Gate-tunable single terahertz meta-atom ultrastrong light-matter coupling

TL;DR

This work demonstrates in-situ gate-tunable ultrastrong coupling between a single terahertz meta-atom (cSRR) and a GaAs 2DEG. By applying an inhomogeneous gate bias, the electron gas is laterally confined beneath the resonator, permitting control over the effective electron number and thus the light-matter coupling strength, which evolves from $\eta \approx 0.46$ toward $\eta \approx 0.18$ as confinement tightens. The experiments reveal gate-induced shifts in the Landau-polariton dispersion, the emergence of a gate-modulated mode (M1) associated with 2DEG confinement, and standing plasma waves whose behavior aligns with a confinement-dependent Hopfield-like description, highlighting the potential for electrically reconfigurable THz quantum electrodynamics in semiconductor heterostructures. These results open avenues for gate-tunable ultrastrong coupling in deeply sub-wavelength platforms and suggest routes toward tailoring light-matter interactions in van der Waals and other low-dimensional systems.

Abstract

We study the electrical tunability of ultrastrong light-matter interactions between a single terahertz circuit-based complementary split ring resonator (cSRR) and a two-dimensional electron gas. For this purpose, transmission spectroscopy measurements are performed under the influence of a strong magnetic field at different set points for the electric gate bias. The resulting Landau polariton dispersion depends on the applied electric bias, as the gating technique confines the electrons in-plane down to extremely sub-wavelength dimensions as small as d = 410 nm. This confinement allows for the excitation of standing plasma waves at zero magnetic field and an effective tunability of the electron number coupled to the THz resonator. This allows the normalized coupling strength to be tuned in-situ from $η$ = 0.46 down to $η$ = 0.18. This is the first demonstration of terahertz far-field spectroscopy of an electrically tunable interaction between a single terahertz resonator and electrons in a GaAs quantum well heterostructure.

Figures (4)

• Figure 1: a) Schematic of the sample mounted with aSIL system. b) An optical image of the cSRR. c) Schematic cut view of the sample across the cSRR gap, overlaid with the electric field confinement at zero electric bias (simulated using FEM). d) Simulated DC field distribution (equipotential lines at $\Phi = 100 \,\textrm{mV}$ indicated with dotted lines) and lateral narrowing of the 2DEG strip due to an increase in DC bias. The aspect ratio between the x and y axis in the schematic panels of c) and d) is set to 1:2 to improve visibility of the thin layers. The computed change in the electron density for increasing potential is shown in the bottom of panel d), according to a Thomas-Fermi distribution. To show the asymptotic values for all cases, the y-axis is squeezed in the right side of the plot.
• Figure 2: THz TDS measurements of the single cSRR sample shown in Figure \ref{['fig:sample_schematic']}, performed at $3\, \mathrm{K}$ without gate bias. The solid purple curve represents the fitted lower polariton branch according to the Hopfield model, while the dotted line represents the expected upper polariton dispersion. We observe broadened transmission instead of a localized branch due to plasmonic broadening. The black line shows the bare cyclotron dispersion corresponding to an effective mass of $m_{\text{eff}} = 0.07 \, m_{\text{e}}$.
• Figure 3: a)-c): THz TDS measurements of the single cSRR shown in Figure \ref{['fig:sample_schematic']}, performed at $3\, \mathrm{K}$ for varying back-gate biases. The purple curve represents the fitted lower polariton branch according to the Hopfield model (Eq. \ref{['eq:hopfield']}). As discussed above, we do not expect to observe an upper polariton branch due to plasmonic broadening, hence why the UP fit curves are omitted. d)-f): Simulations of the sample with varying depletion lengths, overlaid with the transmission peaks extracted from the measured data for comparison.
• Figure 4: Plasma excitations of the bare 2DEG. a-c) Normalized $x$-,$y$- and in-plane component of the simulated electric field for a 2DEG confined to the cSRR geometry without the resonator plane. The cutoff of the cSRR-shaped 2DEG is depicted with a black line. Represented at 200GHz and a confinement width of d = 0.41μ m in the central gap. d) The resulting dependence of the frequency on the in-plane wavevector, as inferred from the field distribution. Overlaid with a square-root fit for comparison.