Universitat Politècnica de Catalunya. Departament de Física, Argüello Luengo, Javier, Bhattacharya, Utso, Celi, Alessio, Chhajlany, Ravindra W., Grass, Tobias Daniel, Plodzien, Marcin, Rakshit, Debraj, Salamon, Tymoteusz Piotr, Stornati, Paolo, Tarruell, Leticia, Lewenstein, Maciej, Universitat Politècnica de Catalunya. Departament de Física, Argüello Luengo, Javier, Bhattacharya, Utso, Celi, Alessio, Chhajlany, Ravindra W., Grass, Tobias Daniel, Plodzien, Marcin, Rakshit, Debraj, Salamon, Tymoteusz Piotr, Stornati, Paolo, Tarruell, Leticia, and Lewenstein, Maciej
The concept of synthetic dimensions works particularly well in atomic physics, quantum optics, and photonics, where the internal degrees of freedom (Zeeman sublevels of the ground state, metastable excited states, or motional states for atoms, and angular momentum states or transverse modes for photons) provide the synthetic space. In this Perspective article we report on recent progress on studies of synthetic dimensions, mostly, but not only, based on the research realized around the Barcelona groups (ICFO, UAB), Donostia (DIPC), Poznan (UAM), Kraków (UJ), and Allahabad (HRI). We describe our attempts to design quantum simulators with synthetic dimensions, to mimic curved spaces, artificial gauge fields, lattice gauge theories, twistronics, quantum random walks, and more., CFOQOT group acknowledges support from: ERC 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 byMCIN/AEI/ 10.13039/501100011033 and by the “European Union NextGenerationEU/ PRTR” (PRTR-C17.I1), FPI); QUANTERA MAQS PCI2019-111828-2); QUANTERA DYNAMITE PCI2022-132919 (QuantERA II Programme cofunded by EuropeanUnion’sHorizon 2020 programunder Grant Agreement No 101017733), Ministry of Economic Affairs and Digital Transformation 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 theDigital Spain 2026Agenda; Fundació Cellex; FundacióMir-Puig; Generalitat de Catalunya (European Social Fund FEDER and CERCA program, AGAUR Grant No. 2021 SGR 01452, QuantumCAT U16-011424, cofunded by ERDF Operational Program of Catalonia 2014-2020); Barcelona Supercomputing Center MareNostrum (FI-2023-1-0013); EU Quantum Flagship (PASQuanS2.1, 101113690); EU Horizon 2020 FET-OPEN OPTOlogic (Grant No 899794); EU Horizon Europe Program (Grant Agreement 101080086 – NeQST), ICFO Internal “QuantumGaudi” project; European Union’s Horizon 2020 program under the Marie Sklodowska-Curie grant agreement No 847648; “La Caixa” Junior Leaders fellowships, La Caixa” Foundation (ID 100010434): CF/BQ/PR23/11980043. RWC acknowledges support fromthePolishNationalScienceCentre (NCN)under theMaestro GrantNo.DEC- 2019/34/A/ST2/00081.M.P. acknowledges the support of the Polish National Agency for Academic Exchange, the Bekker programme no: PPN/BEK/2020/1/00317.A.C. acknowledges the support of MCIN/AEI/10.13039/501100011033 (LIGAS PID2020-112687GB-C22) and Generalitat de Catalunya (AGAUR 2021 SGR 00138). L. T. acknowledges funding from the European Union (ERC CoG-101003295 SuperComp), MCIN/AEI/10.13039/50110001, Peer Reviewed, Postprint (published version)