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The European Physical Journal Special Topics

Droplets and supersolids in ultra-cold atomic quantum gases

K. Mukherjee, T. Arnone Cardinale, L. Chergui, Philipp Stürmer, S. M. Reimann

Published Oct 16, 2023• 13 citations
Publisher

Abstract

Abstract In this mini-review, we briefly summarize some of the main concepts and ideas behind highly dilute self-bound quantum droplets of both binary and dipolar character. The latter type of systems has more recently led to the experimental discovery of a dipolar supersolid state that allows entirely new insights on this long-sought purely quantum state of matter, with exciting prospects for fundamental research as well as future applied quantum sensing technologies. The first half of the review provides a brief history of droplets and supersolidity in various settings and also discusses the self-binding in binary quantum gases, and the second half of the review summarizes our own recent work in the field, presented at the 2022 FQMT conference in Prague.

DOI
10.1140/epjs/s11734-023-00991-6

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Abstract In this mini-review, we briefly summarize some of the main concepts and ideas behind highly dilute self-bound quantum droplets of both binary and dipolar character. The latter type of systems has more recently led to the experimental discovery of a dipolar supersolid state that allows entirely new insights on this long-sought purely quantum state of matter, with exciting prospects for fundamental research as well as future applied quantum sensing technologies. The first half of the review provides a brief history of droplets and supersolidity in various settings and also discusses the self-binding in binary quantum gases, and the second half of the review summarizes our own recent work in the field, presented at the 2022 FQMT conference in Prague.
This habilitation thesis pertains to the theoretical and computational investigation of dilute dipolar Bose-Einstein condensates in the bulk, where atoms interact through both short-range and dipole-dipole interactions. Twelve papers are summarized that were published over the period from 2015 to 2024, with four based on theory-experiment collaborations, and the remaining eight papers being purely theoretical. The papers are grouped thematically into three chapters: the first focuses on quantum droplets, which are dilute liquids resulting from a balance between attractive mean-field interactions and beyond-mean-field quantum fluctuations; the second pertains to the exploration and realization of the long-sought supersolid phase of matter, which simultaneously exhibits properties of both a solid and a superuid; and the third addresses binary supersolids in two-component dipolar Bose-Einstein condensates, whose additional degrees of freedom offer the potential for novel physics and provide a pathway to realizing bulk supersolids.
Quantum fluctuations can stabilize Bose-Einstein condensates (BEC) against the mean-field collapse. Stabilization of the condensate has been observed in quantum degenerate Bose-Bose mixtures and dipolar BECs. The fine-tuning of the interatomic interactions can lead to the emergence of two new states of matter: liquid-like self-bound quantum droplets and supersolid crystals formed from these droplets. We review the properties of these exotic states of matter and summarize the experimental progress made using dipolar quantum gases and Bose-Bose mixtures. We conclude with an outline of important open questions that could be addressed in the future.
Supersolids-the enigmatic phase of quantum matter, with properties resembling both the superfluid and solid states-have been actively sought over the past 70 years. We provide a comprehensive review of the developments to date in experimental and theoretical studies of the supersolid phases of bosons, with a particular focus on their observation in ultracold atomic gases. Additionally, the use of optical lattices facilitates the realization of 'lattice-supersolids', which paves the way to study the effect of correlations in a controlled manner. A brief theoretical framework is presented to characterize this puzzling state with competing orders and to gain insight into its basic properties. Various types of supersolid phases and the different platforms used to achieve them are described. Finally, we discuss the future prospects of research and the potential to achieve supersolids with more exotic features.
Dipolar quantum gases, encompassing atoms and molecules with significant dipole moments, exhibit unique long-range and anisotropic dipole-dipole interactions (DDI), distinguishing them from systems dominated by short-range contact interactions. This review explores their behavior across dimensions, focusing on magnetic atoms in quasi-2D in comparison to 3D. In 3D, strong DDI leads to phenomena like anisotropic superfluidity, quantum droplets stabilized by Lee-Huang-Yang corrections, and supersolid states with density modulations. In 2D, we discuss a new scenario where DDI induces angle-dependent Berezinskii-Kosterlitz-Thouless transitions and potential supersolidity, as suggested by recent experimental realizations of strongly dipolar systems in quasi-2D geometries. We identify key challenges for future experimental and theoretical work on strongly dipolar 2D systems. The review concludes by highlighting how these unique 2D dipolar systems could advance fundamental research as well as simulate novel physical phenomena.
The study of Bose–Einstein condensation (BEC) in lower dimensions plays an important role in understanding the fundamentals of many-body physics as they can be treated theoretically with relative ease and can be verified experimentally. Recently, observation of a liquid-like state in a BEC mixture has been reported along with a theoretical prescription for its observation in the lower dimension. This observation is unique and has serious ramifications in our prevailing conception of the liquid state, which has a deep influence on the van der Waals theory. In explaining the self-bound nature of this state, quantum fluctuation and its fine balance with mean-field (MF) interaction turn out to be playing a key role. Though the experiments are performed predominantly in three dimensions, theoretical studies extend to the lower dimensions. In this brief review, we plan to summarize the recent theoretical advances in droplet research in the lower dimension and elaborate on the description of our contributions. We will mainly focus on analytical results related to this self-bound state in a one-dimension and quasi one-dimension environment. We aim to cover a few results from the family of cnoidal solutions to droplet solutions with smooth transitions between each other, finishing it by carrying a modest discussion on the supersolid phase.
We numerically study the many-body physics of molecular Bose-Einstein condensates with strong dipole-dipole interactions. We observe the formation of self-bound droplets, and explore phase diagrams that feature a variety of exotic supersolid states. In all of these cases, the large and tunable molecular dipole moments enable the study of unexplored regimes and phenomena, including liquidlike density saturation and universal stability scaling laws for droplets, as well as pattern formation and the limits of droplet supersolidity. We discuss a realistic experimental approach to realize both the required collisional stability of the molecular gases and the independent tunability of their contact and dipolar interaction strengths. Our work provides both a blueprint and a benchmark for near-future experiments with bulk molecular Bose-Einstein condensates.