Electrical Modification of Single THz Meta-Atom Ultrastrong Light Matter Interaction

Ultrastrong light matter interaction occurs in a regime where light and matter exchange energy at a rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\Omega_{R})$</tex> comparable to their bare excitation frequencies <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\left(\omega_0\right)$</tex>. This alters the system's dispersion, modifies the ground state, and can have a significant impact on other matter states and their transitions<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1], [2]</sup>. In an attempt to further the understanding of such systems at a fundamental level, we spectroscopically investigate ultrastrong coupling (USC) and tune the coupling strength at the single element level. The platform we chose for this goal is the USC of a single metamaterial unit cell - a meta-atom - and the electronic Landau level transitions in an AlGaAs-GaAs quantum well. The meta-atom itself is a highly subwavelength complementary split ring resonator (cSRR), that hosts a fundamental resonance of around 300 GHz ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda=1 \mathrm{m}\mathrm{m}$</tex> ) with spatial extents of only <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$50 \times 50 \mu \mathrm{m}^2$</tex>. Following a lumped element model, cSRRs can be viewed as an LC circuit, where the capacitive gap will confine the electric field that then interacts with the underlying electron system. In order to excite the single cSRR mode we need to utilize an asymmetric solid immersion lens (aSIL) system. This provides the necessary in-plane momentum modes, usually generated by surrounding meta-atoms in cSRR arrays <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[3]</sup>. To modify the interaction itself, we now apply an electric gate to the 2D-electron gas confined in the quantum well, as done in [4], for an array of cSRRs. This changes the electron density <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n_{e}$</tex>, and therefore has a significant impact on the coupling strength of the interaction, as can be seen from figure 1: THz TDS measurements of the coupled system at different gate biases display very different dispersion behaviors due to their difference in coupling strength. We can infer that the coupling ratio <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\eta=\frac{\Omega_R}{\omega_0}$</tex> decreases from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\eta=0.46$</tex> down to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\eta=0.18$</tex> by fitting the lower polariton branches with the Hopfield model. For the ungated measurement, the electron dispersion used in the model is purely described by the cyclotron frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{c y c}$</tex>. As we increase the gate bias, we observe the formation of a collective magnetoplasmon mode, which dresses the cyclotron dispersion: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tilde{f}^2=f_{c y c}^2+f_{M P}$</tex> and modifies the expected polariton branches accordingly. We further retrieve the upper polariton with increasing bias, as the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 \mu \mathrm{m}$</tex> gap of the utilized cSRR introduces a magnetoplasmon mode in itself<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[5]</sup>, whose frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{max}$</tex> shifts below the upper polariton frequency as we decrease <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n_{e}$</tex>. This is shown in the measurement taken at 4V gate bias. These measurements provide a fabrication platform that enables us to study novel phenomena within the USC regime. We now have optical access to single subwavelength meta-atoms, while also being able to electrically modify them: This offers the possibility to spectroscopically study hybrid light-matter modes in gate-tunable van-der-Waals heterostructures<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[6]</sup>, as well as studying even more strongly confined meta-atom modes coupled to few-electron configurations.