Bose polarons in ultracold atoms in one dimension: beyond the Fröhlich paradigm

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.

Many-body quantum dynamics and induced correlations of Bose polarons

“…To further expose the necessity of taking into account the intra-and the interspecies correlations of the system in order to accurately describe the MB dynamics of the impurities we next solve the time-dependent Schrödinger equation that governs the system's dynamics relying on the previously introduced effective potential picture (equation (15)) via exact diagonalization 6 . Thus our main aim here is to test the validity of¯( ) V x I eff at least to qualitatively capture the basic features of the emergent non-equilibrium dynamics of the two impurities.…”

“…However, the non-equilibrium dynamics of impurities is far less explored and is expected to be dominated by correlation effects which build up in the course of the evolution [34-36, 39, 42-45]. Existing examples include the observation of self-trapping phenomena [46,47], formation of dark-bright solitons [6,42], impurity transport in optical lattices [48][49][50][51], orthogonality catastrophe events [35,52], injection of a moving impurity into a gas of Tonks-Girardeau bosons [53][54][55][56][57][58][59][60] and the relaxation dynamics of impurities [45,61,62]. Besides these investigations, which have enabled a basic description of the quasiparticle states in different interaction regimes, a number of important questions remain open and a full theoretical understanding of the dynamics specifically of Bose polarons is still far from complete.…”

Analytical approach to the Bose-polaron problem in one dimension

“…Therefore, a solution of the problem for weak and moderate boson-boson interaction is enough to complete the picture for all interaction strengths. However, theoretical approaches face challenges in describing these parameter regimes if the boson-impurity interactions are strong [38]. In this case accurate results can be obtained only numerically using Monte-Carlo methods [30,38], and analytical calculations that can unravel underlying physics and correlations are highly desirable.…”

“…However, theoretical approaches face challenges in describing these parameter regimes if the boson-impurity interactions are strong [38]. In this case accurate results can be obtained only numerically using Monte-Carlo methods [30,38], and analytical calculations that can unravel underlying physics and correlations are highly desirable. In this Rapid Communication, we introduce a possible theoretical formalism for performing such calculations.…”

Correlation induced localization of lattice trapped bosons coupled to a Bose–Einstein condensate

“…Since then a lot of progress has been made in the limiting cases of weak [28,29] and strong electron-phonon coupling [30]. While the ongoing theoretical study of 1D polarons [31][32][33][34][35] has predicted a lot of intriguing properties, recent experiments [17,23,36,37] have finally opened the door to the implementation of 1D polaronic systems, providing a deeper understanding of 1D polarons. When immersing more than one impurity in the bath, an induced interaction among the polarons appears, which counteracts the repulsive interaction among the impurities.…”