LETTERS PUBLISHED ONLINE: 12 JANUARY 2015 | DOI: 10.1038/NPHYS3214 Mesoscopic Rydberg-blockaded ensembles in the superatom regime and beyond T. M. Weber, M. Höning, T. Niederprüm, T. Manthey, O. Thomas, V. Guarrera†, M. Fleischhauer, G. Barontini† and H. Ott* The control of strongly interacting many-body systems of a Bose–Einstein condensate of 87Rb atoms. We first load the enables the creation of tailored quantum matter with complex condensate into a one-dimensional optical lattice with a spacing of properties. Atomic ensembles that are optically driven to a 532 nm, to suppress the axial movement of the atoms. We subse- Rydberg state provide many examples for this: atom–atom quently compress the atomic sample in the radial direction to reduce entanglement1,2, many-body Rabi oscillations3, strong its size below the blockade radius and empty all but three (or more) photon–photon interaction4 and spatial pair correlations5. lattice sites using a focused electron beam8–10 (Fig. 1a and Methods). In its most basic form Rydberg quantum matter consists of The atom number within the ensemble (N) can be adjusted between an isolated ensemble of strongly interacting atoms spatially 100 and 500 at a temperature of T D .3.5 0.5/ µK and the typical confined to the blockade volume—a superatom. Here we size of the sample is ≤3 µm in diameter (Fig. 1b). Our preparation demonstrate the controlled creation and characterization scheme is readily scalable to arrays of superatoms (Fig. 1d). of an isolated mesoscopic superatom by means of accurate After preparation we excite the atomic ensemble with a density engineering and excitation to Rydberg p-states. Its single-photon transition from the j5s1=2i ground state to the = variable size allows the investigation of the transition from j51p3=2,mj D3 2i Rydberg state at a wavelength of 297 nm with a eective two-level physics to many-body phenomena. By coupling strength Ω. The single-photon transition circumvents monitoring continuous laser-induced ionization we observe a scattering from any intermediate state, therefore allowing a long strongly anti-bunched ion emission under blockade conditions exposure. The key observable is the string of ions produced by and extremely bunched ion emission under o-resonant excited atoms that are photoionized by the trap laser11 (with ioniza- Γ . / excitation. Our measurements provide insights into both tion rate ion D 455 kHz). Specifically, we detect the initial peak excitation statistics and dynamics. We anticipate applications ion rate as well as the temporal pair correlation function g .2/(τ/, in quantum optics and quantum information as well as extracted from the time-resolved ion signal (see Methods). The many-body physics experiments. ions continuously emitted from the ensemble lead to a slow decay Rydberg superatoms combine single- and many-body quantum of the superatom on a timescale between a few milliseconds (see effects in a unique way and have been proposed as fundamental inset Fig. 2) and seconds. Eventually almost 100% of the constituent building blocks for quantum simulation and quantum information6. atoms are converted into ions, of which we detect .40 8/%. For Owing to the phenomenon of Rydberg blockade7, the ensemble weak resonant driving the superatom mimics an effective two-level collectively forms a system with only two levels of excitation. system where the excitation of more than one atom is suppressed as Provided a range of interaction larger than the sample size, the a result of blockade. This can be clearly observed in the experiment: presence of one excitation shifts all other atoms out of resonance; Fig. 2 shows pronounced anti-bunching, in good agreement with a therefore only one excitation can be created at a time. Changing theoretical rate model (Methods and Supplementary Information). the size or the driving conditions restores the underlying many- We extrapolate a value of g .2/.0/ D 0.08 0.06, taking into account body nature, and the presence of several excited atoms with an uncorrelated background signal (see Methods). The background pronounced correlations becomes possible. This tunability and the constitutes 10–15% of the signal and originates from atoms which possibility of multiple usage within a single experimental sequence are not removed during the preparation of the superatom. The make superatoms a promising complement to single-atom-based anti-bunching amplitude stays constant during the gradual decay of quantum technology. It is therefore important to understand the the superatom, which thus acts as a continuously operating single- significance of the superatom concept, the implications of its finite ion source12. The strong suppression of collective oscillations, spatial extent and its many-body level structure. Here we investigate indicated by the purely exponential shape of g .2/(τ/, shows that the the latter by measuring the mean Rydberg excitation as well as system