Janine Keller

Terahertz quantum Hall effect for spin-split heavy-hole gases in strained Ge quantum wells

Spin-split heavy-hole gases in strained germanium quantum wells were characterized by polarisation-resolved terahertz time-domain spectroscopy. Effective masses, carrier densities, g-factors, transport lifetimes, mobilities and Rashba spin-splitting energies were evaluated, giving quantitative insights into the influence of strain. The Rashba coefficient was found to lower for samples with higher biaxial compressive strain, while heavy-hole mobilities were enhanced to over

Superradiantly Limited Linewidth in Complementary THz Metamaterials on Si-Membranes

1.5\times {10}^{6}

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

cm2 V−1 s−1 at 3 K. This high mobility enabled the observation of the optical quantum Hall effect at terahertz frequencies for spin-split two-dimensional heavy-holes, evidenced as plateaux in the transverse magnetoconductivity at even and odd filling factors.

THz surface plasmon polariton modes coupled to complementary metasurfaces tuned by inter meta-atom distance

We study complementary double split ring THz resonators fabricated on a 10 mum thin Si-membrane. The linewidths of the fundamental LC-mode and dipolar mode are drastically narrowing with increased resonator spacing. The extracted decay rate of the LC-mode as a function of the resonator density shows a linear dependence, evidencing a collective superradiant effect of the resonator array. Furthermore, we show that a metamaterial can be designed for a low superradiant broadening of the resonance at high resonator densities, i.e. in the metamaterial condition. The use of a thin membrane as a substrate is crucial, since it shifts the THz surface plasmon polaritons modes to much higher frequencies, preventing them to couple to the LC mode and unveiling the superradiant broadening mechanism for a large range of lattice spacings. At higher frequencies, not interfering with the high Q LC-mode, other additional modes, which we ascribe to photonic crystal modes, form in the Si-membrane. We map the angle dependent band structure and show corresponding simulated electric field distributions.

Ultra-strong coupling with spin-split heavyhole cyclotron resonances in sGe QWs (Conference Presentation)

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.

Strong coupling of THz surface plasmon polaritons to complementary metasurfaces (Conference Presentation)

Tailoring the electro-magnetic response of materials beyond naturally occurring properties is possible with the concept of meta-materials [1]. Subwavelength elements which are usually closely spaced can influence the electro-magnetic response and form a fundamental building block of modern optics. The influence of the spacing of the meta-atoms has been investigated for direct meta-materials [2] but only little for complementary metamaterials [3], which are of interest e.g. in ultra-strong coupling experiments at THz frequencies [4]. The effective medium condition is changing due to the presence of a metal sheet in between the meta-atoms which has a very high refractive index in the THz.

Ultrastrong coupling with few (<60) electrons at 280 GHz in single LC nanogap resonators(Conference Presentation)

We study the ultra-strong coupling (USC) of Landau level transitions in strained Germanium quantum wells (sGe QW) to THz metasurfaces. The spin-splitting of the heavy-hole cyclotron resonance in sGe QWs due to the Rashba spin-orbit interaction in magnetic field offers an excellent platform to investigate ultra-strong coupling to a non-parabolic system. THz split ring resonators can be tuned to coincide with the single cyclotron transition (around 0.4 THz and a magnetic field of 1.5 T) or the spin-resolved transitions of the sGe QWs (at 1.3 THz and 4.5 T). Coupling to the single cyclotron yields a normalized USC rate of 25%, resulting from fitting with a Hopfield-like Hamiltonian model. Coupling to two or three cyclotron resonances in sGe QWs lead to the observation of multiple polaritons branches, one polariton branch for each oscillator involved in the system. An adaption of the theory allows to also describe this multiple-oscillator system and to determine the coupling strengths. The different Rabi-splittings for the multiple cyclotrons coupling to the same resonator mode relate to the underlying differences in the material. Furthermore, the visibility of an additional transition, possibly a light hole transition with very low carrier density, is strongly enhanced due to the coupling to the LC-resonance with a normalized strong coupling ratio of 4.7%. Future perspectives include controlling spin-flip transitions in USC and studying the impact of non-parabolicity on the ultra-strong coupling physics.

