Controlling Exciton-Phonon Interactions via Electromagnetically Induced Transparency

Highly excited Rydberg states of excitons in ${\mathrm{Cu}}_2\mathrm{O}$ semiconductors provide a promising approach to explore and control strong particle interactions in a solid-state environment. A major obstacle has been the substantial absorption background that stems from exciton-phonon coupling and lies under the Rydberg excitation spectrum, weakening the effects of exciton interactions. Here, we demonstrate that two-photon excitation of Rydberg excitons under conditions of electromagnetically induced transparency (EIT) can be used to control this background. Based on a microscopic theory that describes the known single-photon absorption spectrum, we analyze the conditions under which two-photon EIT permits separating the optical Rydberg excitation from the phonon-induced absorption background, and even suppressing it entir7ely. Our findings thereby pave the way for the exploitation of Rydberg blockade with ${\mathrm{Cu}}_2\mathrm{O}$ excitons in nonlinear optics and other applications.

Figure 1

EIT in ${\mathrm{Cu}}_2\mathrm{O}$. (a) A weak probe laser with a frequency ${\omega }_p$ generates $p$-state excitons of the yellow series. The simultaneous coupling to a continuum of phonon-dressed exciton states gives rise to the typical absorption spectrum of ${\mathrm{Cu}}_2\mathrm{O}$ below the band gap energy $E_{\mathrm{gap}}$ of the yellow series, as shown in (b). As further illustrated in panel (a), an additional control laser field with a frequency ${\omega }_c$ couples the generated excitons to an excited $s$ state of the yellow series to establish conditions of electromagnetically induced transparency. As shown in panel (c), this makes it possible to control the spectroscopic properties of the material and leads to a series of narrow absorption dips at a given $s$-state resonance with a greatly suppressed absorption background at each minimum. The depicted spectrum is scanned by varying ${\omega }_c$ with a fixed ${\omega }_p$ as indicated by the red arrow in panel (b).

Figure 2

The incident probe laser with electric field amplitude $\mathcal{E}$ excites $p$-state excitons with an optical coupling strength $g_p$ and detuning ${\delta }_p$. Simultaneously, the field couples to the continuum of phonon-dressed $1s$ excitons with coupling strength $g$. The dressed states start to appear at an energy $\hslash {\omega }_{{\mathrm{\Gamma }}_3^{-}}$ above the $1s$ state. The combination of the $p$-state excitation and the phonon-dressed excitons generate the broad absorption spectrum sketched on the right [cf. Fig. 1]. As we show in this Letter, this typical absorption can be controlled by a second light field that couples both types of excitons to an $s$ state with coupling strengths ${\mathrm{\Omega }}_s$ and $\mathrm{\Omega }$, respectively, and a two-photon detuning ${\delta }_s$.

Figure 3

Probe field absorption spectra around the $2p$ exciton at an energy $E_p$. In panel (a) the control field is tuned to resonance with the Rydberg-state transition, i.e., ${\delta }_p={\delta }_s$. The parameters of the probe-field transitions are taken from Ref. [42], and the Rydberg decay is neglected, ${\mathrm{\Gamma }}_s=0$. The different colored curves show typical absorption profiles for different indicated values of $\beta =g_p\mathrm{\Omega }/(g{\mathrm{\Omega }}_s)$, whereby the larger of the two Rabi frequencies $\mathrm{\Omega }$ and ${\mathrm{\Omega }}_s$ is chosen to be 0.50 meV. For comparison, the black line shows the absorption spectrum in the absence of EIT, i.e., for ${\mathrm{\Omega }}_s=\mathrm{\Omega }=0$. The thin horizontal lines indicate the resonant probe absorption stemming only from the $2p$ exciton (${\alpha }_{\mathrm{res}}$) and only from the background (${\alpha }_{\mathrm{bg}}$). Panel (b) shows the same quantities for identical parameters, but with the control field tuned to two-photon resonance, ${\delta }_s=0$.

Figure 4

Absorption contrast as a function of $\beta$ for different indicated values of ${\mathrm{\Gamma }}_s$ on $2p$-exciton resonance and two-photon resonance (${\delta }_p={\delta }_s=0$). $\beta$ is varied by changing $\mathrm{\Omega }$ while ${\mathrm{\Omega }}_s=50\mu \mathrm{eV}$ is held constant, and the remaining parameters coincide with those of Fig. 3. The dashed line shows the absorption contrast for ${\mathrm{\Gamma }}_s=0.1\mu \mathrm{eV}$ and probe laser tuned away from the $2p$ resonance at ${\delta }_p=20\mathrm{meV}$. $\beta$ is varied by changing ${\mathrm{\Omega }}_s$ with $\mathrm{\Omega }=50\mu \mathrm{eV}$.