The development of quantum simulation lacks compact on-chip scalable platforms. The recent demonstrations of polariton lattices in semiconductor microcavities, in combination with their extraordinary nonlinearities, place polaritons as one of the most promising candidates to achieve this goal. The aim of the InterPol project is to implement polariton lattices in semiconductor microcavities as a photonic-based solid-state platform for quantum simulations. The polariton platform will allow for the engineering of the lattice geometry and site-to-site hoping, state preparation and detection in individual sites, sensitivity to magnetic fields, and scalability due to the low value of disorder. The driven-dissipative nature of the system opens the exciting possibility of studying out-of-equilibrium strongly correlated phases, but it also calls for new theoretical methods. We combine the expertise in semiconductor physics and technology of four experimental groups and the input of three theoretical groups to push polariton nonlinearities into the strongly interacting regime. We plan on implementing the first polariton simulators by studying quantum correlations and the topological phases in flat bands and in the presence of artificial gauge field acting on polaritons in 1D and 2D lattice geometries, both experimentally and theoretically. This project will provide the first quantum simulation platform using scalable lattices at optical wavelengths.

In the following you can see how each group in the consortium is contributing towards this goal.

**University College London (UCL)**

The role of the UCL partner is to coordinate the activities of the consortium, provide theory support to the experiments and develop new numerical methods to model the strongly correlated many-body states of polariton-lattices.

In the basic operation of an exciton-polariton system, photons are pumped into the polariton lattice, they form light-matter excitations which can interact and after some time the photons escape into the environment. The theoretical techniques used must therefore account for the drive, interaction and dissipation inherent in exciton-polariton lattices. For weakly interacting polaritons this can be achieved by using so called semi-classical methods, however, having strong interactions between polartions will cause these methods to fail. The goal of UCL’s contribution to the InterPol project is therefore to develop new numerical techniques which can account for strongly correlated – “fully quantum” – many-body systems in driven-dissipative environments.

The investigations will focus on techniques based on tensor networks. The standard techniques for these types of systems become much too complex to solve for only a modest number of interacting particles and are therefore limited to small lattice systems. Tensor network methods overcome some of these limitations by imposing a limit on the amount of quantum entanglement present in the system. In practice it is found that very many systems of interest can be well described within this framework.

With these numerical tools in hand, the UCL group will support the efforts of experimentalists in achieving strongly correlated states of exciton-polaritons by providing verification and interpretation of experimental signatures as well in the testing of experimental designs across parameter regimes.

**University of Oxford**

The role of the Oxford partner within InterPol is to fabricate micromirrors that will facilitate the creation of 1-D and 2-D polariton lattices using open microcavity devices. We fabricate the mirrors use focused ion beam milling to machine arrays of concave surfaces into a planar substrate, followed by coating with high reflectivity dielectric mirrors. Our research effort is focused on fabricating arrays in which the depth of each concave mirror is the same to within the required tolerance of less than one nanometre.

The image below shows a scanning electron micrograph of an array of concave surfaces milled into a substrate prior to mirror coating.

**Paul Drude Institute (PDI)**

The subproject at the Paul Drude Institute (PDI) aims at the production and research of polarite gratings in semiconductor microcavities suitable for quantum simulations. For this purpose, we will use static lattices produced by means of a multi-stage molecular beam epitaxy process. The growth process will be optimized for the production of micrometer-sized polariton traps arranged in a two-dimensional lattice, which can trap individual polaritons in each lattice site. In addition, tunable gratings produced by the modulation of the lattice by surface acoustic waves (SAWs) will be investigated.

**Institute of Physics, Warsaw**

The role of the Warsaw partner (Institute of Physics, Polish Academy of Sciences) is twofold: providing accurate numerical simulations of the experiments, with the emphasis on topological and quantum phases, and the development of new theoretical methods for dissipative quantum many body systems.

Warsaw node is developing tools for investigating many-body states, with particular emphasis on the so-called semi-classical methods. These methods, although not able to fully grasp the complexity of many body states, can be successfully used to describe systems which are on the limit between single- and many-body physics. The advantage of using these methods is the much-reduced level of computational complexity with respect to fully quantum methods, and the possibility to describe systems with a large number of particles. We compare these two classes of methods which will provide us with the knowledge of the limits of applicability of semi-classical methods.

The theoretical support of Warsaw partner consists of both the interpretation of the experimental results in view of the theoretical concepts as well as numerical simulations that will confirm and verify the underlying assumptions. Furthermore, modeling will allow for proposing a most appropriate design, experimental conditions, and system parameters that will allow for a clear observation of many-body quantum and topological effects.