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Séminaire doctorants 2^{e} année

**Titre** : Symmetries of One-dimentional Strongly Correlated Quantum Mixtures

**Encadrement** : Mathias Albert, Patrizia Vignolo

**Résumé** : Ultracold atom experiments allow to engineer and probe, with an in- credible and alwaysimproving precision, a yet inaccessible variety of many- body quantum systems. One-dimensional models, which display several unique features associated to the reduced dimensionality, are the object of intense theoretical and experimental interest. Quantum gases in one di- mension can be realized in actual experiments by trapping atoms in tight optical waveguides. Moreover, these experiments offer the possibility to tune the interactions between the atoms, and hence to access the strongly correlated regime for various kinds of quantum mixtures. In these sys- tems, the exchange symmetry between identical particles is fixed by their bosonic or fermionic nature, but not between distinguishable particles. Thus, a natural question is this one : How to characterize, both theoreti- cally and experimentally, the global exchange symmetry of the many-body wavefunction in our system ?

In this talk, I will first try to define all these concepts, and to explain how this question is interesting. I will then briefly present the theoreti- cal results obtained during my two first years of PhD, which bring some elements of a response.

**Titre** : Shape and dynamics of semi-conductor islands in hetero-epitaxy

**Encadrement** : Médéric Argentina, Thomas Frisch

**Résumé** : The shapes of nano-crystals have a great interest in science both from fundamental and applied perspectives. The formation, morphology and properties of a nano-crystal (islands) results from the competition between several subtle effects, such as for example temperature, mechanical stresses and surface energy anisotropy.

In this work, I describe the morphology and the dynamic of an elastically strained semi-conductor film in hetero-epitaxy using the framework of continuum elasticity. This island undergoes a Grinfeld instability and their morphology play an important role in the optical properties of quantum dots.

I investigate the formation and the coarsening dynamics of an array of islands in a strained epitaxial semiconductor film using a new analytical method. This model takes into account the presence of the wetting layer, the effect of elasticity and capillarity (surface energy) and it includes surface diffusion. I describe the dynamic of coarsening using both an isotropic and anisotropic form for the surface energy.

Using an analytical method, I describe the shape of an island by solving the equation of elasticity. Secondly using a new dynamical punctual model, I show that the coarsening of two islands can be described analytically. I find that the characteristic time for the coarsening of two islands increases linearly with the distance between the two islands [1]. Furthermore, I find that the coarsening time increases due to the anisotropy of surface energy [2]. These results pave the way for a deeper understanding of coarsening in strained semi-conductor film and for the formation of quantum dots in hetero-epitaxy.

I will also present my future work on the effect of anisotropy of the surface energy using three-dimensional simulation.

[1] Shape and coarsening dynamics of strained islands, G Schifani, T Frisch, M Argentina, J.-N. Aqua, Physical Review E 94 (4), 042808, 2016

[2] Dynamics of anisotropic strained islands, G Schifani, M Argentina, T Frisch, submitted to Physical Review E, 2017.

**Titre** : Synchronization of a network of lasers as coupled oscillators

**Encadrement** : Stéphane Barland

**Résumé** : There are many examples of oscillators in nature : they can range from biological systems like fireflies, heart cells and neurons, to electronic components or physical systems such as lasers. In this study we investigate a system of lasers as a network of coupled oscillators under different kinds of coupling (all to all, nearest neighbors or random) and we study the dynamics of the overall population in order to observe some synchronization pattern between of a part or the whole population.

Before we plunge into the study of the whole system, we analyze the behavior of a single laser with an injected signal. We already know that a laser with an injected signal behaves as an excitable medium, whose phase dynamics can be basically described by the Adler equation. In particular, this system reacts to an input perturbation by producing a spike in intensity, where the control of these spikes was only achieved recently. As a first approximation, the system behaves as a leaky integrate-and-fire type of neuron, so that it will integrate all the incoming pulses and generate a spike only when the integral surpasses a certain threshold. However, a more refined analysis shows that this picture is too simple, as it was soon noticed that whenever the pure phase dynamics reduction ceases to be valid, more complex dynamical phenomena can take place, leading to multipulse excitability and a switch of dynamics from an integrator type of neuron to a resonator one.

We then extend our system of study to that of a network of oscillators, namely a matrix of around 500 Vcsels laser. After a characterization of the threshold and wavelength distribution of the population of lasers, we couple them with different configurations, and we observe some first proof of a synchronization of the population.

Dans la même rubrique :

- Thomas Bickel
- Nicolas Cherroret
- Maureen Clerc
- Fabien Bretenaker
- Alexandre Ponomarenko
- Christian Bracco
- Frédéric Moisy
- Mathieu Bellec
- Christophe Galland
- Carlo Massimo Casciola
- Thomas Frisch
- Erika Di Giuseppe
- Stephane Barland
- Cord Mueller
- Marcus Roper
- Tristan Baumberger
- Stefania Malaguti
- Médéric Argentina
- Lionel Gil
- Valérie Vidal