• polaritoni intersottobanda
• plasmoni di superficie
• nanofabbricazione
• grafene
• accoppiamento forte

This thesis reports a research work on the development of graphene plasmonic gratings for applications in few-electron strong coupling experiments in a quantum well.
Thanks to its extraordinary properties and multifunctionality, graphene has emerged in recent years as one of the most promising nanomaterials for optoelectronic applications. Thinness, high conductivity and good optical transparency are only a few of its major qualities.
One of the most interesting applications of graphene is the possibility to generate surface plasmon polaritons, which are quantum collective oscillations of the graphene surface charge density coupled to electromagnetic fields localized at the surface. The generation of the surface plasmons in graphene cannot occur directly by illuminating graphene with an incident light beam, but the presence of a periodic structure that can impart an additional momentum to the incident light is necessary. In the mid-infrared spectral range, the electromagnetic fields of the surface plasmons show subwavelength confinement over a distance down to tens of nanometres.
Owing to this strong optical confinement of graphene surface plasmon polaritons (GSP), graphene gratings appear a promising platform for the realization of arrays of extremely small nanocavities, where the presence of a quantum well can produce strong light-matter coupling between surface plasmon polaritons and intersubband excitations. If the size of these nanocavities is reduced, the strong light-matter interaction could take place also at the level of few electrons per cavity: when this situation occurs, the system exhibits strong nonlinearities at the single photon level, as a consequence of the anharmonicity of the Jaynes-Cummings ladder states.
A periodic array of GSP-based nanocavities may represent an original solution for the realization of coupled cavity arrays, which are important so as to produce systems of strongly interacting photons. The applications of these systems range from the realization of superfluid states of light, to the implementation of quantum simulators. Moreover, single-photon nonlinear systems have applications in the realization of all-optics devices, such as single-photon switchers or transistors.
The most common periodic arrangement employed for the generation of graphene surface plasmon polaritons is the graphene nanoribbon array, which we study in depth in the presence of a GaAs substrate. Besides this configuration, in this work we present a new promising graphene periodic structure for the generation of surface plasmon polaritons: a GaAs square-wave grating covered by a flat continuous sheet of graphene.

The center of this thesis project is making the graphene gratings suitable for the strong interaction with intersubband excitations in a single quantum well. We have employed finite element simulations in order to study the frequency-domain response of both grating systems, showing that the electromagnetic fields are confined in a TM mode localized at the graphene surface. The effects of a variation of the graphene grating parameters have been deeply analysed in order to obtain a sharp, tunable plasmonic resonance in the mid-infrared spectral range.
In our simulations, we have verified that the resonance frequency can be tuned by changing the grating periodicity or the doping level of graphene. We have also verified that the Q-factor of the cavities is related to the electronic scattering time in graphene, which can be controlled by changing either the mobility or the Fermi energy of graphene.
In this thesis work we have studied the presence of a quantum well extremely close to each graphene grating, by using finite element simulations. We have demonstrated that both grating systems are able to produce two distinct resonance peaks with Rabi splitting values up to 3 THz, which is the signature of the strong coupling regime.
Both graphene grating configurations have been implemented experimentally using different nano-fabrication techniques, such as electron beam lithography and reactive ion etching, achieving values of widths down to 30nm for the GaAs grating and producing arrays of nanoribbons with ribbon widths smaller than 50nm.
Throughout this experimental work we have characterized each plasmonic grating by Raman spectroscopy, microscopy imaging techniques (AFM, SEM) and we have performed spectroscopic measurements on the samples using Fourier transform infrared spectroscopy (FTIR). These methods have been employed to prove that the use of polycrystalline graphene on the undoped GaAs substrate is not sufficient to achieve the values of mobility and Fermi energy necessary for the generation of graphene surface plasmons.
In order to overcome this limit, we have fabricated nanoribbon arrays of monocrystalline graphene, controlled by an external gate voltage in the back-gate configuration. We have used HfO2 (hafnia) as oxide layer because of its high dielectric constant, so as to improve to tunability of the graphene Fermi energy.
By means of field-effect measurements, we have characterized the electric response of the devices and we extracted the value of the mobility of graphene, obtaining values up to 4000 cm2/Vs. We have demonstrated that, with this configuration, the Fermi energy can be raised up to 0.4eV using gate voltages of 5V. Moreover, the resonance frequency of the nanocavities can be tuned by varying the gate bias in a range of few Volts.
In conclusion, in this thesis we have simulated the response of two graphene plasmonic gratings in the frequency-domain, and analysed how they couple with a single GaAs/AlGaAs quantum well. Moreover, we have fabricated and characterized experimentally both gratings, even in the presence of an external gate voltage.
This thesis work proposes a new approach for designing nonlinear systems at the single-photon level, by introducing one of the most promising material of the last years. The optimization of the systems described in this thesis, the research of new methods to produce graphene with extremely high quality and high doping and the technological improvement of the nanofabrication techniques could be accessible in the next few years. Therefore, we believe that this approach has a high potential and paves the way to the realization of new quantum optics experiments.