# Project Area A:

Rydberg Quantum Optics

Quantum optics deals with phenomena that cannot be solely described as resulting from the wave nature of light, but must be attributed to the particle character of radiation, which can only be understood within quantum theory. Such quantum phenomena can occur in the emission, propagation and absorption of light. As both the generation and detection of light involves matter, atom-photon interactions are at the very heart of quantum optics. Their detailed understanding opens the possibility to prepare and control quantum light states to the level of dynamically engineering the nonlinear optical properties of atomic media.

Material properties like the refractive index can be explained within a linear-response theory, which considers the effect of matter on a light beam only in the lowest order and thus treats the effect of light on the medium as a small perturbation neglecting fluctuations. Although nonlinear quantum phenomena, such as the generation of light with intensity fluctuations below the shot-noise level, have been observed, their effect on the excitation beam is usually small. The reason is that the nonlinear response of conventional media is so weak that high laser intensities and thus large photon numbers are required. Under such conditions, the granular character of the light beam does not play an important role. The situation, however, would change dramatically if one could prepare a medium whose optical nonlinearity is so strong that a light beam containing just a few photons would be sufficient to trigger nonlinear processes.

Inducing nonlinear light-matter phenomena in the few-photon regime is by no means straightforward. A possibility is to enhance the light-matter interaction by placing the emitter/absorber into an optical high-finesse, small-volume resonator. However, it seems difficult in practice to scale these systems to larger photon numbers and to larger resonator arrays in which quantum nonlinear optical effects can be investigated.

The extraordinary properties of Rydberg atoms as nonlinear media offer a decisive advantage. The large radius of a Rydberg atom makes the particle insensitive to the details of its core and instead very sensitive to its environment. If the environment consists of another Rydberg atom, a strong van-der-Waals interaction will emerge. In fact, the interaction between two highly polarisable Rydberg atoms is gigantic. For a principal quantum number of 100, this interaction can be 12 orders of magnitude larger than for two atoms in their electronic ground-state. This property was the key for the recent demonstration of the first quantum logic gate between two neutral atoms.

When coupling light to Rydberg states, it becomes possible to exploit the huge atom-atom coupling to generate an effective interaction between photons. A very fruitful scheme for generating this interaction is electromagnetically induced transparency (EIT), a phenomenon based on quantum interference: An EIT medium is for instance an atomic ensemble, which becomes transparent to light when appropriately driven by external lasers. If a photon enters an EIT medium composed of Rydberg atoms, then it becomes a Rydberg polariton, an excitation that has a slowly propagating photonic component accompanied by a co-propagating Rydberg component, and that propagates unperturbed across the medium. If more than one polariton is inside a certain microscopic volume, however, the polariton-polariton interaction is so gigantic that the EIT medium becomes absorptive. Hence, the trans-mission of dense bunches of polaritons is blocked, an effect called Rydberg blockade. The first observation of Rydberg blockade in EIT was a landmark experiment (1) showing that the blockade phenomenon can be mapped onto photons. Together with the above-mentioned quantum gate, this led to an explosion of research activities worldwide. Indeed, the number of groups working on Rydberg quantum optics has grown immensely over the past few years.

Beyond the Rydberg blockade, the emerging field of Rydberg quantum optics has already achieved several outstanding experimental results, including the observation of photon anti-bunching combined with the demonstration of a single-photon source (2), the observation of photon bunching together with the measurement of a conditional phase shift (3), and the realization of a single-photon transistor in simultaneous experiments at the University of Stuttgart and the Max Planck Institute of Quantum Optics in 2014 (4) (5). These experiments are accompanied by considerable theoretical progress, with several of the worldwide leading groups located in Germany. Here, one recent highlight was the non-perturbative theoretical description of the collision of two Rydberg polaritons at the University of Stuttgart (6). Owing to weakness of nonlinear interactions in conventional materials, many-body effects in photonic systems are typically restricted to Bose enhancement. This could dramatically change with Rydberg polaritons and photons could become another versatile model system to study many-body physics.

The universal Rydberg nature can however also be exploited in systems other than atomic gases. A prominent example is a recent experiment with Rydberg excitons in cuprous oxide (Cu2O), a rarely-studied semiconductor material (7). The impressive observation of a Rydberg blockade shift on a very different platform offers a new approach for studying semiconductor systems and also provides entirely new and exciting long-term perspectives for developing novel devices, which are more robust and compact than atomic systems.

1. J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams. Cooperative atom-light interaction in a blockaded Rydberg ensemble. *Phys. Rev. Lett. 105, 193603 (2010) *.

2. Y. O. Dudin, and A. Kuzmich. Strongly interacting Rydberg excitations of a cold atomic gas. *Science 336, 887-889 (2012) *.

3. O. Firstenberg, T. Peyronel, Q.-Y. Liang, A. V. Gorshkov, M. D. Lukin, and V. Vuletic. Attractive photons in a quantum nonlinear medium. * Nature 502, 71-75 (2013) *.

4. S. Baur, D. Tiarks, **G. Rempe**, and S. Dürr. Single-photon switch based on Rydberg blockade. *Phys. Rev. Lett. 112, 073901 (2014) *.

5. H. Gorniaczyk, C. Tresp, J. Schmidt, H. Fedder, and S. Hofferberth. Single Photon Transistor Mediated by Inter-State Rydberg Interaction. * Phys. Rev. Lett. 113, 053601 (2014) *.

6. P. Bienias, S. Choi, O. Firstenberg, M. F. Maghrebi, M. Gullans, M. D. Lukin, A. V. Gorshkov, and H. P. Büchler. Scattering resonances and bound states for strongly interacting Rydberg polaritons. * arXiv:1402.7333V1 [quant-ph] 28 Feb 2014 *.

7. T. Kazimierczuk, D. Fröhlich, **S. Scheel**, H. Stolz, and M. Bayer. Giant Rydberg excitons in cuprous oxide. * arXiv:1407.0691 (2014) *.