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Coupling Quantum Emitters to Graphene Plasmons: a new route towards fast Quantum Optics

Periodic Reporting for period 1 - E-GRA-MONS OPTICS (Coupling Quantum Emitters to Graphene Plasmons: a new route towards fast Quantum Optics)

Reporting period: 2015-03-01 to 2017-02-28

In this project we address the problem of coupling quantum emitters to graphene plasmons. The realization of such a hybrid quantum system represents a major step forward for quantum technologies, because it enables fast quantum operations using the strong electromagnetic field of the plasmon. We investigate methods to exploit the coupling between quantum emitters and graphene plasmons for fast quantum operations such as entanglement generation.

Our results until now mean an important advance in our understanding of the coupling between quantum emitters and graphene plasmons. The creation of a working quantum interface between an quantum emitters and graphene will be of crucial importance for the further development of quantum technologies. These promise new applications that utilize the non-classical features of quantum mechanics to perform tasks that are very difficult or impossible with current technologies.

The main objective is the creation of a stable, solid-state nanomaterial in which the quantum states of the emitters can be manipulated in the strong electromagnetic field of graphene plasmons. To accomplish that goal we investigate the spectroscopic properties of quantum emitters and graphene, and perform numerical simulations of fast quantum operations.
Our work has included computer simulations, time-resolved spectroscopic measurements of quantum emitters and the nanofabrication of graphene. In the computer simulations we demonstrate a novel method for entanglement generation by means of plasmon-mediated interactions between quantum emitters. In the experimental part of the project, we have carried out spectroscopic measurements to select the most suitable kind of quantum emitter for the hybrid quantum system, following the requirements of narrow inhomogeneous broadening. Also, using magneto-optical Kerr spectroscopy, in combination with numerical Stoner-Wohlfarth model, we have design an experimental method in which the coupling of quantum emitters to plasmonic cavities can be tested by assessing the populations of Zeeman sublevels. We have not been able to reach the visible or near infrarred sepectrum in the nanofabricated plasmonic nanocavities. For this reason, we have theoretically investigated a four-level scheme, in which the probe laser, in the range of optical communication wavelengths, can couple a long-lived state of the emitter to an excited state, while this is coupled to another excited state by the plasmon.

In the theoretical part of the project, we have developed a software that numerically simulates the dynamics of the hybrid quantum system and its interaction with light. For that task, we have used computer techniques of quantum optics, such as the Monte Carlo method of quantum trajectories, in combination with numerical techniques for the calculation of the near field of graphene nanostructures. Our investigations have covered the strong-coupling regime as well as the weak coupling regime:
A. Strong-coupling regime: In this situation we can assume that cavity-mediated interactions induce collective energy shifts in some states of the quantum emitters. In our protocol the population transfer between two qubit states of the emitters is conditional on the cavity-mediated interactions. Our method uses four energy levels in such a way that the wavelength of the graphene plasmons can be different from those of the lasers.
B. Weak-coupling regime: This situation is more realistic than the strong-coupling regime. Here, we cannot assume energy shifts, but we can assume cooperative spontaneous emission into the plasmonic modes. We have calculated the generation of quantum non-local correlations between the emitters as a result of the cooperative spontaneous emission. We notice that only the ions at distances from graphene below 5nm are the subject of strong cooperative emission. This may be a drawback for absorption spectroscopy.

In the experimental part of the project, time-resolved spectroscopic measurements of a variety of quantum emitters have provided us with rich information to select the most suitable quantum emitters to couple to graphene plasmons. We have measured colloidal quantum dots, covalent organic frameworks, laser dyes and Erbium-doped yttria thin films. Erbium ions in yttria thin films show the narrowest inhomogeneous linewidth at 1550 nm. These are the quantum emitters of preference.

The interaction between quantum emitters and graphene plasmons is effective only at very short distances below 5nm. For such thin films, magneto-optical spectroscopy can be much more precise than absorption spectroscopy if the sample has unbalanced populations in the Zeeman sublevels. In our coupling schemes the qubit states can be two Zeeman sublevels that fulfil the requirements for Kerr spectroscopy. Parallel to the research activities with quantum emitters and graphene, I carried out various measurements of magnetic thin films. For the analysis of the measured data, I developed a software to fit the measured magnetic remanence to a Stoner-Wohlfarth model in order to obtain the anisotropic magnetic constants.
Our research activities have addressed some of the most scientifically exciting and technologically relevant issues in the field of hybrid quantum systems. In particular, we have investigated hybrid systems of quantum emitters coupled to graphene plasmons, where the high coupling energies boost up the speed of quantum operations.
Our results have clarified fundamental questions about the manipulation these hybrid quantum systems and their interactions with light. i) we have selected the most suitable kinds of quantum emitters to couple graphene plasmons, ii) we have theoretically design a protocol with four energy levels that allow strong emitter-graphene coupling at a longer wavelength than the lasers used to excite and read the quantum states of the emitter, thus overcoming the need of graphene plasmons in the visible spectrum. iii) We have also showed the effect of cooperative spontaneous emission of quantum emitters into plasmonic modes on the populations of Zeeman sublevels. This is of great importance for Kerr spectroscopy of the thin layer of emitters coupled to graphene. We think that our findings are going to have a high impact on the future design of new hybrid quantum systems.
Sketch of quantum emitters coupled to graphene nanostructures