Highly non-parabolic strained Ge quantum well for THz ultra-strong light-matter coupling

Summary form only given. Ultra-strong light-matter interactions can be realized in various physical systems and has thus attracted many experimental and theoretical investigations [1-4]. One possible realization is to couple strongly subwavelength split ring resonators (SRR) to the Landau level transition of a two dimensional electron (or hole) gas [2, 3]. In a previous work on parabolic AlGaAs/GaAs QWs, we showed that very high values of the normalized vacuum Rabi frequency Ω/ω = 0.87 can be reached [5]. Strained Ge quantum wells, which are used for the present study, are very appealing as the material exhibits a strong non-parabolicity. The non-parabolicity can be directly observed in THz spectroscopy [6, 7]. The heavy-hole cyclotron resonance spin-splits at a magnetic field of B ~ 4.5 T [6, 7]. A THz split ring resonator array is deposited on top of the sGe QW, as shown in a sample sketch in Fig. 1 d) with the resonances shown in Fig. 1 b). Coupling a LC-resonance at f = 0.4 THz to the single cyclotron resonance at B ~ 1.5 T leads to an anti-crossing, as shown in Fig. 1 a). In Fig. 1 c) a zoom to the LC-resonance with fitted polaritons branches is shown and reveals a normalized coupling ratio of Ω/ω = 0.25. The polaritons branches are fitted with a Hopfield-like Hamiltonian [1, 2] and is in good agreement with the experiment. The dipole-like mode of the resonator couples to the spin-splitted heavy-hole cyclotron resonance at B = 4.5 T and f = 1.25 THz. Multiple polaritons can be observed [8], as shown in Fig. 1 a). A modeling of this multiple oscillator system is done by expanding the Hopfield-like Hamiltonian to include all involved oscillators.