### Next seminar : Séminaire du LPTMS : Jacqueline Bloch (C2N)

##### Tuesday, January 25 2022 at 11:00:00

## Using cavity polariton lattices as analog simulators

### Jacqueline Bloch (Center for Nanoscience **and Nanotechnology**)

Hybrid seminar: onsite + zoom.
Zoom link: https://cnrs.zoom.us/j/97201630000?pwd=MlhLSFBtUkJQcXZDdXZHWkQrRm9hUT09
Meeting ID: 972 0163 0000
Passcode: 36PnNs
An analog simulator is a synthetic physical system, which emulates in a controlled way a physical problem. You can get answers about the physical problem by directly performing experiments on the simulator. This approach is particularly relevant for quantum problems where computation times grows exponentially with the system’s size. In the present seminar, I will present the polariton platform and explain how it is relevant for analog simulation of many interesting open problems.
Cavity polaritons are hybrid exciton-photon quasi-particle emerging from the strong coupling regime between photons confined in an optical cavity and excitons confined in quantum wells. They present physical properties reflecting their mixed nature. From the photon part, they inherit a small effective mass and can be confined in lattices with typical dimensions of the order of a few microns. Their excitonic part endows them with inter-particle interactions resulting in a giant Kerr non linearity. Moreover the system is intrinsically open and out of equilibrium because photons constantly leak out from the cavity. Cavity polaritons have been shown to present fascinating properties such as Bose Einstein condensation at elevated temperature, superfluidity, multistability etc [1].
In the present talk, I will explain how the polariton plateform is particularly suitable to realize analog simulation of open complex systems and explore fundamental physical phenomena.
I will describe a few recent results of our group:
- How do wave localize in exotic quasi-crystals and how fractality does develop? This physics can be emulated with polariton lattices [2]
- Polariton condensates are out of equilibrium and their phase dynamics has been predicted to obey the celebrated Kardar Parisi Zhang (KPZ) equation. We have been able to reveal experimentally universal KPZ scaling laws in the first order coherence of a 1D polariton condensate.[3]
- Polariton lattices are also very interesting for the investigation of topological photonics. In particular, the ability to drive the system with controlled phases opens a new paradigm for non-linear topological photonics. [4]

*Quantum fluids of light*, Rev. Mod. Phys.

**85**, 299 (2013) [2] V. Goblot et al. Emergence of criticality through a cascade of delocalization transitions in quasiperiodic chains, Nature Physics 16, 832 (2020) [3] Q. Fontaine et al., Observation of KPZ universal scaling in a one-dimensional polariton condensate, arXiv:2112.09550 (2021) [4] N. Pernet et al., N. Pernet, et al.,

*Topological gap solitons in a 1D non-Hermitian lattice*, arXiv:2101.01038 (to appear 2022)

### Last Highlight : A short perspective on Giorgio Parisi’s achievements

Giorgio Parisi belongs to a rare class of universal scientists. His large breadth of interests and creative intuition has led to a wealth of ideas in remote areas of Science. Over more than 50 years, he made seminal contributions to Quantum Field Theory, Fluid Dynamics, the construction of Supercomputers, Numerical Simulations, Theoretical Biology, Collective Animal Motion and more. The Altarelli-Parisi equations in QCD, the Kardar-Parisi-Zhang interface growth equations, the Multifractal nature of Turbulence, the mechanism of Stochastic Resonance, the pioneering study of the dynamics of Starling Flocks are just but a few of his fundamental contributions to science. It is however in the field of Statistical Physics and Complex and Disordered Systems that he obtained his most original results, contributing to considerably widen the scope of the discipline. Parisi's journey in the physics of disordered systems began towards the end of the theoretical physics golden decade of the 1970’s, on his way back to Rome, after two prolific years in France as a visiting scientist at IHES and Ens in Paris. At that time, condensed matter theoreticians like Phil Anderson, Sam Edwards, David Thouless, to cite a few, were interested in the properties of strange disordered magnets called ‘Spin Glasses’. These are systems of magnetic moments (or spins) in interactions where the strength, as well as the sign of couplings between them, are effectively random. The system is said to be `frustrated’: it is impossible to find a configuration of the spins minimizing all the terms of the energy at the same time. Theoretically, Edwards and Anderson had proposed the ‘replica trick’, where the disordered interactions could be traded in favor of perfectly ferromagnetic interactions between n replicas of the original system, with the caveat that a strange limit of the number n tending to zero had to be taken at the end of the computation. Early attempts by David Sharrington and Scott Kirkpatrick to use replicas on a solvable model of a Spin Glass led to inconsistencies. Parisi found the exact solution of the Sherrington-Kirkpatrick spin glass in 1979, proposing an astonishing symmetry breaking pattern of the permutation group of n elements in the limit n → 0. The use of a daringly unconventional mathematical formalism together with difficulties of interpretations of the Parisi Replica Symmetry Breaking, later called RSB by the practitioners, generated a lot of enthusiasm, but also some skepticism in the community. After a few years, in the first half of the 1980s, the meaning of RSB was clarified, mainly by Parisi and his collaborators (Marc Mézard, Gérard Toulouse, Nicolas Sourlas, Miguel Virasoro), and independently by Bernard Derrida. Replica Symmetry Breaking was encoding for a glassy phase, with many possible equilibria organized in a hierarchical tree of states. Moreover, Mézard Parisi and Virasoro were able to recover the replica results by a more conventional physical ansatz called Cavity Method. In trying to explain the freezing properties of disordered magnets, a new deep organization of matter emerged. Paraphrasing N. Sourlas, Parisi’s RSB became the third known pattern of phase transition after Landau-Wilson symmetry breaking and Berezinskii-Kosterlitz-Thouless topological transitions. The mathematization of these results has required more than 25 years, culminating in the work of Francesco Guerra and Michel Talagrand in the years 2000.

But this is just the beginning of a long story that is lasting till today. The high interdisciplinary potential of the theoretical methods invented by Parisi in the new field of Complex Systems soon became evident: Statistical Physics was enlarging its scope beyond the premises of Condensed Matter Physics, to study Collective Phenomena in Biology, Neurosciences, Computer Science, Sociology, Economics Mathematics and more. In this change of perspective, the results of Spin Glass theory remain as one, perhaps the, most profound methodological tool. Strong and lasting ties ensued between Rome and Paris, that led the foundation of a school which has a deep influence in the landscape of the research in statistical physics in the Paris area. The LPTMS is proud to be part of these developments, and congratulates Giorgio Parisi for his beautiful prize.

Silvio Franz et Christophe Texier pour le graphisme, Oct 5 2021