Ultracold atoms have emerged as unique tools to study strongly correlated quantum systems. 50 years ago, an intriguing prediction was made by Fulde, Ferrell, Larkin and Ovchinnikov (FFLO) for a superconductor in a magnetic field with imbalanced electron spin populations. They predicted the existence of a superfluid phase where the order parameter is inhomogeneous and oscillates spatially across the sample. In SPIFBOX, we aim at producing and studying this FFLO phase using spin-imbalanced Fermi gases in a box-shaped potential where the density of atoms is uniform. The experimental part of the project will be realized at ENS with two experimental setups using lithium isotopes. The first one is already operational and the flat bottom potential is realized in 3 dimensions by the repulsive mean field of a Bose-Einstein condensate of lithium 7 mixed with the spin-imbalanced Fermi superfluid in an harmonic trap. The second setup is a new generation experiment with much greater flexibility where the flat bottom potential is realized optically using a digital micro-mirror device (DMD). This new machine will enable us to search for the FFLO phase in reduced dimensions for which theoretical predictions and numerical simulations predict a much wider domain of stability for the FFLO state in the phase diagram. The construction of this setup has already started and the SPIFBOX funding will be used to bring it to completion. The theoretical part of the project will be conducted by Giuliano Orso from Paris Diderot University, a specialist of spin imbalanced Fermi systems, and one post-doc that we wish to recruit with SPIFBOX funding. The theory team will determine the optimal conditions for producing the FFLO phase. In particular, exact solutions exist when the fermions live in one dimension for which the existence of the FFLO phase is clearly established. They will also construct the phase diagram when the Fermi gas is mixed with a Bose gas and they will explore the possible stabilization of the FFLO phase in two and three dimensions by controlling the Fermi-Bose interaction strength. Numerical simulations using DMRG and Monte-Carlo methods will be compared to the ENS experimental observations. With the powerful tools of atomic physics, in SPIFBOX we gather together the best experimental conditions for the observation of the FFLO state: no orbital coupling, no disorder, low dimensional samples, and, most importantly, direct spin-resolved imaging of the associated spatial modulation of the atomic cloud. We hope that by solving one of the most outstanding quantum many-body problems, the outcome of SPIFBOX will stimulate new theoretical and experimental concepts at the interface with condensed matter systems. Ultimately this advanced understanding of quantum matter will help to design new materials with unprecedented properties.

I will study out-of-equilibrium dynamics of two-dimensional Bose gases. I will create samples with spatial variations of density, temperature or internal state and investigate their relaxation towards an equilibrium or metastable state. The two main breakthroughs of this project will consist in the experimental realization of (i) quantum transport of bosons through a single-mode channel. (ii) diffusion of a few single-particle impurities in a bath of atoms in another internal state, realizing a quantum Brownian motion experiment. This project is based on an experimental setup that I have recently developed in my team and which is fully operational today. This platform allows us to confine Bose gases in a light sheet restricting the motion of the atoms to a two-dimensional plane and to limit their in-plane motion to an arbitrary-shaped potential. Such a setup, allowing high resolution tailoring of optical potentials is rather original in our field and will offer us a large flexibility to investigate out-of-equilibrium dynamics. A first line of research will be devoted to transport properties of an atomic channel. We will start our work two-dimensional channels of a few micron width, directly available in our setup and hosting many conducting modes. We will study particle and heat transport and characterize the influence of disorder in the channel, which is expected to modify much more strongly the behavior of the normal part with respect to the superfluid part. Then, we will decrease the thickness of the channel to enter the single mode regime and where dramatic effects, like the quantification of heat of conductance, are expected. A second line of research will focus on spin dynamics. The rubidium atom that we use has several internal hyperfine states in the electronic ground state. These states can be easily coupled thanks to a microwave field or a two-photon Raman transition, the latter easily allowing spatial resolution. We will focus on binary mixtures. For instance, we will realize quenches by abruptly superimposing two immiscible internal states and monitor their relaxation, a situation for which we already obtained preliminary results. Then, we will move to the study of the dynamics of an impurity in a bath of atoms in another internal state with tunable interaction. We will develop new tools to measure the motion of a few individual particles with sub-micron resolution. By doing so, we will achieve an experimental configuration where we will observe the diffusive behavior of quantum Brownian particles. A superdiffusive behavior is expected in this regime, which goes beyond the memory-less Markov regime for diffusion. The duration of the project will be of 48 months. A large part of the proposed objectives can be directly tackled in our team. In addition, we will develop new tools (optical aberration correction techniques to achieve single mode channels, spatially resolved Raman coupling with tunable momentum transfer, single-atom fluorescence imaging) to achieve original regimes that goes beyond the current state-of-the-art.

