• Electromagnetically-induced transparency
• Nonlinear optics
• Rydberg atoms

Interfacing light with matter is one of the fundamental tasks in physics. To understand and control atom-light interactions at the level of individual quanta is at the heart of modern quantum optics (see, for instance, Nobel prize in physics 2012).
Of great interest in current experiments is the regime of strong coupling between light and matter, in which the coherent and reversible light-matter coupling dominates over dissipative processes. This almost ideal light-matter interface can be practically realized using electromagnetically-induced transparency (EIT) [1]. The key element of EIT is the creation of a dark state [2] as a consequence of a quantum interference effect arising in a three-level system coherently coupled by a weak probe field and a strong coupling field, with two stable or metastable states and one rapidly decaying level. The destructive interference of the two different excitation pathways driven by the laser fields leads to cancellation of absorption on resonance and renders the medium transparent for the probe light.
Even more interesting is to investigate what happens when light is coupled to a strongly interacting atomic many-body system. Rydberg atoms are the optimal candidates for studying the effects of strong dipole-dipole interactions on light propagation.
Rydberg atoms are atoms excited in high-lying energy states (principal quantum number n > 20), with a relatively long lifetime (∽100μs) and a large orbital radius (∽1μm) [3]. The large radius of Rydberg atoms is responsible for their enormous dipole moments, resulting in an exaggerated response to electric fields and in very strong long-range dipole-dipole interactions between atoms excited in Rydberg states.
When atoms are excited to Rydberg states with coherent light fields, the interactions give rise to strong atomic correlations and lead to many-body phenomena, of which the most outstanding is the dipole blockade [4], for which the presence of a previously excited Rydberg atom prevents the excitation of another atom to a Rydberg state within a certain blockade volume. This enables deterministic creation of a single excitation for atoms confined within the blockade volume, making Rydberg atoms ideally suited for applications in quantum information processing, such as the implementation of quantum gates. Moreover, since each blockade volume collectively shares a single excitation, also the interaction with the light field is modified and all the atoms within this volume act as an effective two-level atom with enhanced
coupling to the light field.
Lately, several experiments combining the extraordinary properties of Rydberg atoms with the strong atom-light coupling achievable under EIT conditions have been performed, revealing the striking effect of dipole blockade on EIT. A single Rydberg excitation can switch the optical response of the surrounding atoms within a blockade volume from the transparent EIT condition to the resonant scattering limit, thus restoring the absorption of the probe light on resonance. This controlled switching between different optical responses due to Rydberg-Rydberg interactions leads to a huge nonlinear optical response of the atomic system to the probe light field, which depends on the atomic density, as well as on the probe intensity.
EIT in Rydberg gases has been extensively studied, both theoretically and experimentally, in recent years. One motivation is the possibility of exploiting the nonlinear optical response of the gas to achieve effective photon-photon interactions in the atomic medium. However, already the simulation of classical light propagating through a strongly interacting gas is a theoretical challenge due to the high complexity of the underlying many-body physics. Various approaches using different approximations have been pursued to tackle light propagation through Rydberg-EIT media.
In this thesis a theoretical as well as an experimental study of the nonlinear optical response of a strongly interacting Rydberg gas under EIT configuration is presented. The theoretical investigation of the many-body state of the system is performed applying a simplified model based on a rate equation (RE) approach, where interactions among Rydberg atoms are only included as energy shifts of the Rydberg states. The combination of the RE model with a semianalytical model recently developed to treat the collective effects emerging at high atomic densities (≥ 10¹² cm⁻³), allows to demonstrate that the nonlinear optical susceptibility of an interacting Rydberg-EIT medium can be calculated very efficiently in terms of single atom properties alone. Numerical simulations are performed assuming realistic values for the parameters of the system such as atomic density, laser intensities, interaction strengths. The results are then compared to experimental data. The experimental study is carried out on an ultracold cloud of ⁸⁷Rb atoms confined in an optical dipole trap.
The setup used to prepare the cold atomic sample and to excite the atoms to Rydberg states under EIT configuration is outlined in the thesis. Measurements of probe light absorption are obtained by analysing absorption images of the atomic cloud taken at different atomic densities. The comparison of the theoretical model with the data reveals that the model well reproduces the experimental results in a wide range of densities and for different sets of parameters. Moreover, compared with previous similar works, the model developed in this thesis allows to achieve a better quantitative understanding of the nonlinear optical response of the Rydberg-EIT medium to a resonant probe light.
Another feature of EIT in interacting Rydberg gas which is covered in this thesis concerns the possibility of exploiting the strong interactions between atoms in different Rydberg states combined with the optical nonlinearity of the atomic gas to develop a powerful non-destructive and spatially resolved imaging technique, potentially able to detect a single Rydberg "impurity" embedded in a background of
"probe" atoms subject to EIT conditions. Such an imaging technique has been recently experimentally realized within the research group where I performed my thesis work, following a prevoius theoretical proposal [5].
The model described in this thesis is extended to treat the effects of one impurity at the center of the atomic cloud on the absorption of the probe light. Performing simulations of the imaging process, including experimentally relevant noise sources, it is shown that it should be possible to achieve the single particle sensitivity. It is furthermore demonstrated that interactions between background atoms heavily decrease the sensitivity of the imaging scheme, consequently, minimizing these interactions is crucial to achieve the desired high sensitivity.
The experimental implementation of the imaging technique is presented, together with measurements of nonlinear absorption in presence of different number of impurities, at different atomic densities. The experimental results show that a minimum number of around 30 impurities excited at the center of the atomic cloud is necessary to clearly distinguish the absorption of the probe light due to the impurities, from
that due to interactions among background atoms. This demonstrates that with the current experimental setup it is not possible to detect a single impurity. As a consequence, the theoretical model for the absorption in presence of only one impurity at the center of the cloud can not be tested. The motivations which prevent achieving the single atom sensitivity with the present imaging technique are discussed, together
with possible improvements of the experimetal setup.

References:
[1] M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Electromagnetically induced transparency: Optics in coherent media, Rev. Mod. Phys. 77, 633 (2005).
[2] E. Arimondo, G. Orriolis, Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping, Nuovo Cimento Lett., 17, 133 (1976).
[3] T. Gallagher, Rydberg Atoms, Cambridge Monographs on Atomic, Molecular and Chemical Physics, Cambridge University Press (2005).
[4] M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, P. Zoller, Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles, Phys. Rev. Lett. 87, 037901 (2001).
[5] G. Günter, M. Robert-de-Saint-Vincent, H. Schempp, C. S. Hofmann, S. Whitlock, and M. Weidemüller, Interaction-Enhanced Imaging of Individual Rydberg Atoms in Dense Gases, Phys. Rev. Lett. 108, 013002 (2012).