Periodic Reporting for period 2 - MADAME (Mesoscopic lAttices of ryDbergs for quAntuM thErmalization) Reporting period: 2018-11-01 to 2019-10-31 Summary of the context and overall objectives of the project "The advent of laser cooling and manipulation techniques at the single atom level has opened the door to the realization of controllable, idealized many-body systems, which in many cases constitute physical realization of toy-models. A successful and popular approach is to engineer cold dilute gases of mesoscopic size whose atoms can be spatially ordered with light beams to mimic condensed matter systems. Recreating the essence of a complex quantum system in a simpler quantum system to let nature ""compute"" the output is the basis of quantum simulation. This approach is extremely beneficial for systems of more than a few interacting atoms where in many cases no ab initio calculation is possible, even in simplified models. In this context much effort has been put into a variety of problems that are intractable by classical computation (e.g. quantum magnetism, quantum phase transition, frustrated systems, spin glasses, superconductivity and topological phases). One of the most intriguing open question in quantum many-body physics is how and under what circumstances a system evolves into thermal equilibrium. This fundamentally important problem has very recently received a surge of attention and the approach to equilibrium (or the absence of it) is the subject of a number of current experimental and theoretical efforts.The aim of this proposal is therefore to answer: under what conditions does a quantum system thermalize?This broad question is divided here into two aspects, each focused on a precise goal within the Fellowship. The outgoing phase, corresponding to the first period reported here, addressed the compelling phenomenon of thermalizationin in the presence of a strong coupling to the environment. It was hosted by Prof. Porto, from the Laser Cooling and Trapping (LCT) group led by W.D. Phillips at the Joint Quantum Institute (JQI), Gaithersburg/College Park, Maryland, USA. The JQI is an institution joining the National Institute for Standards and Technology (NIST) and the University of Maryland (UMD) and research was conducted at both sites. The group owns a powerful quantum simulation apparatus consisting of a double-well optical lattice for Rubidium87 where single atoms can be localized to lattice sites. This forms an excellent experimental platform for our quantum dissipative studies. We started with strongly-interacting, dissipative Rydberg atoms pinned to the optical lattice and excited for many Rydberg lifetimes, so as to study the long time limit of an initially-ordered, strongly interacting dissipative system. We discovered a spontaneous mechanism of collective dephasing, valid whenever many rydberg atoms interact strongly. This is an important contribution for coherent control, because it imposes an upper limit on the size of quantum simulators based on rydberg interactions, and explains the difficulties observed around the world with dense samples.This Grant included a short post-doctoral internship in the team of Tilman Esslinger at the Eidgenössische Technische Hochschule Zürich (ETHZ), Switzerland, where I went from April to June 2017. This internship allowed me to acquire the skills necessary to add a new component to the JQI experiment: Floquet engineering. With it, we found a new type instability based on non-equilibrium collective dynamics, which amounts to heating the atoms to infinite temperature.In the incoming phase at the Laboratoire Charles Fabry, Palaiseau, France, we worked on a quantum simulation experiment based on a small number of individually trapped rydberg atoms. We developed a new laser trapping scheme for rydberg states, and studied non-trivial topological states with few atoms.In total, this 3-years MSCA grant produced 5 papers in international refereed journals and as many conference proceedings." Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far Before the Action begun, we observed spectroscopic anomalies during the initial tests. We investigated this anomaly and found it to be a high-impact, fundamental mechanism intrinsic to large ensembles of Rydberg atoms: Due to spontaneous emission and ambient blackbody radiation, an initially homogeneous ensemble of Rydberg atoms has a high probability to populate opposite-parity states. These new states interact strongly with the rest of the sample, and act as impurities which dephase the whole atomic ensemble. This makes coherent manipulations impossible, and posseses interesting avalanche-like dynamics under continuous excitation. A large part of our time was dedicated to the detailed study of this unexpected phenomenon. It is an important object of study, but which prevents further Rydberg experiments under the conditions used at UMD. This pushed us toward a new type of system for the study of thermalization in open quantum systems. We then switched direction in favor of the new system, which does not rely on Rydberg atoms. We used ground-state atoms coupled to the environment via an external drive. The drive consists in periodically modulating the optical lattice position (“shaking” the lattice). This opens the question of heating, as energy can be absorbed from the drive, which is crucial for the novel field of Floquet engineering. Theory predicts heating to infinite temperature under most (but not all) conditions, and the mechanism is not completely understood. In particular, recent theoretical predictions dating from about the Action’s starting date expect the excitation spectrum of a condensate under periodic driving to become unstable, leading to yet-unobserved parametric instabilities in bosonic Floquet systems. We directed our research towards understanding the heating mechanism and experimentally testing this prediction. This required the innovation of new experimental techniques for precise shaking and heating rate measurements, and resulted in several articles (1 published, 1 under review).In the second period, small systems were considered. We first developed new tools for controlling individual rydberg atoms, then applied them to the study of non-trivial artificial systems supporting intrinsic spin-orbit coupling. This resulted in 2 articles (1 accepted, 1 under review). Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) In both of the two systems studied, important progress was made and novel physics was experimentally demonstrated. On the many-Rydberg system, the avalanche dephasing was discovered which, for the first time, explains worldwide difficulties for large-scale Rydberg dressing. We studied the mechanism in depth and explored ways to circumvent it, which resulted in 3 publications. On the Floquet system, we experimentally observed, for the first time, a recent prediction concerning a previously unsuspected instability. This instability is quantum many-body at its core, since based upon collective excitations feeding from the drive energy. These results represent genuinely new insights into collective quantum behavior driven by interactions and a coupling to an environment.The results from the second (IOGS) part are important, both from an application and fundamental perspective. The first expands the quantum simulation toolbox, which is an important strategic point for future quantum technologies. The second achievement is fundamentally important since intrinsic spin-orbit coupling is naturally present in complex quantum matter, and being able to re-create it in a controlled artificial setting is a crucial step for future quantum engineering of robust complex states, as well as our fundamental understanding. An artist's rendering of a contaminant Rydberg atom in a lattice of rubidium. Credit: S. Kelley/JQI
