Electromagnetically induced transparency in strongly interacting Rydberg gases

We develop an efficient Monte Carlo approach to describe the optical response of cold three-level atoms in the presence of electromagnetically induced transparency (EIT) and strong atomic interactions. In particular, we consider a Rydberg-EIT medium where one involved level is subject to large shifts due to strong van der Waals interactions with surrounding Rydberg atoms. Agreement with much more involved quantum calculations is excellent, demonstrating its applicability over a wide range of densities and interaction strengths. The calculations show that nonlinear absorption due to Rydberg-Rydberg atom interactions exhibits universal behavior.

Figure 1

Illustration of the considered three-level ladder scheme. Two laser fields successively couple the states $|1\rangle$, $|2\rangle ,$ and $|3\rangle$. For isolated atoms, EIT is realized on two-photon resonance, ${\Delta }_1=-{\Delta }_2$. The van der Waals interaction shift $C_6/r_{\mathit{ij}}^6$ between atoms in the Rydberg state $|3\rangle$ modifies this ideal transparency and leads to a nonlinear optical response of the medium.

Figure 2

Calculated probe-beam absorption spectra for a rubidium Rydberg-EIT medium at various densities. The lines show results of the Monte Carlo simulations, compared to quantum calculations based on a reduced-density matrix expansion [12] (symbols). The atoms are resonantly (${\Delta }_2=0$) excited to $55S$ Rydberg states. The probe and coupling beams have Rabi frequencies of ${\Omega }_1=1\hspace{0.5em}$MHz and ${\Omega }_2=2\hspace{0.5em}$MHz, respectively, with linewidths of ${\gamma }_{12}={\gamma }_{23}=100\hspace{0.5em}$kHz.

Figure 3

Complex susceptibility ${\chi }_{12}$ as a function of gas density ${\rho }_0$ under EIT conditions, ${\Delta }_1={\Delta }_2=0$. The reduced-density matrix calculations (symbols) start to deviate from the Monte Carlo results (lines) for densities $\gtrsim {10}^{10}$cm${}^{-3}$. Remaining parameters are identical to those of Fig. 2.

Figure 4

(a) Nonlinear absorption coefficient $\mathrm{Im}({\chi }_{12})$ as a function of the density of rubidium atoms for ${\Omega }_2=2\hspace{0.5em}$MHz and ${\gamma }_{12}={\gamma }_{23}=0$. The different symbols correspond to different principal quantum numbers and probe Rabi frequencies: ${\Omega }_1=1\hspace{0.5em}$MHz, $n=50$ (squares); ${\Omega }_1=0.5\hspace{0.5em}$MHz, $n=50$ (circles); ${\Omega }_1=1\hspace{0.5em}$MHz, $n=70$ (triangles); and ${\Omega }_1=1\hspace{0.5em}$MHz, $n=70$ (diamonds). (b) After proper scaling [cf. Eqs. (10) and (9)] all data points follow the simple universal scaling relation, Eq. (11) (line).