Dimer problem on a spherical surface

Abstract

We solve the problem of a dimer moving on a spherical surface and find that its binding energy and wave function are sensitive to the total angular momentum. The dimer gets squeezed in the direction orthogonal to the center-of-mass motion and can qualitatively change its geometry from two dimensional to one dimensional. These results suggest that combining the curved geometry with finite angular momentum may give rise to qualitatively new many-body phenomena in ultracold shell-shaped gases.

A.T. acknowledges financial support of the Horizon Europe programme HORIZON-CL4-2022-QUANTUM-02-SGA via the Project No. 101113690 (PASQuanS2.1). The ICFO-QOT group acknowledges support from the European Research Council AdG NOQIA; MCIN/AEI [PGC2018-0910.13039/501100011033, CEX2019-000910-S/10.13039/501100011033, Plan National FIDEUA PID2019-106901GB-I00, Plan National STAMEENA PID2022-139099NB-I00, project funded by MCIN/AEI/10.13039/501100011033 and by the “European Union NextGenerationEU/PRTR” (PRTR-C17.I1), FPI]; QUANTERA DYNAMITE PCI2022-132919, QuantERA II Programme co-funded by European Union's Horizon 2020 program under Grant Agreement No. 101017733; Ministry for Digital Transformation and of Civil Service of the Spanish Government through the QUANTUM ENIA project call - Quantum Spain project, and by the European Union through the Recovery, Transformation and Resilience Plan - NextGenerationEU within the framework of the Digital Spain 2026 Agenda; Fundació Cellex; Fundació Mir-Puig; Generalitat de Catalunya (European Social Fund FEDER and CERCA program; Barcelona Supercomputing Center MareNostrum (FI-2023-3-0024); Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union, European Commission, European Climate, Infrastructure and Environment Executive Agency (CINEA), or any other granting authority. Neither the European Union nor any granting authority can be held responsible for them (HORIZON-CL4-2022-QUANTUM-02-SGA PASQuanS2.1, 101113690, EU Horizon 2020 FET-OPEN OPTOlogic, Grant No 899794, QU-ATTO, 101168628). EU Horizon Europe Program (This project has received funding from the European Union's Horizon Europe research and innovation program under Grant Agreement No. 101080086 NeQSTGrant Agreement 101080086—NeQST); ICFO Internal “QuantumGaudi” project.

Peer Reviewed

Postprint (author's final draft)