Andrea Tononi (ICFO, Barcelona)

Quantum gases in low-dimensional curved geometries

While condensed matter systems have been extensively studied in one- and two-dimensional configurations, the impact of confinement beyond mere dimensionality has received comparatively little attention. Over the past decade, however, research into quantum systems with spatially-curved geometries has gained significant momentum. Notably, experimental advancements with ultracold atoms now enable the confinement of bosonic gases in curved setups such as ellipsoidal shells. A fundamental model, capturing the interplay between spatial curvature, quantum physics, and nontrivial topology, is a bosonic gas confined on the surface of a sphere.Following a broad review of my previous findings, I will present our recent study of bosons on a sphere with zero-range attractive interactions [1]. As a main result, we observe a first-order phase transition from a weakly attractive uniform state to a solitonic state as the sphere's radius increases. Two additional insights emerge from this study: (a) the one-dimensional counterpart of the sphere (the ring) undergoes a second-order phase transition [2], and (b) we predict the possibility to create macroscopic superpositions between uniform and solitonic states for systems with a relatively large number of particles (10 < N < 20). We thus find an instance of a system whose few- to many-body physics can be controled via its curved geometry. Looking ahead, the research direction of quantum gases in curved geometries could both yield technological applications and further foundational understanding of quantum physics [3]. 

References:

[1] A. Tononi, G. Astrakharchik, D. S. Petrov, Gas-to-soliton transition of attractive bosons on a spherical surface, AVS Quantum Sci. 6, 023201 (2024). 

[2] L. D. Carr, C. W. Clark, and W. P. Reinhardt, Stationary solutions of the one-dimensional nonlinear Schrödinger equation. II. Case of attractive nonlinearity, Phys. Rev. A 62, 063611 (2000).

[3] A. Tononi and L. Salasnich, Low-dimensional quantum gases in curved geometries, Nat. Rev. Phys. 5, 398 (2023).