Cavity modification of magnetoplasmon mode through coupling with intersubband polaritons

TL;DR

This work investigates how a multi-mode MIM cavity coupled to a 2DEG in GaAs quantum wells behaves under a strong magnetic field, revealing that the TM cavity mode hybridizes with the intersubband transition to form ultrastrongly coupled ISB polaritons, while the TE mode remains largely photonic. By introducing a magnetic field, the magnetoplasmon couples to both TM and TE modes with distinct spatial inhomogeneities, leading to a cavity-induced nonlocal Coulomb effect that shifts the magnetoplasmon frequency away from its bare value, effectively breaking translational invariance and violating Kohn’s theorem in the inhomogeneous field regime. The authors develop a classical Maxwell-based model projected onto a three-mode subspace and incorporating the longitudinal Coulomb contribution via Green’s functions to reproduce the observed spectra, including a blue-shift of the MP and spectral broadening of the ISB polariton. They further demonstrate that nonlocality and its strength can be tailored through cavity design and through choosing different QW structures (e.g., parabolic wells), enabling a tunable platform to probe Coulomb interactions in ultrastrongly coupled light–matter systems and to explore cavity-mediated control of electronic excitations.

Abstract

We investigate the coupling of a multi-mode metal-insulator-metal cavity to a two-dimensional electron gas (2DEG) in a quantum well in the presence of a strong magnetic field. The TM cavity mode is strongly hybridized with an intersubband transition of the 2DEG, forming a polaritonic mode in the ultrastrong coupling regime, while the TE mode remains an almost purely cavity mode. The magnetoplasmon excitation emerging from the presence of the magnetic field couples with both TM and TE modes, exhibiting different coupling strengths and levels of spatial field inhomogeneity. While the strong homogeneity of the bare TE mode gives rise to the standard anticrossing of strong coupling, the inhomogeneous polaritonic TM mode is shown to activate an observable Coulombic effect in the spectral response, often referred to as non-locality. This experiment demonstrates a cavity-induced modification of the 2DEG response and offers a new route to probing the effect of Coulomb interactions in ultrastrongly coupled systems via reshaping of their cavity mode profiles.

Figures (6)

• Figure 1: Metal-Insulator-Metal Cavities: a) Schematic showing the sample, indicating multi quantum well layer (red), magnetic (B) field direction, incident THz field and intersubband ($P_{ISB}$) and MP ($P_{MP}$) resonances in the QW. Below: side profile of cavity showing dimensions in $\mathrm{{\mu}m}$. b). Finite-element simulation of the reflectance spectra of cavity in the absence of QW, indicating the TM and TE modes. In the following of the work, both modes couple to the MP resonance; in addition, the TM mode is strongly coupled to the ISB resonance. c) Simulated in-plane electric field in a cavity cross-section at frequencies corresponding to the TM and TE modes. Color map shows electric field magnitude in the y-z plane, white arrows show the in-plane field orientation.
• Figure 2: a) Schematic of experimental reflection THz-TDS set up. THz transmitter and receiver indicated with a 'T' and 'R' respectively. b) Measured reflectance spectra of the QW-loaded cavity as a function of temperature (with no applied magnetic field). The lower polariton branch (LP) is indicated. Below schematic indicating the frequency mismatch between the cavity and ISB resonances. Inset - single spectra slice at 10K. c) Measured THz-TDS transmission spectra of semiconductor heterostructure in the absence of a cavity at 3K. The black dashed line indicates the unperturbed MP frequency given by $\omega_B=eB/m^*$, where $m^* = 0.067m_e$. Inset - single spectra slice at 3T.
• Figure 3: Interaction of cavity modes with MP resonance through magnetic field tuning: a). Measured reflectance spectra at 3K as a function of magnetic field strength. Dashed line indicates the cyclotron frequency, $\omega_B$. TM (LP) indicates the lower polariton branch of the ISB polariton with the TM mode, TE indicates the TE mode. b) Calculated spectra using the formalism in Section \ref{['sec:coulomb']}, accounting for Coulombic interaction. For the theory parameters, see Table \ref{['tab:numerical_params']} in App. \ref{['sec:params']}. Both TM upper (UP) and lower (LP) polaritons are visible, as well as TE mode. c) Close-up of non-smoothed spectra of lower polariton branch. In (a,c), the black dashed line indicates the bare MP resonance as illustrated in Fig.\ref{['fig:fig2']}(c). d) Individual spectra of TM LP for three values of the magnetic field corresponding to $\omega_B < \omega_{TM}$ (purple), $\omega_B = \omega_{TM}$ (orange) and $\omega_B > \omega_{TM}$ (yellow).
• Figure 4: a) Cavity containing parabolic quantum well heterostructure: schematic (above) and simulated cavity fields (below) b) Experimentally measured spectra with magnetic field for cavity in a. Arrows indicate positions of line cuts in (c) for lower polariton (bottom) and upper polariton (top). c) Individual spectra of TM LP (left) and UP (right) for three values of the magnetic field corresponding to the purple, orange and yellow arrows in Fig. 4a. d) Calculated transmission of sample in b. For the theory parameters, see Table \ref{['tab:numerical_params']} in App. \ref{['sec:params']}.
• Figure 5: Schematic of the TM-modes spatial field polarization.