Measurement of the Angular Dependence of the Dipole-Dipole Interaction Between Two Individual Rydberg Atoms at a F\"orster Resonance

We measure the angular dependence of the resonant dipole-dipole interaction between two individual Rydberg atoms with controlled relative positions. By applying a combination of static electric and magnetic fields on the atoms, we demonstrate the possibility to isolate a single interaction channel at a F\"orster resonance, that shows a well-defined angular dependence. We first identify spectroscopically the F\"orster resonance of choice and we then perform a direct measurement of the interaction strength between the two atoms as a function of the angle between the internuclear axis and the quantization axis. Our results show good agreement with the expected angular dependence $\propto(1-3\cos^2\theta)$, and represent an important step towards quantum state engineering in two-dimensional arrays of individual Rydberg atoms.Comment: 5 pages, 4 figure

Coherent dipole-dipole coupling between two single atoms at a F\"orster resonance

Resonant energy transfers, i.e. the non-radiative redistribution of an electronic excitation between two particles coupled by the dipole-dipole interaction, lie at the heart of a variety of chemical and biological phenomena, most notably photosynthesis. In 1948, F\"orster established the theoretical basis of fluorescence resonant energy transfer (FRET), paving the ground towards the widespread use of FRET as a "spectroscopic ruler" for the determination of nanometer-scale distances in biomolecules. The underlying mechanism is a coherent dipole-dipole coupling between particles, as already recognized in the early days of quantum mechanics, but this coherence was not directly observed so far. Here, we study, both spectroscopically and in the time domain, the coherent, dipolar-induced exchange of electronic excitations between two single Rydberg atoms separated by a controlled distance as large as 15 microns, and brought into resonance by applying a small electric field. The coherent oscillation of the system between two degenerate pair states occurs at a frequency that scales as the inverse third power of the distance, the hallmark of dipole-dipole interactions. Our results not only demonstrate, at the most fundamental level of two atoms, the basic mechanism underlying FRET, but also open exciting prospects for active tuning of strong, coherent interactions in quantum many-body systems.Comment: 4 pages, 3 figure

Single-Atom Addressing in Microtraps for Quantum-State Engineering using Rydberg Atoms

We report on the selective addressing of an individual atom in a pair of single-atom microtraps separated by $3\;\mu$m. Using a tunable light-shift, we render the selected atom off-resonant with a global Rydberg excitation laser which is resonant with the other atom, making it possible to selectively block this atom from being excited to the Rydberg state. Furthermore we demonstrate the controlled manipulation of a two-atom entangled state by using the addressing beam to induce a phase shift onto one component of the wave function of the system, transferring it to a dark state for the Rydberg excitation light. Our results are an important step towards implementing quantum information processing and quantum simulation with large arrays of Rydberg atoms.Comment: 4 pages, 3 figure

Realizing quantum Ising models in tunable two-dimensional arrays of single Rydberg atoms

Spin models are the prime example of simplified manybody Hamiltonians used to model complex, real-world strongly correlated materials. However, despite their simplified character, their dynamics often cannot be simulated exactly on classical computers as soon as the number of particles exceeds a few tens. For this reason, the quantum simulation of spin Hamiltonians using the tools of atomic and molecular physics has become very active over the last years, using ultracold atoms or molecules in optical lattices, or trapped ions. All of these approaches have their own assets, but also limitations. Here, we report on a novel platform for the study of spin systems, using individual atoms trapped in two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100% with exact knowledge of the initial configuration. When excited to Rydberg D-states, the atoms undergo strong interactions whose anisotropic character opens exciting prospects for simulating exotic matter. We illustrate the versatility of our system by studying the dynamics of an Ising-like spin-1/2 system in a transverse field with up to thirty spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. For geometries where the anisotropy is expected to have small effects we find an excellent agreement with ab-initio simulations of the spin-1/2 system, while for strongly anisotropic situations the multilevel structure of the D-states has a measurable influence. Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism.Comment: This is the version of the manuscript as initially submitted to Natur

Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries

We demonstrate single-atom trapping in two-dimensional arrays of microtraps with arbitrary geometries. We generate the arrays using a Spatial Light Modulator (SLM), with which we imprint an appropriate phase pattern on an optical dipole trap beam prior to focusing. We trap single $^{87}{\rm Rb}$ atoms in the sites of arrays containing up to $\sim100$ microtraps separated by distances as small as $3\;\mu$m, with complex structures such as triangular, honeycomb or kagome lattices. Using a closed-loop optimization of the uniformity of the trap depths ensures that all trapping sites are equivalent. This versatile system opens appealing applications in quantum information processing and quantum simulation, e.g. for simulating frustrated quantum magnetism using Rydberg atoms.Comment: 9 pages, 10 figure

La dynamique et correlations d'excitations Rydberg dans des matrices 2D des atomes unique

