Time-difference of arrival model for spherical microphone arrays and application to direction of arrival estimation

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 (<;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- ||