Rydberg excitons in Cu$_2$O at millikelvin temperatures

TL;DR

Rydberg excitons in Cu2O are studied at millikelvin temperatures to understand how temperature and optical excitation power constrain the observable Rydberg series. The authors perform high-resolution absorption spectroscopy in a dilution refrigerator, varying temperature below 1 K and laser intensity to map the dependence of the maximum observable principal quantum number $n_{ ext{max}}$. They find that $n_{ ext{max}}$ is dominated by impurity-induced internal electric fields and laser-induced ionization, with $n_{ ext{max}}$ reaching 28–29 only at very low power and favorable sample spots; $D$-exciton features reveal Stark-type mixing consistent with local fields. The work clarifies the competing roles of temperature, impurities, and excitation power in shaping high-$n$ Rydberg excitons, informing strategies to realize strong nonlinearities and exciton-polaritons in solid-state systems.

Abstract

Rydberg excitons in the semiconductor Cu$_2$O have been observed in absorption experiments up to a principal quantum number of n = 28 at millikelvin temperatures [1]. Here, we extend the experimental parameter space by variing both temperature and excitation power. In particular, we show that the P excitons close to the band gap react more sensitively to an increase of the excitation power than states of the associated D exciton multiplet, even though the latter are located at comparatively higher energy. This finding is similar to the one observed when applying an external electric field, suggesting that the observed behavior arises from internal electric fields created by charged impurities that are optically ionized. At laser intensities below 1 $μ$W/cm$^2$, absorption lines of excitons with n=29 are observed.

Figures (4)

• Figure 1: (a) Comparison of absorption spectra measured at 1.35 K and 0.76 K with an laser intensity of 0.3 mW/cm$^2$. Below 1 K, the absorption coefficient rises for all $n$. This results in an improvement for the visibility of states up to $n=26$, as highlighted in the inset. (b) Absorption spectra at three different temperatures below 1 K. $n=28$ becomes visible for temperatures equal and below 450 mK. (c) Also at 110 mK and 50 mK $n_{max}=28$ at laser intensities of 0.3 mW/cm$^2$ and 0.03 mW/cm$^2$. The photon energy is given relative to the band gap energy $E_g$. Vertical dashed lines mark the expected resonance energies according to $E_g-Ryd/n^2$, using a Rydberg energy of $Ryd=91$ meV and a band gap energy of $E_g=2.17208$ eV. Adapted with permission from Ref. heckotterExperimentalLimitationExtending2020.
• Figure 2: (a)Absorption spectra of Rydberg excitons as a function of laser intensity at a temperature of 830 mK. At an intensity of 0.08 mW/cm$^2$, $n=28$ is visible. The maximum observable $n$ decreases with increasing laser intensity to $n=23$ at 34 mW/cm$^2$. The inset shows $n_\text{max}$ as a function of intensity. (b) On the high-energy side of each $P$ exciton line, small $D$ exciton absorption lines are visible. (c)/(d) Maximum absorption of $P$ and $D$ lines as a function of laser intensity for (c) $n=22$ and (d) $n=23$. The signal is normalized to unity at lowest applied power. $D$ excitons are less sensitive to the increasing laser intensity compared to $P$ excitons.
• Figure 3: Absorption spectra of Rydberg excitons for series of laser intensities below 0.3 mW/cm$^2$ at a temperature of 130 mK. The vertical dashed lines mark the expected resonance energies according to $E_g-Ryd/n^2$, using a Rydberg energy of $Ryd=91$ meV and a bandgap energy of $E_g=2.17208$ eV.
• Figure 4: Absorption spectrum at 120 mK and a laser intensity of 0.0003 mW/cm$^2$. The spectrum is an average of five single absorption spectra to reduce the noise.