Electromagnetically Induced Transparency with Rydberg Atoms

Abstract

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 recent experiment of Pritchard et al. [Phys. Rev. Lett. 105, 193603 (2010) Recently, several experiments on EIT [18][19][20][21], and the closely related CPT (coherent population trapping) [22], with Rydberg atoms were performed. Strong VdW interactions between the atomic Rydberg states were prominently manifest in Ref. [21]: Increasing the probe field amplitude led to reduction of its transmission within the EIT window, which, quite surprisingly, was accompanied by negligible broadening and indiscernible shift of the EIT line. Here we develop a theoretical model for EIT with Rydberg atoms, whose predictions fully reproduce the experimental observations [21]. The crux of our approach is the coarse-grained treatment of the atomic medium composed of effective superatoms (SAs), with each SA represented by collective states of atoms in the blockade volume that can accommodate only one Rydberg excitation. A weak probe field propagates through the EIT medium with little attenuation, but for a stronger field with more than one photon per SA, the excess photons are subject to enhanced-essentially twolevel atom-absorption. This leads to the field attenuation with the simultaneous buildup of an avoided volume between the probe photons [17]. The inclusion of twophoton correlations is the key feature of our work, not present in the numerical simulations of [21] and recent theoretical studies [23] which agreed with the experiment at weak probe fields but had significant discrepancies for stronger fields. Our theory is not limited to weak probe fields and/or low atomic densities, yet, despite intrinsic nonlinearity, it is intuitive and numerically efficient, amounting to the solution of a pair of coupled differential equations for the probe field intensity and its secondorder correlation, in the spirit of the BBGKY hierarchy.Consider an ensemble of N = V d 3 r ρ(r) cold atoms of density ρ(r) in the (quantization) volume V interacting with two optical fields. The quantized probe fieldÊ p of frequency ω p acts on the atomic transition between the ground |g and excited |e states, and the control field of frequency ω c drives the transition |e → |r with Rabi frequency Ω c [see Fig. 1(a)]. A pair of atoms i and j at positions r i and r j excited to the Rydberg states |r interact with each other via a VdW potentialh∆(r i − r j ) =hC 6 /|r i − r j | 6 [24]. In the frame rotating with frequencies ω p,c , the system Hamiltonian H = H a + V af + V VdW co...

Quantum nonlinear optics — photon by photon

“…In the simplest case of resonant Rydberg EIT (both lasers resonant with their respective transitions, Fig. 4), the strong interaction between two Rydberg atoms tunes the two-photon transition out of resonance, thereby destroying the transparency and leading to absorption 22,58,59,[62][63][64] for two or more photons. The quantum nonlinearity in this case arises from the Rydberg excitation blockade 61 , which precludes the simultaneous excitation of two Rydberg atoms that are separated by less than the blockade radius r b (Fig.…”

Quantum nonlinear optics with single photons enabled by strongly interacting atoms

“…For a single incident probe photon, the control field induces a transparency window in the otherwise opaque medium via Electromagnetically Induced Transparency (EIT), and the probe photon travels at much reduced speed in the form of a coupled excitation of light and matter (Rydberg polariton). However, in stark contrast to conventional EIT 5 , if two probe photons are incident onto the Rydberg EIT medium, the strong interaction between two Rydberg atoms tunes the EIT transition out of resonance, thereby destroying the EIT and leading to absorption 14,22,23,25,26 . The experimental demonstration of an extraordinary optical material exhibiting strong two-photon attenuation in combination with single-photon transmission is the central result of this work.…”

“…The interactions between cold Rydberg atoms have been explored in ensembles [6][7][8][9][10] and have been used to realize quantum logic gates between two Rydberg atoms 11,12,24 . Giant optical nonlinearities using Rydberg EIT 14,22,23 have been observed in a classical, multi-photon regime 13 . Very recently, the Rydberg blockade in a dense, mesoscopic atomic ensemble has been used to implement a deterministic single-photon source 30 .…”

Attractive photons in a quantum nonlinear medium

“…Our approach is to couple a light field propagating in a dispersive medium to highly excited atomic states with strong mutual interactions (Rydberg states) 13,14 . Similar to previous studies of quantum nonlinearities via Rydberg states that were based on dissipation [15][16][17][18][19] rather than dispersion 20 , we make use of electromagnetically induced transparency (EIT) to slow down the propagation of light 21 in a cold atomic gas. By operating in a dispersive regime away from the intermediate atomic resonance (Fig.…”