THz ultra-strong light-matter coupling up to 200K with continuously-graded parabolic quantum wells

TL;DR

This work demonstrates ultra-strong light-matter coupling in terahertz intersubband polaritons by using continuously graded parabolic quantum wells, overcoming the low-frequency and thermal limits of square wells. By embedding the active region in both microcavity and deeply sub-wavelength LC resonators, the authors achieve a Rabi frequency of about $0.25\,\text{THz}$ with a coupling ratio $\eta\approx 0.12$, persisting up to $200\,\text{K}$ and featuring narrow polariton linewidths that improve coherence. The sub-wavelength devices enable USC with roughly $3{,}000$ electrons per resonator, suggesting a route toward few-electron polaritons and ultrafast cavity modulation. These results establish a scalable THz platform for exploring quantum vacuum radiation phenomena and non-classical light generation at elevated temperatures.

Abstract

Continuously graded parabolic quantum wells with excellent optical performances are used to overcome the low-frequency and thermal limitations of square quantum wells at terahertz frequencies. The formation of microcavity intersubband polaritons at frequencies as low as 1.8 THz is demonstrated, with a sustained ultra-strong coupling regime up to a temperature of 200K. It is additionally shown that the ultra-strong coupling regime is preserved when the active region is embedded in sub-wavelength resonators, with an estimated relative strength $η= Ω_R / ω_0 = 0.12$. This represents an important milestone for future studies of quantum vacuum radiation because such resonators can be optically modulated at ultrafast rates, possibly leading to the generation of non-classical light via the dynamic Casimir effect. Finally, with an effective volume of $2.10^{-6} λ_0^3$, it is estimated that fewer than 3000 electrons per resonator are ultra-strongly coupled to the quantized electromagnetic mode, proving it is also a promising approach to explore few-electron polaritonic systems operating at relatively high temperatures.

Figures (4)

• Figure 1: (a) Schrödinger-Poisson simulation of the parabolic quantum well with a continuously graded alloy. In black is the Conduction band energy, the green lines are the squared moduli of the wave functions $\left| \Psi \right|^2$, while the dash line marks the energy position of the Fermi level. (b) Calculated absorption of the system with a linewidth of 10%.
• Figure 2: (a) Transmittance measurement of the grown heterostructure as function of the temperature. (b) Extracted linewidth using Voigt fitting formula as function of the temperature. We measured 69$$ GHz linewidth at 10$$ K. (c) Central frequency of the transition as function of the temperature. The dashed line is a guide for the eye to show the stability of the transition central frequency (d) Integrated absorption of the transition as function of the temperature.
• Figure 3: (a) Experimental reflectance of the ISB polaritonic system as function of the temperature. The dots mark the positions of the reflectance minima (b) Fit (dashed line) of the experimental reflectance at 78$$ K (full line), using finite element simulations. In inset is a schematic of the micro-ribbon resonator.(c) Simulation of the polaritonic system dispersion, attesting that the system is at the anti-crossing. The dots mark the experimental positions of the polaritonic peaks in the sample having a ribbon size of 18$$ µ m. (d) Coupling strength parameter ($\eta = \Omega_R/\omega_0$) as function of the temperature. The dashed line marks the limit of the ultra-strong coupling regime.
• Figure 4: (a) Scanning electron microscope image of the LC resonators array. Colorized in red is the capacitive section hosting the parabolic quantum wells, the rest being gold (b) Simulated confined electric field in the direction orthogonal to the growth plane (Ez). (c) Dispersion of the polaritonic system as a function of the antenna length. Dashed lines are the secular equation while the dots are the experimental points. The dotted parallel lines mark the edges of the polaritonic gap. (d) Experimental reflectance of the array with antenna length of 11$$ µ m at a temperature of 78$$ K, attesting of the excellent optical performances of the system.