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arXiv:2108.03175

From Efimov Physics to the Bose Polaron using Gaussian States

Arthur Christianen, J. I. Cirac, Richard Schmidt

Published Aug 6, 2021• 1 citation
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Abstract

Since the Efimov effect was introduced in 1970, a detailed theoretical understanding of Efimov physics has been developed in the few-body context. However, it has proven to be challenging to describe the role Efimov-type correlations play in many-body systems such as quenched or collapsing Bose-Einstein condensates (BECs). To study the impact the Efimov effect can have in such scenarios, we consider a light impurity immersed in a weakly interacting BEC, forming a Bose polaron. In this case, the higher-order correlations are localized around the impurity, making it more feasible to develop a theoretical description. Specifically, we employ a Gaussian state variational Ansatz in the reference frame of the impurity, capable of both capturing the Efimov effect and the formation of the polaron cloud. We find that the Efimov effect leads to a cooperative binding of bosons to the impurity and the formation of a many-body bound state. As a result, the polaron is not the ground state, but rendered a metastable excited state which can decay into these Efimov clusters. While this decay is slow for small interaction strengths, it becomes more prominent as the attractive scattering length increases, up to the point where the polaron becomes completely unstable. This critical scattering length can be interpreted as a many-body shifted Efimov resonance, where the scattering of two excitations of the bath with the polaron can lead to bound state formation. Compared to the few-body case, the resonance is shifted to smaller attractive scattering lengths due to the participation of the polaron cloud in the cooperative binding process. This corresponds to an intriguing scenario of polaron-assisted chemistry, where many-body effects lead to enhanced signal of the chemical recombination process, which can be directly probed in state-of-the-art experiments.