Few-Electron Ultrastrong Light-Matter Coupling at 300 GHz with Nanogap Hybrid LC Microcavities

We study the transmission of complementary THz split ring resonator (cSRR) arrays with THz time domain spectroscopy. Utilizing complementary THz metasurfaces and, varying the inter meta-atom separation, a regime of resonant coupling to surface plasmon polaritons (SPPs) is entered. The effective medium condition valid for the direct metasurface is not applicable anymore in the complementary case because of the high THz dielectric constant of gold. We observe a normalized strong coupling of 3.5% to the lattice SPP mode when tuned into resonance with the LC-mode of the cSRR at a frequency of 1.07 THz. The lattice constant is varied from 40 um to 160 um. Finite element simulations with CST MWS show the characteristic field distribution of the two modes and the intermixing of the LC-mode with the SPP-mode very clearly. Analytical modeling with a simple two oscillator model well describes the coupling. An effective relative permittivity of 11.6 for the coupled system was extracted. For broader linewidths, an apparent modulation of the effective Quality-factor can be observed which is of crucial importance for designing metasurfaces for applications. Measurements of the broader lambda/2 mode in orthogonal excitation direction reveal instead a Fano-like interaction. Rectangular array configuration reveal the excitation direction of the SPP modes being along the polarization of the exciting THz pulse. We demonstrate that the understanding of the SPP modes is fundamental for research and applications in which the metasurface has to be designed for special needs.

Large-area gate-tunable terahertz plasmonic metasurfaces employing graphene based structures

Strong light-matter coupling lies at the heart of quantum optics and recently has been successfully explored also in the GHz and THz range. New, intriguing quantum optical phenomena have been predicted in the ultrastrong coupling regime, when the coupling strength Omega becomes comparable to the unperturbed frequency of the system omega_c. We recently proposed a new experimental platform where the physics of the ultrastrong coupling can be investigated at GHz-THz frequencies. We couple the inter-Landau level transition of an high-mobility 2 dimensional electron gas (2DEG) to the subwavelength photonic mode of an LC meta-atom. Our system benefits from the collective enhancement of the light-matter coupling which comes from the scaling of the coupling constant Omega with the square root of the number of electrons in the last Landau level. In our previous experiments and in literature this number varies from 10000-1000 electrons per resonator. Here we present ultrastrong coupling between a high-mobility 2DEG (mu=2.3X 10^6 cm^2/Vs) and an extremely subwavelength hybrid-LC resonator ensemble (11 resonators) with an highly reduced effective mode volume V_eff=4 x 10^-19 m^3=4 x 10^(-10) lambda^3 at a frequency of 300 GHz. The number of optically active electrons is given by the flux quantum multiplied by the effective resonator area and is proportional to the magnetic field. At the anticrossing field of B=0.73 T we measure less than 80 electrons ultrastrongly coupled to the resonator with a normalized coupling ratio Omega/omega_c=0.35. This experiment paves the way towards the study of ultrastrong coupling physics in the regime of quantum non-linearities.

Coupling Surface Plasmon Polariton Modes to Complementary THz Metasurfaces Tuned by Inter Meta-Atom Distance

Ultrastrong light-matter coupling allows the exploration of new states of matter through the interaction of strong vacuum fields with huge electronic dipoles. By using hybrid dipole antenna-split ring resonator-based cavities with extremely small effective mode volumes Veff/λ03 ≃ 6 × 10-10 and surfaces Seff/λ02 ≃ 3.5 × 10-7, we probe the ultrastrong light-matter coupling at 300 GHz to less than 100 electrons located in the last occupied Landau level of a high mobility two-dimensional electron gas, measuring a normalized coupling ratio of ΩR/ωc = 0.36. Effects of the extremely reduced cavity dimensions are observed as the light-matter coupled system is better described by an effective mass heavier than the uncoupled one. These results open the way to ultrastrong coupling at the single-electron level in two-dimensional electron systems.