The manipulation of neutral atoms by light is at the heart of countless scientific discoveries in the field of quantum physics in the last three decades. The level of control that has been achieved at the single particle level within arrays of optical traps, while preserving the fundamental properties of quantum matter (coherence, entanglement, superposition), makes these technologies prime candidates to implement disruptive computation paradigms. In this paper, we review the main characteristics of these devices from atoms / qubits to application interfaces, and propose a classification of a wide variety of tasks that can already be addressed in a computationally efficient manner in the Noisy Intermediate Scale Quantum\cite{Preskill_NISQ} era we are in. We illustrate how applications ranging from optimization challenges to simulation of quantum systems can be explored either at the digital level (programming gate-based circuits) or at the analog level (programming Hamiltonian sequences). We give evidence of the intrinsic scalability of neutral atom quantum processors in the 100-1,000 qubits range and introduce prospects for universal fault tolerant quantum computing and applications beyond quantum computing.

In a quantum world, a watched arrow never moves. This is the Quantum Zeno Effect [1]. Repeatedly asking a quantum system "are you still in your initial state ?" blocks its coherent evolution through measurement back-action. Quantum Zeno Dynamics (QZD) [2,3] leaves more freedom to the system. Instead of pinning it to a single state, it sets a border in its evolution space. Repeatedly asking the system "are you beyond the border ?" makes this limit impenetrable. Since the border can be designed by choosing the measured observable, QZD allows one to tailor dynamically at will the system's Hilbert space. Recent proposals, particularly in the Cavity Quantum Electrodynamics (CQED) context [4,5], highlight the interest of QZD for quantum state engineering tasks [6][7][8][9][10][11], which are the key to quantum-enabled technologies and quantum information processing. We report the observation of QZD in the 51-dimension Hilbert space of a large angular momentum J = 25. Continuous selective interrogation limits the evolution of this angular momentum to an adjustable multi-dimensional subspace. This confined dynamics leads to the production of non-classical 'Schrödinger cat' states [12,13], quantum superpositions of angular momentums pointing in different directions. These states are promising for sensitive metrology of electric and magnetic fields. This QZD approach could also be generalized to cavity and circuit QED experiments [4,5,13], replacing the angular momentum by a photonic harmonic oscillator.Quantum Zeno dynamics modifies the classical motion of a system by its observation in a quantum context [4][5][6][7][8][9][10][11]. However, an actual projective quantum measurement is not mandatory, and QZD can be equivalently attained by performing a pulsed unitary acting only on the states at the border ("Bang Bang" control) or even by applying a strong continuous coupling to these states. This has been predicted theoretically [3] and verified in a recent experiment [14]. In that experiment, however, the evolution of the system is restricted to a dimension 2 subspace. The dynamics is simply that of a spin 1/2, and do not exhibit the most striking features of QZD [4].In this Letter we implement QZD in a large atomic angular momentum J = 25 ('spin' or top), represented as an arrow pointing on a generalized Bloch sphere. In the 51-dimensional Hilbert space, we isolate tailorable multi-dimensional manifolds. We show how QZD induces a very non-classical dynamics inside the Zeno subspace, leading to the generation of Schrödinger cat spin states [12], in which the arrow points at the same time in two different directions. As spin-squeezed states [15], which are the focus of an intense attention, these cat states lead to quantum-enabled metrological applications [13].The angular momentum projection on the polar axis of the generalized Bloch sphere is quantized, taking the values J − k, with k = 0 . . . 2J (the corresponding eigenstates being |J, J − k ). The dynamical evolution from the initial state |J, J (North pole of the Bl...

How do isolated quantum systems approach an equilibrium state? We experimentally and theoretically address this question for a prototypical spin system formed by ultracold atoms prepared in two Rydberg states with different orbital angular momenta. By coupling these states with a resonant microwave driving, we realize a dipolar XY spin-1/2 model in an external field. Starting from a spin-polarized state, we suddenly switch on the external field and monitor the subsequent many-body dynamics. Our key observation is density dependent relaxation of the total magnetization much faster than typical decoherence rates. To determine the processes governing this relaxation, we employ different theoretical approaches that treat quantum effects on initial conditions and dynamical laws separately. This allows us to identify an intrinsically quantum component to the relaxation attributed to primordial quantum fluctuations.

