Electromagnetically Induced Transparency with Rydberg Atoms

We present a theory of electromagnetically induced transparency in a cold ensemble of strongly interacting Rydberg atoms. Long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our model is computationally very efficient and is in quantitative agreement with the results of the recent experiment of Pritchard et al. [Phys. Rev. Lett. 105, 193603 (2010)]

Figure 1

(a) Level scheme of atoms interacting with probe ${\Omega }_p$ and control ${\Omega }_c$ fields with detunings ${\Delta }_p$ and ${\delta }_c$. ${\Gamma }_e$ and ${\Gamma }_r$ are (population) decay rates of states $|e⟩$ and $|r⟩$, and ${\mathcal{V}}_{\mathrm{vdW}}$ denotes vdW interaction between atoms in Rydberg state $|r⟩$. (b) Truncated level scheme of the superatom, composed of $n_{\mathrm{SA}}$ atoms, with corresponding transition amplitudes due to the probe and control fields.

Figure 2

Top: Probe field transmission $I_p(L)/I_p(0)$ versus detuning ${\Delta }_p$, for different input intensities corresponding to ${\Omega }_p(0)/2\pi =0.15$, 0.5, 1.0 MHz. Thin lines are experimental curves from [21], thicker lines are obtained via stochastic simulations of Eqs. (5, 6, 7) averaged over 10 independent realizations. Bottom: The corresponding intensity correlation functions $g_p^{(2)}(L)$.

Figure 3

(a) Transmission (top) and intensity correlation (bottom) spectra of the probe field, for various input intensities. (b) The same, but setting $g_p^{(2)}(z)=1\forall z\in [0,L]$. (c) Peak probe transmission $T_{\max }$ around the EIT line center, (d) EIT linewidth $\delta {\omega }_{\mathrm{EIT}}$ (FWHM), and (e) detuning ${\Delta }_p^{\max }$ at the maximum $T_{\max }$, versus the input probe Rabi frequency ${\Omega }_p(0)$. The black lines (circles) correspond to case (a) and the brown lines (squares) to (b). ${\Delta }_p$, $\delta {\omega }_{\mathrm{EIT}}$, ${\Omega }_p$ are in MHz.