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arXiv:1810.03933 · Physical Review A

Ground-state properties of interacting Bose polarons

Senne Van Loon, Wim Casteels, Jacques Tempere

Published Dec 26, 2018• 16 citations
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Abstract

We theoretically investigate the role of multiple impurity atoms on the ground-state properties of Bose polarons. The Bogoliubov approximation is applied for the description of the condensate resulting in a Hamiltonian containing terms beyond the Fr\"ohlich approximation. The many-body nature of the impurity atoms is taken into account by extending the many-body description for multiple Fr\"ohlich polarons, revealing the static structure factor of the impurities as the key quantity. Within this formalism various experimentally accessible polaronic properties are calculated such as the energy and the effective mass. These results are examined for system parameters corresponding to two recent experimental realizations of the Bose polaron, one with fermionic impurities and one with bosonic impurities.

DOI
10.1103/physreva.98.063631

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We theoretically investigate the role of multiple impurity atoms on the ground-state properties of Bose polarons. The Bogoliubov approximation is applied for the description of the condensate resulting in a Hamiltonian containing terms beyond the Fr"ohlich approximation. The many-body nature of the impurity atoms is taken into account by extending the many-body description for multiple Fr"ohlich polarons, revealing the static structure factor of the impurities as the key quantity. Within this formalism various experimentally accessible polaronic properties are calculated such as the energy and the effective mass. These results are examined for system parameters corresponding to two recent experimental realizations of the Bose polaron, one with fermionic impurities and one with bosonic impurities.
The weak-coupling many-polaron formalism is applied to the case of the polaronic system consisting of impurities in a Bose-Einstein condensate. This allows investigating the ground-state properties and the response of the system to Bragg spectroscopy. Then, this theory is applied to the system of spin-polarized fermionic lithium-6 impurities in a sodium condensate. The Bragg spectrum reveals a peak that corresponds to the emission of Bogoliubov excitations. Both the ground-state properties and the response spectrum show that the polaronic effect vanishes at high densities. We also look at two possibilities to define the polaronic effective mass and observe that this results in a different quantitative behavior if multiple impurities are involved.
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.
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.
In this paper we study an impurity in Bose-Einstein-Condensate system at T=0KT=0KT=0K and suppose the contact forms for boson-boson and boson-impurity interactions. Using Bogoliubov theory and a further approximation corresponding to only think over the forward scattering of impurity by bosons, we derive a reduced Hamiltonian whose form is the same as the Fröhlich Hamiltonian for large polaron. By using Lee-Low-Pines (LLP) theory for large polaron, we obtain the effective mass of impurity, the phonon number carried by impurity and the energy related to the existence of impurity. In addition, we also discuss the valid range for forward-scattering approximation.
The system of a charged impurity in an interacting Bose gas has gained significant attention due to the long-range ion-atom interactions and the study of transport properties. Here, the ground state energy of a charged Bose polaron is calculated within the Bogoliubov approximation for both the Fröhlich and beyond-Fröhlich Hamiltonians using a generalized Feynman variational path-integral approach, which obtained accurate results for other polaron problems. The generalized approach, which was used to improve the energy result for the neutral polaron, has resulted in a minor improvement, indicating that Feynman's approach is sufficient when the impurity-boson interaction is long-range. Beyond-Fröhlich corrections results in the emergence of a divergence in the polaronic energy indicating a transition between the repulsive and attractive polaron regime. The path-integral approach with the beyond-Fröhlich Hamiltonian is also compared to a field-theory calculation from Christensen et al, 2021. The validity of the Bogoliubov approximation is investigated. The optical absorption has also been calculated within the Bogoliubov approximation for weak ion-atom interactions, and the effect of finite temperature has been studied. We show that the coupling of the ion to an oscillating external electric field offers a straigtforward experimental probe for the charged polaron in a Bose gas, different from but complementary to existing spectroscopic techniques.
Abstract Bose polarons are quasiparticles formed through the interaction between impurities and Bose–Einstein condensates. In this paper, we derive an effective Fröhlich Hamiltonian using the generalized Bogoliubov transformation. The effective Fröhlich Hamiltonian encompasses two types of effective interactions: impurity-density (ID) coupling and impurity-spin (IS) coupling. Furthermore, we employ the Lee–Low–Pines variational approach to investigate the relevant properties of Bose polarons induced by the ID and IS coupling. These properties include the ground state energy, effective mass, and average number of virtual phonons. Our findings reveal that the contribution resulting from IS couplings to the ground energy decreases to zero near the miscible–immiscible boundary. Additionally, the increase of the IS coupling induces a greater number of virtual phonons, impeding the movement of impurities and leading to a significant increase in the effective mass of Bose polarons.