In this thesis, we measure the coherent dynamics and the pair correlations of Rydberg excitations in two-dimensional arrays of single atoms.We use a spatial light modulator to shape the spatial phase of a single optical dipole trap beam before focusing it with a high numerical-aperture aspheric lens. By imprinting an appropriate phase pattern on the trap beam, we can create arbitrarily shaped and easily reconfigurable 2D arrays of high-quality single-atom traps, with trap-spacings of a few micrometers for up to 100 traps. The traps are loaded from a cloud of cold 87Rb atoms, and due to fast light-assisted collisions of atoms inside the traps, at most one atom can be present in each trap at the same time. A sensitive CCD camera allows the real-time, site-resolved imaging of the atomic fluorescence from the traps, enabling us to detect the presence of an atom in each individual trap with almost perfect accuracy.In order to induce strong, tunable interactions between the atoms in the array, we coherently laser-excite them to Rydberg states, which are electronic states with a high principal quantum number.An additional addressing beam allows the individual manipulation of an atom at a selected site in the array.The precise knowledge of both the prepared atom array and the positions of the Rydberg excitations allowed us to measure the collective enhancement of the optical coupling strength in the regime of full Rydberg blockade, where one single excitation is shared symmetrically among all atoms in the array.In the regime where the strong interaction only extends over a few sites, we measured the dynamics and the spatial pair-correlations of Rydberg excitations, in one- and two-dimensional atom arrays. The comparison to a numerical simulation of a quantum Ising model of a spin-1/2 system shows an exceptional agreement for trap geometries where the effect of the anisotropy of the Rydberg-Rydberg interaction is small. The obtained results demonstrate that single Rydberg atoms are a suitable platform for the quantum simulation of spin systems.Dans cette thèse, nous mesurons la dynamique cohérente et les corrélations spatiales des excitations Rydberg dans des matrices 2D d’atomes uniques.Nous utilisons un modulateur spatial de lumière pour façonner la phase spatiale d'un faisceau laser de piégeage optique avant de le focaliser avec une lentille asphérique de grande ouverture numérique. En imprimant une phase appropriée sur le faisceau laser, nous pouvons créer des matrices 2D de pièges optiques, de forme arbitraire et facilement reconfigurables, avec jusqu'à 100 pièges séparées de quelques micromètres. Les pièges sont chargés à partir d'un nuage d'atomes froids de 87Rb, et due aux collisions assistées par la lumière, au plus un seul atome peut être présent dans chaque piège en même temps. Une caméra CCD sensible permet en temps réel l'imagerie de la fluorescence atomique émanant des pièges, ce qui nous permet de détecter individuellement la présence d'un atome dans chaque piège avec une précision presque parfaite.Pour créer des interactions importantes entre les atomes uniques, nous les excitons vers des états de Rydberg, qui sont des états électroniques avec un nombre quantique principal élevé.Un faisceau supplémentaire d'adressage permet la manipulation individuelle d'un atome sélectionné dans la matrice.La connaissance précise, de la fois de la matrice des atomes préparé et des positions des excitations Rydberg, nous a permis de mesurer l’augmentation collective de la couplage optique dans le régime de blocage Rydberg, où une seule excitation est partagée de façon symétrique entre tous les atomes de la matrice.Dans le régime où l'interaction ne s’étend que sur quelques sites, nous avons mesuré la dynamique et les corrélations spatiales des excitations Rydberg, dans des matrices d’atomes à une et deux dimensions. La comparaison à une simulation numérique d'un modèle d'Ising quantique d'un système de spin-1/2 montre un accord exceptionnel pour les matrices où l'effet de l'anisotropie de l’interaction Rydberg-Rydberg est faible. Les résultats obtenus démontrent que les atomes Rydberg uniques sont une plate-forme bien adaptée pour la simulation quantique des systèmes de spin

Creating arbitrary 2D arrays of single atoms for the simulation of spin systems with Rydberg states

We present an experimental setup for creating arbitrary two-dimensional arrays of optical microtraps to trap single atoms for experiments with Rydberg atoms. We use a spatial light modulator to manipulate the spatial phase of a far red-detuned optical dipole trap beam, which allows us to create arbitrary arrays of optical microtraps, by focusing the beam with an in-vacuum high numerical-aperture aspheric lens. We load atoms in the microtraps from a dilute cloud of cold atoms, having at most one atom in each trap due to fast light-assisted collisions. Real-time analysis of the atomic fluorescence with a sensitive CCD camera allows us to determine the filling of each trap individually with a  >10 Hz rate. We can create strong interactions between the atoms by exciting them to Rydberg states, with an efficiency of single atom resolved Rydberg detection of  >95%

Measurement of the angular dependence of the dipole-dipole interaction between two individual Rydberg atoms at a Förster resonance

We measure the angular dependence of the resonant dipole-dipole interaction between two individual Rydberg atoms with controlled relative positions. By applying a combination of static electric and magnetic fields on the atoms, we demonstrate the possibility to isolate a single interaction channel at a Förster resonance, that shows a well-defined angular dependence. We first identify spectroscopically the Förster resonance of choice and we then perform a direct measurement of the interaction strength between the two atoms as a function of the angle between the internuclear axis and the quantization axis. Our results show good agreement with the angular dependence ∝(1−3cos2θ) expected for this resonance. Understanding in detail the angular dependence of resonant interactions is important in view of using Förster resonances for quantum state engineering with Rydberg atoms.We acknowledge financial support by the EU [ERCStg Grant ARENA, Project HAIRS, H2020 FET Proactive project RySQ (Grant No. 640378), Marie-Curie Program ITN COHERENCE FP7-PEOPLE-2010-ITN-265031 (H.L.)], and by the PALM Labex (project QUANTICA).Peer reviewe