Abstract
Mobile impurity atoms immersed in Bose–Einstein condensates provide a new platform for exploring Bose polarons. Recent experimental advances in the field of ultracold atoms make it possible to realize such systems with highly tunable microscopic parameters and to explore equilibrium and dynamical properties of polarons using a rich toolbox of atomic physics. In this paper we present a detailed theoretical analysis of Bose polarons in one-dimensional systems of ultracold atoms. By combining a non-perturbative renormalization group approach with numerically exact diffusion Monte Carlo calculations we obtain not only detailed numerical results over a broad range of parameters but also qualitative understanding of different regimes of the system. We find that an accurate description of Bose polarons requires the inclusion of two-phonon scattering terms which go beyond the commonly used Fröhlich model. Furthermore we show that when the Bose gas is in the strongly interacting regime, one needs to include interactions between the phonon modes. We use several theoretical approaches to calculate the polaron energy and its effective mass. The former can be measured using radio-frequency spectroscopy and the latter can be studied experimentally using impurity oscillations in a harmonic trapping potential. We compare our theoretical results for the effective mass to the experiments by Catani et al (2012 Phys. Rev. A 85 023623). In the weak-to-intermediate coupling regimes we obtain excellent quantitative agreement between theory and experiment, without any free fitting parameter. We supplement our analysis by full dynamical simulations of polaron oscillations in a shallow trapping potential. We also use our renormalization group approach to analyze the full phase diagram and identify regions that support repulsive and attractive polarons, as well as multi-particle bound states.
Highlights
When a mobile particle interacts with a surrounding bath of bosons, it becomes dressed by a cloud of excitations and forms a polaron [1, 2]
From the comparison of our Diffusion Monte Carlo (DMC) calculations with Renormalization group (RG) predictions we find that phonon-phonon interactions always need to be included to obtain quantitative agreement for the polaron energy and mass
We present a detailed discussion of our RG analysis of 1D Bose polarons in Appendix B
Summary
When a mobile particle interacts with a surrounding bath of bosons, it becomes dressed by a cloud of excitations and forms a polaron [1, 2]. Impurity atoms immersed in a Bose gas provide a promising new platform for studying the long standing polaron problem Advantages of such systems include the tunability of both interactions [3,4,5] and the single particle dispersion [6]. In two and three dimensional systems, the MF approach [24] is a convenient theoretical tool that can be used to study models beyond the simplified Frohlich Hamiltonian It is a non-perturbative method which includes strong correlations between the phonons and the impurity, whereas phonon-phonon correlations are neglected. Theoretical analysis has to study strongly interacting systems, and understand its dynamical properties and their connection to equilibrium quantities This provides an additional challenge, since most of the standard tools, such as Monte-Carlo methods, are not applicable.
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