Light has been since the beginning of the XXth century described as a gas of photon, with limited interactions. Since the recent development in semiconductor fabrication, this picture tends to be overcome, to welcome a new analogy connecting light to fluid. Nowadays the interaction between photons can be engineered such as the light behaviour inside nano-structured devices mimic a fluid system. One of the most emblematic system described in this new paradigm is polaritonic devices. Exciton-polariton are quasi–particle rising form the strong coupling between cavity electromagnetic modes and a quantum well exciton transition. These particles half-way between light and matter were observed in different quantum state of matter such as superfluidity and Bose-Einstein condensate paving the way for correlated fluid of light studies. The dynamic acting appears to be dominated by an interplay of strong dissipation and non-linear properties leading to rich features such as optical bistability, cavity soliton or other typical properties of non-linear dynamics. The conjonction of these outstanding features leads to unprecedented physics such as out-of-equilibrium quantum fluids, which remains mostly unexplored. Simon Pigeon and the Quantum Optic Group at Laboratoire Kastler Brossel (Université Pierre et Marie Curie, École Normale Supérieure and CNRS) are world-recognised experts of this important field. In this project, we propose significant advances on the understanding of out-of-equilibrium quantum fluids. Moreover based on Simon Pigeon expertise, an insight of the corresponding physics will be given on through hydrodynamic and thermodynamic approaches. — The first research line is dedicated to the in-depth study of polariton fluids properties. Focusing on the spin properties and the topological excitations taking place in such fluid, we expect to provide genuine progresses in the understanding of polariton systems and the link to other non-linear optical devices presenting similar dynamics. ?— The second component of the C-FLigHT project is to use polariton systems to simulate quantum states of matter. Thanks to the great controllability of these systems, polariton quantum fluids can provide an efficient simulator of phenomena such as Anderson localisation or Mott-Superfluid transition. ?— The third axis of C-FLigHT relies on recent advances in the emerging field of Quantum Thermodynamics. By studying microcavity polaritons from an innovative thermodynamics of open-quantum-systems perspective we expect to gain a finer understanding of these system dynamics. The goal is to describe thermodynamic phenomenon and to explore universal mechanism such as Kibble-Zurek mechanism in the general context of quantum optics and solid-state physics using polariton devices as a benchmark. ? C-FLigHT is expected to simultaneously impact two separated field of physics building a bridge in between. Quantum gas physics will gain on this project through experimenting quantum state of matter in unexplored situation, while semiconductor optical devices sciences will profit for an original insight on there devices operating behaviour. Applied and fundamental outcomes are expected from C-FLigHT, paving the way to the exploration of correlated fluid of light.

Terahertz research has undergone breakthroughs over the past 20 years, both for fundamental science and industrial applications. Despite extremely promising applications, THz radiation is still a challenging spectral domain in need of technological and conceptual advances. The main aim of the HYPSTER proposal is to investigate innovative 3D lens-less techniques, to extract amplitude and phase information, with performances well beyond the current state-of-the-art in real time. To this end, we will transfer to the THz range, wavefront concepts and tools developed in the optical domain. Potential applications range from non-destructive testing of plastics, composites, electronic devices, and ceramics up to the biomedical field. To do so, the objectives of the HYPSTER project are to perform multispectral THz holography and ptychographic imaging systems to improve phase retrieval and surpass the resolution limit. We will use state of the art real-time camera illuminated by a high power multispectral QCL source. The proposal aims to create and understand 3D diffractive imaging thanks to the leadership of 2 academic experienced research institutes gathered in an interdisciplinary and complementary consortium. The success of the research program relies on shared experience at a high level of specialization from these well-established internationally renowned laboratories.

The goal of the project is to study the potential of optical semiconductor microcavities as THz detectors and emitters. We propose here to explore the possibility of detecting and generating THz radiation in semiconductor microcavities by using THz radiative transitions between polaritonic states. Polariton physics is now well known and especially well mastered by the three project partners (LKB, LPA, LPN). The investigated polariton states are separated in energy by typically a few meV (i.e. in the THz range). If the THz radiative transitions between the polariton branches are normally forbidden by the selection rules, different theoretical proposals open the way for engineering the band structure to allow the absorption or radiative emission of THz photons. A particularly interesting aspect of this project lies in using the peculiar properties of polaritons to avoid the low temperature constraint usually required by thermodynamics principles. The objective of the project is the realization of THz detectors operating at liquid nitrogen temperature with high detectivity in compact geometries, compatible with the development of semiconductor based devices. Conversely and in similar schemes, we will study the potential of such semiconductor microcavities for THz emission by using the bosonic stimulation regime (polariton lasing).. Different strategies proposed by the theory to allow THz radiative transitions will be implemented in the design and fabrication of a new family of semiconductor microcavities and micropillars. These structures will then be studied in the field of optics and THz using methods controlled by three partners: - LPA brings its expertise and experimental facilities in the field of THz spectroscopy, optical spectroscopy and theory - LKB brings its expertise and experimental facilities in the optical study of polaritons under "two-photon" and non-linear excitation of the polariton states - LPN provides expertise on the sample fabrication as well as its expertise on polariton lasers.