The control of light-matter coupling at the single electron level is currently a subject of growing interest for the development of quantum devices and quantum electrodynamics research. In the THz frequency domain, the wavelength in the 100's µm range makes the interaction of light with nanoscale single emitters difficult. THz resonators are used to enhance the light-matter interaction, and it is often desirable to develop resonators that conciliate high quality factors Q, to promote coherent energy exchange between light and matter, with small mode volumes V for the electromagnetic field spatial concentration.
Two families of THz resonators have emerged as mature technologies. First, Fabry-Perot type resonators based on photonic crystal structures enable high quality factor up to multiple thousands by using low loss dielectric materials (Fig. 1a), but the mode volume is limited by the large THz wavelength due to diffraction limit. A very appealing alternative approach is the use of metallic metamaterials based on micrometer-size LC circuit, for which the mode volume can be reduced to scales multiple orders on magnitude smaller than the wavelength (Fig. 1a). The losses of these systems are however high due to both the losses of metals in the THz spectral range and the "openness" of such planar structures.
To address this problem, Simon Messelot, PhD student, and Dr. Juliette Mangeney, the research group leader from Laboratoire de Physique de l'Ecole Normale Supérieure, proposed a hybrid photonic THz architecture, where a Tamm cavity is ultra-strongly coupled with a LC metasurface. The hybrid modes that emerge then combine the high-quality factor typical for the Tamm cavities with the deep subwavelength confinement provided by the LC resonators.
The relevant research results are published in Photonics Research, Volume. 11, Issue 7, 2023 (Simon Messelot, Solen Coeymans, Jérôme Tignon, Sukhdeep Dhillon, Juliette Mangeney. High Q and sub-wavelength THz electric field confinement in ultrastrongly coupled THz resonators[J]. Photonics Research, 2023, 11(7): 1203)
The spectral properties of the coupled resonators system investigated experimentally show a splitting into two separate hybrid modes (Fig. 1b) and an anti-crossing pattern characteristic of the strong coupling regime between the two resonators, with a resonator-to-resonator coupling constant G∼0.1ω0. Theoretical description of the coupled system using temporal coupled mode theory is presented, showing that the relative "openness" or large radiative coupling rate of usual THz LC metamaterials is turned into a large value of the resonator coupling constant G. This explains how the ultra-strong resonator coupling regime is achievable, but also why this coupling is responsible for a large increase of the quality factor compared to uncoupled metamaterials (Fig. 1c) as radiative coupling is usually the main decay channel in LC metamaterials. Using finite element method simulations, the mode volume properties of the hybrid modes are demonstrated to be only about 2.3 times higher than the deeply sub-wavelength mode volume of the LC metamaterials, despite being coupled to a Tamm cavity of mode volume multiple orders of magnitude higher (Fig. 1d). Using a model based on the contribution to the electric field of the two modes, this result is theoretically understood as a dilution by a factor 2 of photon density in the two resonators.
Fig. 1 (a), Reflection and transmission spectra of the Tamm cavity (orange) and LC metamaterial (black). (b) Transmission spectra of the Tamm cavity-LC metamaterial coupled resonators. The quality factor Q (c) and the Mode Volume (d) of the Tamm cavity-LC metamaterial coupled resonators.
This THz photonic platform offers a large degree of coherence of the light-matter coupling as the cooperativity figure C∝Q/V is enhanced, opening this way a route for the development of single photon THz emitters and detectors and quantum technologies applications.
Future work will couple the metamaterial/Tamm cavity with 2-level systems for cavity quantum electrodynamics in the THz range. It will be possible to limit the in-plane spatial extension of the coupled resonator mode by designing a finite-size disk as the top metallic layer, thus achieving mode confinement in all spatial directions.