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We realize a coherent transfer between a laser-accessible low-angular-momentum Rydberg state and the circular Rydberg level with maximal angular momentum. This transfer is induced by a radiofrequency field with a high-purity σ + polarization tuned at resonance on Stark transitions inside the hydrogenic Rydberg manifold. We observe over a few microseconds more than twenty coherent Rabi oscillations between the initial Rydberg state and the circular Rydberg level. We characterize in details these complex oscillations involving many Rydberg levels and find them to be in perfect agreement with a simple theoretical model. This coherent transfer procedure opens the way to hybrid quantum gates bridging the gap between optical communication and quantum information manipulations based on microwave Cavity and Circuit Quantum Electrodynamics.The long-lived Circular Rydberg Levels (CRLs) are ideal tools for quantum manipulation of microwave (mw) fields stored in ultra-high-Q 3D superconducting resonators. They led to early demonstrations of basic quantum information processing operations [1] and to the generation of non-classical field state superpositions [2]. More recently, they have been instrumental in the exploration of fundamental Cavity Quantum Electrodynamics (Cavity-QED) effects, such as QND measurements of the photon number [3] and quantum feedback [4]. Recent advances on the manipulation of Rydberg atoms near atom chips [5] indicate that they could also be interfaced with the resonant structures used in the flourishing field of Circuit-QED [6,7].However, the photons used in mw Cavity-and Circuit-QED are unable to propagate over long-range transmission lines [8]. Optical to mw interfaces are thus the focus of an intense activity [9,10]. A new realm for mw quantum information manipulation would open if the CRLs could be coherently interfaced with optical photons, which are ideal quantum information carriers over fiber and free-space communication networks [11]. Unfortunately, the CRLs, with their large orbital quantum number = n − 1 (n is the principal quantum number), do not couple directly to optical photons.In contrast, low-angular momentum Rydberg states are accessible from the ground state by coherent laser excitation [12][13][14]. They were recently used for optical quantum information processing operations such as photon-photon gates relying on single-photon optical non-linearities induced by the dipole blockade mechanism [15][16][17][18]. They could also lead to quantum gates entangling a mw photon with a collective hyperfine excitation in a ground state atomic ensemble [19] and hence, through the DLCZ protocol [20], to gates entangling optical and mw photons. However, the short lifetime of these levels, of the order of 100 µs, sets limits on the quantum transfer fidelity and on their use in CQED experiments.The missing link between mw and optical photons is a fast coherent transfer from a laser-accessible low-state to the CRLs. The most efficient CRL preparation technique so far involves a series of radiof...

We report on an extensive study of the elastic scattering time τs of matter-waves in optical disordered potentials. Using direct experimental measurements, numerical simulations and comparison with first-order Born approximation based on the knowledge of the disorder properties, we explore the behavior of τs over more than three orders of magnitude, spanning from the weak to the strong scattering regime. We study in detail the location of the crossover and, as a main result, we reveal the strong influence of the disorder statistics, especially on the relevance of the widely used Ioffe-Regel-like criterion kls ∼ 1. While it is found to be relevant for Gaussian-distributed disordered potentials, we observe significant deviations for laser speckle disorders that are commonly used with ultracold atoms. Our results are crucial for connecting experimental investigation of complex transport phenomena, such as Anderson localization, to microscopic theories. arXiv:1810.07574v4 [cond-mat.quant-gas]

The simple resonant Rabi oscillation of a two-level system in a single-mode coherent field reveals complex features at the mesoscopic scale, with oscillation collapses and revivals. Using slow circular Rydberg atoms interacting with a superconducting microwave cavity, we explore this phenomenon in an unprecedented range of interaction times and photon numbers. We demonstrate the efficient production of 'cat' states, quantum superposition of coherent components with nearly opposite phases and sizes in the range of few tens of photons. We measure cuts of their Wigner functions revealing their quantum coherence and observe their fast decoherence. This experiment opens promising perspectives for the rapid generation and manipulation of non-classical states in cavity and circuit Quantum Electrodynamics. PACS numbers:The Rabi oscillations of a two-level atom in a resonant, single-mode coherent field state is one of the simplest phenomena in quantum optics. Nevertheless, it exhibits surprisingly complex features at the mesoscopic scale (few tens of photons) [1][2][3][4]. The oscillations, at an angular frequency Ω 0 √ n, collapse and revive (n is the average photon number in the coherent state; Ω 0 is the vacuum Rabi frequency measuring the atom-field coupling). The collapse, occurring on a time scale T c = 2 √ 2/Ω 0 , results from the quantum field amplitude uncertainty and from the corresponding dephasing of the Rabi oscillations. The (first) revival, around T r = 4π √ n/Ω 0 , results from the rephasing of oscillations associated to different photon numbers [5]. This revival provides a landmark illustration of field amplitude quantization [6]. Between collapse and revival, the field evolves into an entangled atom-field state, involving two coherent states with different phases [7,11,[35][36][37]. It is called a "cat state" in memory of Schrödinger's metaphor. Close to t = T r /2, the atomic state factors out of a field "cat", superposition of coherent states with opposite phases [5].These phenomena can be observed in systems implementing the Jaynes and Cummings model, a spin-1/2 coupled to a one-dimensional harmonic oscillator [12]. Ions in traps [13,14], cavity quantum electrodynamics (CQED) [3,6] and circuit quantum electrodynamics (cQED) [16, 39] are thus ideal platforms for this observation.Nevertheless, revival observations have so far been limited to small photon numbers since experiments face formidable challenges. For microwave CQED with superconducting cavities crossed by fast Rydberg atoms, the interaction time is limited to a few vacuum Rabi periods, 2π/Ω 0 . Revivals have been observed only for n 1 [6,17]. Early revivals induced by a time-reversal of the collapse can be observed for larger n values (about 10), but the maximum separation of the cat compo-nents is small [18,19]. Ion traps have similar limitations [13,20]. In cQED, the limited coherence time of tunable superconducting qubits makes it difficult to observe long-term dynamics in the resonant regime [21]. Large cat-state preparation so far relie...

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