Quantum nanophotonics in two-dimensional materials

The field of two-dimensional (2D) materials-based nanophotonics has been growing at a rapid pace, triggered by the ability to design nanophotonic systems with in situ control, unprecedented number of degrees of freedom, and to build material heterostructures from the bottom up with atomic precision. A wide palette of polaritonic classes have been identified, comprising ultraconfined optical fields, even approaching characteristic length-scales of a single atom. These advances have been a real boost for the emerging field of quantum nanophotonics, where the quantum mechanical nature of the electrons and polaritons and their interactions become relevant. Examples include quantum nonlocal effects, ultrastrong light–matter interactions, Cherenkov radiation, access to forbidden transitions, hydrodynamic effects, single-plasmon nonlinearities, polaritonic quantization, topological effects, and so on. In addition to these intrinsic quantum nanophotonic phenomena, 2D material systems can also be used as sensitive probes for the quantum properties of the material that carries the nanophotonics modes or quantum materials in its vicinity. Here, polaritons act as a probe for otherwise invisible excitations, for example, in superconductors, or as a new tool to monitor the existence of Berry curvature in topological materials and superlattice effects in twisted 2D materials. In this Perspective, we present an overview of the emergent field of 2D-material quantum nanophotonics and provide a future perspective on the prospects of both fundamental emergent phenomena and emergent quantum technologies, such as quantum sensing, single-photon sources, and quantum emitters manipulation. We address four main implications: (i) quantum sensing, featuring polaritons to probe superconductivity and explore new electronic transport hydrodynamic behaviors, (ii) quantum technologies harnessing single-photon generation, manipulation, and detection using 2D materials, (iii) polariton engineering with quantum materials enabled by twist angle and stacking order control in van der Waals heterostructures, and (iv) extreme light−matter interactions enabled by the strong confinement of light at atomic level by 2D materials, which provide new tools to manipulate light fields at the nanoscale (e.g., quantum chemistry, nonlocal effects, high Purcell enhancement).H.L.K. acknowledges support from the Government of Spain (FIS2017-91599-EXP; Severo Ochoa CEX2019-000910-S), Fundacio ' Cellex, Fundacio ' Mir-Puig, and Generalitat de Catalunya (CERCA, AGAUR, SGR 1656). Furthermore, the research leading to these results has received funding from the European Union's Horizon 2020 under Grant Agreements 785219 (Graphene flagship Core2), 881603 (Graphene flagship Core3), and 820378 (Quantum flagship). This work was also supported by the ERC TOPONANOP under Grant Agreement No. 726001. I.T. acknowledges funding from the Spanish Ministry of Science, Innovation and Universities (MCIU) and State Research Agency (AEI) via the Juan de la Cierva Fellowship No. FJC2018-037098-I. F.H.L. K. and A.R.-P. acknowledge BIST Ignite Programme Grant from the Barcelona Institute of Science and Technology (QEE2DUP). N.M.R.P. acknowledges support from the European Commission through the project "Graphene-Driven Revolutions in ICT and Beyond" (ref. No. 881603, CORE 3), COMPETE 2020, PORTUGAL 2020, FEDER, and the Portuguese Foundation for Science and Technology (FCT) through Project POCI-01-0145-FEDER028114, and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing UID/FIS/04650/2019. N.A.M. is a VILLUM Investigator supported by VILLUM FONDEN (Grant No. 16498) and Independent Research Fund Denmark (Grant No. 702600117B). The Center for Nano Optics is financially supported by the University of Southern Denmark (SDU 2020 funding). The Center for Nanostructured Graphene (CNG) is sponsored by the Danish National Research Foundation (Project No. DNRF103). J.C.W.S. acknowledges support from the National Research Foundation (NRF) Singapore under its NRF fellowship programme Award No. NRF-NRFF2016-05 and the Ministry of Education (MOE) Singapore under its MOE AcRF Tier 3 Award MOE2018-T3-1-002

Measurement of the Quark and Gluon Fragmentation Functions in Z0Z^0 Hadronic Decays

The fragmentation functions and multiplicities in $b\overline{b}$ and light quark events are compared. The measured transverse and longitudinal components of the fragmentation function allow the gluon fragmentation function to be evaluated

Investigation of the splitting of quark and gluon jets

The splitting processes in identified quark and gluon jets are investigated using longitudinal and transverse observables. The jets are selected from symmetric three-jet events measured in Z decays with the Delphi detector in 1991-1994. Gluon jets are identified using heavy quark anti-tagging. Scaling violations in identified gluon jets are observed for the first time. The scale energy dependence of the gluon fragmentation function is found to be about two times larger than for the corresponding quark jets, consistent with the QCD expectation TeX . The primary splitting of gluons and quarks into subjets agrees with fragmentation models and, for specific regions of the jet resolution TeX , with NLLA calculations. The maximum of the ratio of the primary subjet splittings in quark and gluon jets is TeX . Due to non-perturbative effects, the data are below the expectation at small TeX . The transition from the perturbative to the non-perturbative domain appears at smaller TeX for quark jets than for gluon jets. Combined with the observed behaviour of the higher rank splittings, this explains the relatively small multiplicity ratio between gluon and quark jets

Measurements of the leptonic branching fractions of the τ\tau

Data collected with the DELPHI detector from 1993 to 1995 combined with previous DELPHI results for data from 1991 and 1992 yield the branching fractions B({\tau \rightarrow \mbox{\rm e} \nu \bar{\nu}}) = (17.877 \pm 0.109_{stat} \pm 0.110_{sys} )\% and $B({\tau \rightarrow \mu \nu \bar{\nu}}) = (17.325 \pm 0.095_{stat} \pm 0.077_{sys} )\%$

Search for scalar fermions and long-lived scalar leptons at centre-of-mass energies of 130 GeV to 172 GeV

Data taken by DELPHI during the 1995 and 1996 LEP runs have been used to search for the supersymmetric partners of electron, muon and tau leptons and of top and bottom quarks. The observations are in agreement with standard model predictions. Limits are set on sfermion masses. Searches for long lived scalar leptons from low scale supersymmetry breaking models exclude stau masses below 55~GeV/c$^2$ at the 95\% confidence level, irrespective of the gravitino mass