is in the overdamped regime, where the coherent coupling its time-resolved two-particle correlations in an optically excited, is overcome by decoherence from the laser linewidth, thermal mesoscopic superatom for varying excitation strength and under motion of atoms and residual field fluctuations as well as intrinsic resonant and non-resonant conditions, revealing very different dephasing mechanisms13. excitation dynamics. The ability to adjust the size of the atomic sample allows a The realization of superatom-based quantum systems requires continuous transition from the superatom limit to a many-body the implementation of arbitrary arrangements of isolated meso- system, where blockade conditions break down. First, this can be scopic atomic ensembles in a scalable way. Here we prepare an used to determine the blockade radius. In Fig. 3a the initial ion rate individual superatom by carefully shaping the density distribution per atom is shown for increasing axial size l of the sample, keeping Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany. †Present addresses: LNE-SYRTE, Observatoire de Paris, CNRS, UPMC, 61 avenue de l’Observatoire, 75014 Paris, France (V.G.); Laboratoire Kastler Brossel, ENS, UPMC-Paris 6, CNRS, 24 rue Lhomond, 75005 Paris, France (G.B.). *e-mail: [email protected] NATURE PHYSICS | VOL 11 | FEBRUARY 2015 | www.nature.com/naturephysics 157 © 2015 Macmillan Publishers Limited. All rights reserved LETTERS NATURE PHYSICS DOI: 10.1038/NPHYS3214 ab c ∼ 6 d U 1/R Γ |rr〉 2 ion Ω Ω Δ Γ |rg〉 ion Ω Ω 2 μm |gg〉 10 μm 0 rB R Figure 1 | Preparation of superatoms and excitation level scheme. a, Starting from a Bose–Einstein condensate in an optical dipole trap with superimposed optical lattice (left) the atoms are radially compressed (middle) and removed from all but a few lattice sites with the help of a focused electron beam (right). b, The resulting—almost spherical—atomic sample contains between 100 and 500 atoms at a temperature of 3–4 µK and dimensions smaller than 3 µm (4σ of a Gaussian fit) in each direction. The axial size of this atomic sample can be varied arbitrarily. c, The superatom is excited with a single-photon transition (λD297 nm) into the j51p3=2i state. Eective three-level scheme, comprising the ground state, the singly excited state and the doubly excited state, whose energy has a dependence on r−6 owing to the van der Waals interaction. Black (blue) arrows denote (o-)resonant excitation and the blockade radius rB is denoted by the excitation linewidth (grey shaded area). The decay due to ionization and the ion detection are also indicated. R, interatomic distance. d, A one-dimensional array of superatoms, demonstrating the scalability of our approach. 1.1 j51p3=2,1=2, 51p3=2,1=2i pair state, which is energetically separated by 1.0 an external magnetic field of 35 G, the potential curves which have 0.9 a negative C6 coefficient for large distances bend into a repulsive 35 interaction for smaller distances. Thus, the interaction potential for 0.8 all angles becomes repulsive, enabling an overall blockade. 30 0.7 To describe the complex interaction potential structure in an 25 τ 0.6 effective but simple way, we assume an isotropic repulsive inter- () 20 (2) action and solve the many-body problem within an approximate g 0.5 15 rate equation model with a C eff coefficient as the only free pa- 0.4 6 Ion rate (kHz) 10 rameter (see Methods). We chose a van der Waals coefficient of 0.3 eff= D C48 6 5 C6 2π 16−10 MHzµm to compare the model to the experimental 0.2 0 results. The resulting potential curves are indicated by the green 02468101214161820 0.1 shaded area in Fig. 3b. Throughout this paper, we apply the effective t (ms) model with these parameters to our data and find good agreement 0.0 0 20 40 60 80 100 over a wide range of laser intensities and detunings. τ (μs) Our mesoscopic superatom permits inter-atomic distances R of up to ≈3 µm. As a consequence, when the excitation is off-resonant Figure 2 | Resonant excitation of an isolated superatom. a, Second-order the blockade conditions can be tuned into an anti-blockade14 and temporal correlation function of ions emitted from the resonantly excited pronounced bunching of the ion emission can be observed (Fig. 4a). superatom (Ω=2πD6 kHz, blue circles). Data points are fitted with an We find bunching values of up to g .2/.0/D618 for large detunings. exponential function (blue curve), revealing a value of This behaviour can be understood from the full level structure of g(2)(0)D0.080.06. The black line and the grey shaded area result from a the mesoscopic superatom, including excited states with more than rate model (see Methods and Supplementary Information). The inset one excitation, and is captured well by our rate model: whereas the shows the data as well as the model curves of the absolute ion rate as a transition to the first collective Rydberg state is out of resonance, function of time.