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Bose polarons in superfluids and supersolids

Laurent H. A. Simons

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Bose-Einstein condensation is a macroscopic quantum phenomenon where cooling down a gas of bosonic particles to ultracold temperatures results in the macroscopic occupation of the lowest energy state. This new state of matter has been used as a quantum simulator of many-body phenomena and theories due to its extreme tunability and controllability. An important example of such a many-body system is the polaron which, in its most general form, describes an impurity interacting with a bosonic bath. In the case of ultracold Bose gases, the impurity interacts with and is dressed by the Bogoliubov excitations of the gas. A supersolid is a state of matter that exhibits both superfluidity and crystalline order, which are seemingly irreconcilable properties. It has recently been observed in dipolar ultracold Bose gases, where it arises from the long-range anisotropic dipole-dipole interactions, and also other systems. The breaking of both translational symmetry and gauge symmetry results in multiple excitation modes in the supersolid. In this thesis, the charged Bose polaron and an impurity in a dipolar ultracold Bose gas exhibiting supersolidity (the supersolid Bose polaron) are studied. The ground-state properties of the charged Bose polaron are discussed using a variational path-integral approach. Absorption spectroscopy is proposed as a probe of the charged Bose polaron, and the optical response is studied for weak impurity-boson interactions. Next, the one-dimensional dipolar supersolid Bose polaron is investigated where multiple approaches are used for the derivation of the ground-state properties. The study of the polaron problem with a supersolid background is of particular interest because of the rich excitation spectrum of the supersolid. Interesting phenomena, such as possible localization of the polaron to a single droplet for strong interactions, are observed. The absorption spectrum of a charged impurity in the supersolid is also derived, which, because of the different excitation modes of the supersolid, shows multiple peaks from which information such as the superfluid fraction may be obtained.