DOI
10.48550/arxiv.2108.03175

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Since the Efimov effect was introduced in 1970, a detailed theoretical understanding of Efimov physics has been developed in the few-body context. However, it has proven to be challenging to describe the role Efimov-type correlations play in many-body systems such as quenched or collapsing Bose-Einstein condensates (BECs). To study the impact the Efimov effect can have in such scenarios, we consider a light impurity immersed in a weakly interacting BEC, forming a Bose polaron. In this case, the higher-order correlations are localized around the impurity, making it more feasible to develop a theoretical description. Specifically, we employ a Gaussian state variational Ansatz in the reference frame of the impurity, capable of both capturing the Efimov effect and the formation of the polaron cloud. We find that the Efimov effect leads to a cooperative binding of bosons to the impurity and the formation of a many-body bound state. As a result, the polaron is not the ground state, but rendered a metastable excited state which can decay into these Efimov clusters. While this decay is slow for small interaction strengths, it becomes more prominent as the attractive scattering length increases, up to the point where the polaron becomes completely unstable. This critical scattering length can be interpreted as a many-body shifted Efimov resonance, where the scattering of two excitations of the bath with the polaron can lead to bound state formation. Compared to the few-body case, the resonance is shifted to smaller attractive scattering lengths due to the participation of the polaron cloud in the cooperative binding process. This corresponds to an intriguing scenario of polaron-assisted chemistry, where many-body effects lead to enhanced signal of the chemical recombination process, which can be directly probed in state-of-the-art experiments.
Similar to an electron in a solid, an impurity in an atomic Bose-Einstein condensate (BEC) is dressed by excitations from the medium, forming a polaron quasiparticle with modified properties. This impurity can also undergo chemical recombination with atoms from the BEC, a process resonantly enhanced when universal three-body Efimov bound states cross the continuum. To study the interplay between these phenomena, we use a Gaussian state variational method able to describe both Efimov physics and arbitrarily many excitations of the BEC. We show that the polaron cloud contributes to bound state formation, leading to a shift of the Efimov resonance to smaller interaction strengths. This shifted scattering resonance marks the onset of a polaronic instability towards the decay into large Efimov clusters and fast recombination, offering a remarkable example of chemistry in a quantum medium.
We study the effect of Efimov physics (in the few-body sector) on the spectral response of the Bose polaron, a many-body system consisting of an impurity immersed in a bath of bosonic atoms. We find that the Efimov correlation can be greatly enhanced by increasing the mass ratio between the bosons and the impurity, which results in visible signatures in the rf spectrum of the polaron. Using a diagrammatic approach up to the third-order virial expansion, we show how the mass imbalance and the enhanced three-body effect modify the line shape and linewidth of the polaron spectrum. Moreover, we study the effect of a finite boson-boson interaction on the spectrum. Taking the realistic system of Li impurities immersed in Cs bosons with a positive Cs-Cs scattering length, we find a visible Efimov branch, which is associated with the second lowest Efimov trimer, in the polaron spectrum. In particular, by adjusting the boson density the Efimov branch can greatly hybridize with the attractive polaron branch, leading to spectrum broadening near their avoided level crossing. Our results can be directly probed in the cold atoms experiments on Li-Cs and Li-Rb Bose polarons.
The Bose polaron is a quasiparticle of an impurity dressed by surrounding bosons. In few-body physics, it is known that two identical bosons and a third distinguishable particle can form a sequence of Efimov bound states in the vicinity of interspecies scattering resonance. On the other hand, in the Bose polaron system with an impurity atom embedded in many bosons, no signature of Efimov physics has been reported in the existing spectroscopy measurements to date. In this Letter, we propose that a large mass imbalance between a light impurity and heavy bosons can help produce visible signatures of Efimov physics in such a spectroscopy measurement. Using the diagrammatic approach in the virial expansion to include three-body effects from pair-wise interactions, we determine the impurity self-energy and its spectral function. Taking the ^{6}Li-^{133}Cs system as a concrete example, we find two visible Efimov branches in the polaron spectrum, as well as their hybridizations with the attractive polaron branch. We also discuss the general scenarios for observing the signature of Efimov physics in polaron systems. This work paves the way for experimentally exploring intriguing few-body correlations in a many-body system in the near future.
We investigate the zero-temperature properties of an impurity particle interacting with a Bose-Einstein condensate (BEC), using a variational wave function that includes up to two Bogoliubov excitations of the BEC. This allows one to capture three-body Efimov physics, as well as to recover the first nontrivial terms in the weak-coupling expansion. We show that the energy and quasiparticle residue of the dressed impurity (polaron) are significantly lowered by three-body correlations, even for weak interactions where there is no Efimov trimer state in a vacuum. For increasing attraction between the impurity and the BEC, we observe a smooth crossover from atom to Efimov trimer, with a superposition of states near the Efimov resonance. We furthermore demonstrate that three-body loss does not prohibit the experimental observation of these effects. Our results thus suggest a route to realizing Efimov physics in a stable quantum many-body system for the first time.
The mobile impurity in a Bose-Einstein condensate (BEC) is a paradigmatic many-body problem. For weak interaction between the impurity and the BEC, the impurity deforms the BEC only slightly and it is well described within the Fröhlich model and the Bogoliubov approximation. For strong local attraction this standard approach, however, fails to balance the local attraction with the weak repulsion between the BEC particles and predicts an instability where an infinite number of bosons is attracted toward the impurity. Here we present a solution of the Bose polaron problem beyond the Bogoliubov approximation which includes the local repulsion between bosons and thereby stabilizes the Bose polaron even near and beyond the scattering resonance. We show that the Bose polaron energy remains bounded from below across the resonance and the size of the polaron dressing cloud stays finite. Our results demonstrate how the dressing cloud replaces the attractive impurity potential with an effective many-body potential that excludes binding. We find that at resonance, including the effects of boson repulsion, the polaron energy depends universally on the effective range. Moreover, while the impurity contact is strongly peaked at positive scattering length, it remains always finite. Our solution highlights how Bose polarons are self-stabilized by repulsion, providing a mechanism to understand quench dynamics and nonequilibrium time evolution at strong coupling.