logarithmic corrections in comparison with predictions by the mean-field approach. We demonstrate that they are a consequence of the polaronic mass renormalization which is due to quantum fluctuations of correlated phonons in the polaron cloud. arXiv:1704.02605v2 [cond-mat.quant-gas]

We propose a class of variational Gaussian wavefunctions to describe Fröhlich polarons at finite momenta. Our wavefunctions give polaron energies that are in excellent agreement with the existing Monte Carlo results for a broad range of interactions. We calculate the effective mass of polarons and find smooth crossover between weak and intermediate impurity-bosons coupling. Effective masses that we obtain are considerably larger than those predicted by the mean-field method. A novel prediction based on our variational wavefunctions is a special pattern of correlations between host atoms that can be measured in time-of-flight experiments. We discuss atomic mixtures in systems of ultracold atoms in which our results can be tested with current experimental technology.PACS numbers: 71.38.Fp,67.85.PqRenormalization of particle masses due to their interaction with the environment is a ubiquitous phenomenon in physics. In the standard model of high energy physics elementary particles acquire a mass through interaction with the Higgs field [1]. In solid state systems heavy fermion materials exhibit renormalization of electron masses of up to two orders of magnitude due to interaction of electrons with localized spins [2]. Complete localization of quantum degrees of freedom caused by interaction with the environment has been discussed in spin-bath models [3, 4] and quantum Josephson junctions [5][6][7]. Surprisingly one of the first systems in which strong mass renormalization due to particle-bath interaction has been predicted, the so-called polaron model introduced by Landau in 1933 [8, 9], remains a subject of considerable debate. This model describes interaction of a quan-