DOI
10.63028/10067/2184840151162165141

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Bose-Einstein condensation is a macroscopic quantum phenomenon where cooling down a gas of bosonic particles to ultracold temperatures results in the macroscopic occupation of the lowest energy state. This new state of matter has been used as a quantum simulator of many-body phenomena and theories due to its extreme tunability and controllability. An important example of such a many-body system is the polaron which, in its most general form, describes an impurity interacting with a bosonic bath. In the case of ultracold Bose gases, the impurity interacts with and is dressed by the Bogoliubov excitations of the gas. A supersolid is a state of matter that exhibits both superfluidity and crystalline order, which are seemingly irreconcilable properties. It has recently been observed in dipolar ultracold Bose gases, where it arises from the long-range anisotropic dipole-dipole interactions, and also other systems. The breaking of both translational symmetry and gauge symmetry results in multiple excitation modes in the supersolid. In this thesis, the charged Bose polaron and an impurity in a dipolar ultracold Bose gas exhibiting supersolidity (the supersolid Bose polaron) are studied. The ground-state properties of the charged Bose polaron are discussed using a variational path-integral approach. Absorption spectroscopy is proposed as a probe of the charged Bose polaron, and the optical response is studied for weak impurity-boson interactions. Next, the one-dimensional dipolar supersolid Bose polaron is investigated where multiple approaches are used for the derivation of the ground-state properties. The study of the polaron problem with a supersolid background is of particular interest because of the rich excitation spectrum of the supersolid. Interesting phenomena, such as possible localization of the polaron to a single droplet for strong interactions, are observed. The absorption spectrum of a charged impurity in the supersolid is also derived, which, because of the different excitation modes of the supersolid, shows multiple peaks from which information such as the superfluid fraction may be obtained.
The supersolid phase of a dipolar Bose-Einstein condensate has an intriguing excitation spectrum displaying a band structure. Here, the dressing of an impurity in a one-dimensional dipolar supersolid with the excitations of the supersolid is studied. The ground-state energy of the supersolid polaron is calculated using a variational path integral approach, which obtained accurate results for other polaron systems within the Bogoliubov and Fr\"ohlich approximations. A divergence is observed at the superfluid-supersolid phase transition. The polaron radius is also computed, showing that, as a function of impurity-atom interactions, the polaron can become localized to a single droplet, behaving like a small solid-state polaron.
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 using a generalized Feynman variational path-integral approach, which obtained accurate results for other polaron problems. We find that compared to other existing approaches, our approach gives similar and improved results while being numerically less intensive. Optical absorption, which is a standard tool to study the solid-state polaron, is introduced here as a probing method for the Bose polaron. It is calculated within the Bogoliubov approximation for weak ion-atom interactions, and the effect of finite temperature is studied. We show that the coupling of the ion to an oscillating external electric field offers a straightforward experimental probe for the charged polaron in a Bose gas, different from but complementary to existing spectroscopic techniques.
This thesis discusses the experiments on 2D dipolar Bose gas of ultracold erbium atoms. Long-range and anisotropic dipole-dipole interaction induces complex orders in quantum many-body systems. Highly magnetic lanthanide atoms such as dysprosium and erbium have the largest magnetic moment in the periodic table, which has attracted significant attention in the past decades. Starting from quantum degenerate dysprosium and erbium atoms, exotic phases like quantum droplets, supersolid, dipolar quantum solid in the Hubbard regime have been studied. However, the 2D dipolar superfluid still remains understudied, despite being theoretically discussed for over two decades. Although tremendous theoretical proposals predict different phenomena in 2D dipolar superfluids, our first interest is to know how the superfluidity emerges in the 2D dipolar gases at finite temperatures. Our observations suggest that the superfluid transition can be well described by the Berezinskii-Kosterlitz-Thouless transition with an effective contact interaction as a function of dipolar orientation. With the 2D dipolar superfluid with strong DDI, we characterized the elementary excitation of the matter: the collective breathing mode. Our measurements establish how the competition between local and nonlocal interaction in strongly dipolar 2D superfluid retains quasi-scale invariance or strongly breaks scale invariance. By further searching the interaction parameters, we created stripes with global coherence, which are the first supersolid stripes in 2D. Experiments including measuring density fluctuation, coherence, and collective mode have been performed to understand the 2D supersolid. At last, we also observe unconventional light scattering from round-disk dipolar BECs, which provides new possibilities for atom optics.
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.
This review describes the field of Bose polarons, arising when mobile impurities are immersed into a bosonic quantum gas. The latter can be realized by a Bose-Einstein condensate (BEC) of ultracold atoms, or of exciton polaritons in a semiconductor, which has led to a series of experimental observations of Bose polarons near inter-species Feshbach resonances that we survey. Following an introduction to the topic, with references to its historic roots and a presentation of the Bose polaron Hamiltonian, we summarize state-of-the-art experiments. Next we provide a detailed discussion of polaron models, starting from the ubiquitous Fröhlich Hamiltonian that applies at weak couplings. We proceed by a survey of concurrent theoretical methods used for solving strongly interacting Bose polaron problems. The subsequent sections are devoted to the large bodies of work investigating strong coupling Bose polarons, including detailed comparisons with radio-frequency (RF) spectra obtained in ultracold atom experiments; to investigations of universal few-body and Efimov states associated with a Feshbach resonance in atomic mixtures; to studies of quantum dynamics and polarons out of equilibrium; Bose polarons in low-dimensional; induced interactions among polarons and bipolaron formation; and to Bose polarons at non-zero temperatures. We end our review by detailed discussions of closely related experimental setups and systems, including ionic impurities, systems with strong light-matter interactions, and variations and extensions of the Bose polaron concepts e.g. to baths with topological order or strong interactions relevant for correlated electrons. Finally, an outlook is presented, highlighting possible future research directions and open questions in the field as a whole.
Abstract Lattice polarons, quasiparticles arising from the interaction between an impurity and its surrounding bosonic environment confined to a lattice system, have emerged as a platform for generating complex few-body states, probing many-body phenomena, and addressing long-standing problems in physics. In this study, we employ a variational ansatz to investigate the quasiparticle and spectral properties of an impurity coupled to a condensate gas of hard-core bosons in a two-dimensional optical lattice. Our findings demonstrate that the polaron features can be tuned by adjusting the filling factor of the bath, revealing intriguing polaron characteristics in the strongly interacting regime. These results offer valuable insights for lattice polaron experiments with ultracold gases and can serve as a guide for new experiments in emergent quantum devices, such as moiré materials, where optical excitations can be described in terms of hard-core bosons.