# Biblio

Summary form only given. Strong light-matter coupling has been recently successfully explored in the GHz and THz [1] range with on-chip platforms. New and intriguing quantum optical phenomena have been predicted in the ultrastrong coupling regime [2], when the coupling strength Ω becomes comparable to the unperturbed frequency of the system ω. We recently proposed a new experimental platform where we couple the inter-Landau level transition of an high-mobility 2DEG to the highly subwavelength photonic mode of an LC meta-atom [3] showing very large Ω/ωc = 0.87. Our system benefits from the collective enhancement of the light-matter coupling which comes from the scaling of the coupling Ω ∝ √n, were n is the number of optically active electrons. In our previous experiments [3] and in literature [4] this number varies from 104-103 electrons per meta-atom. We now engineer a new cavity, resonant at 290 GHz, with an extremely reduced effective mode surface Seff = 4 × 10-14 m2 (FE simulations, CST), yielding large field enhancements above 1500 and allowing to enter the few (\textbackslashtextless;100) electron regime. It consist of a complementary metasurface with two very sharp metallic tips separated by a 60 nm gap (Fig.1(a, b)) on top of a single triangular quantum well. THz-TDS transmission experiments as a function of the applied magnetic field reveal strong anticrossing of the cavity mode with linear cyclotron dispersion. Measurements for arrays of only 12 cavities are reported in Fig.1(c). On the top horizontal axis we report the number of electrons occupying the topmost Landau level as a function of the magnetic field. At the anticrossing field of B=0.73 T we measure approximately 60 electrons ultra strongly coupled (Ω/ω- \textbackslashtextbar\textbackslashtextbar

Tensor decompositions, which are factorizations of multi-dimensional arrays, are becoming increasingly important in large-scale data analytics. A popular tensor decomposition algorithm is Canonical Decomposition/Parallel Factorization using alternating least squares fitting (CP-ALS). Tensors that model real-world applications are often very large and sparse, driving the need for high performance implementations of decomposition algorithms, such as CP-ALS, that can take advantage of many types of compute resources. In this work we present ReFacTo, a heterogeneous distributed tensor decomposition implementation based on DeFacTo, an existing distributed memory approach to CP-ALS. DFacTo reduces the critical routine of CP-ALS to a series of sparse matrix-vector multiplications (SpMVs). ReFacTo leverages GPUs within a cluster via MPI to perform these SpMVs and uses OpenMP threads to parallelize other routines. We evaluate the performance of ReFacTo when using NVIDIA's GPU-based cuSPARSE library and compare it to an alternative implementation that uses Intel's CPU-based Math Kernel Library (MKL) for the SpMV. Furthermore, we provide a discussion of the performance challenges of heterogeneous distributed tensor decompositions based on the results we observed. We find that on up to 32 nodes, the SpMV of ReFacTo when using MKL is up to 6.8× faster than ReFacTo when using cuSPARSE.