Microscopic Characterization of Scalable Coherent Rydberg Superatoms

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Microscopic Characterization of Scalable Coherent Rydberg Superatoms

Johannes Zeiher, Peter Schauß, Sebastian Hild, Tommaso Macrì, Immanuel Bloch, and Christian Gross

Phys. Rev. X 5, 031015 – Published 12 August 2015

Abstract

Strong interactions can amplify quantum effects such that they become important on macroscopic scales. Controlling these coherently on a single-particle level is essential for the tailored preparation of strongly correlated quantum systems and opens up new prospects for quantum technologies. Rydberg atoms offer such strong interactions, which lead to extreme nonlinearities in laser-coupled atomic ensembles. As a result, multiple excitation of a micrometer-sized cloud can be blocked while the light-matter coupling becomes collectively enhanced. The resulting two-level system, often called a “superatom,” is a valuable resource for quantum information, providing a collective qubit. Here, we report on the preparation of 2 orders of magnitude scalable superatoms utilizing the large interaction strength provided by Rydberg atoms combined with precise control of an ensemble of ultracold atoms in an optical lattice. The latter is achieved with sub-shot-noise precision by local manipulation of a two-dimensional Mott insulator. We microscopically confirm the superatom picture by in situ detection of the Rydberg excitations and observe the characteristic square-root scaling of the optical coupling with the number of atoms. Enabled by the full control over the atomic sample, including the motional degrees of freedom, we infer the overlap of the produced many-body state with a $W$ state from the observed Rabi oscillations and deduce the presence of entanglement. Finally, we investigate the breakdown of the superatom picture when two Rydberg excitations are present in the system, which leads to dephasing and a loss of coherence.

Received 6 March 2015

DOI:https://doi.org/10.1103/PhysRevX.5.031015

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Johannes Zeiher^1,*, Peter Schauß¹, Sebastian Hild¹, Tommaso Macrì², Immanuel Bloch^1,3, and Christian Gross¹

¹Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
²QSTAR, Largo Enrico Fermi 2, 50125 Firenze, Italy
³Ludwig-Maximilians-Universität, Fakultät für Physik, 80799 München, Germany

^*johannes.zeiher@mpq.mpg.de

Popular Summary

Understanding and controlling complex quantum systems is a prerequisite for future quantum technologies, which is one of the fundamental challenges in modern physics. In particular, strongly interacting systems are most interesting but also the hardest to handle. Rydberg atoms—highly exited atoms in strongly polarizable states—exhibit enormously strong interactions. When a micrometer-sized sample, containing up to hundreds of atoms, is illuminated by laser light, this interaction induces an extreme nonlinearity, blocking all but a single Rydberg excitation. As a result, the many-body system behaves collectively as if it was a single two-level “superatom.” We coherently manipulate such superatoms, whose constituent atoms are controlled in all degrees of freedom. By precisely selecting the sample size, we demonstrate scalable superatoms containing between a few and approximately 200 atoms. Our direct, single-atom-sensitive detection method enables us to infer the presence of entanglement in the collective system.

We employ an ensemble of ultracold rubidium-87 atoms in an optical lattice in which only one atom occupies each lattice site. A red and a blue laser are used to excite the atoms to a Rydberg state chosen such that the dipole blockade radius is larger than the system size. In addition, we ensure this by preparing the system size with single-lattice-site precision, such that only a single excitation can be present among multiple atomic absorbers (i.e., the excited Rydberg state, which persists for only a few millionths of a second, is shared among all atoms). Using a special optical microscope with single-atom-sensitive detection, we shed light on the spatial structure of the superatom and confirm its entangled nature. Since there is redundant storage of information in each of the constituent atoms, our system is more robust to data loss than a single-atom absorber.

We expect that our results will be important for the advance of Rydberg-based quantum information applications and especially systems based on collective qubits that feature enhanced light-matter coupling.

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Vol. 5, Iss. 3 — July - September 2015

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Figure 1
Superatom preparation. (a) Illustration of the symmetric ground and singly excited state ( $W$ state). Left: $N$ -atom collective Bloch sphere with its basis states (labeled by excitation numbers $n_{e}$ ) and coupled states highlighted [south pole ( $n_{e} = 0$ ) and singly excited state ( $n_{e} = 1$ ), represented by the red plane]. The small pictograms above and below the sphere depict the lattice system with atoms in the ground (red) and Rydberg (blue) states. The dashed red line indicates a zoom into the subspace spanned by the lowest two states. The Husimi distribution of these states and their enhanced coupling $Ω_{N}$ is shown in the center. This accessible state space defines a superatom represented by the standard Bloch sphere on the right. (b) Atom-number histograms of the initially prepared samples (blue bars) with Gaussian fits (solid green line). The numbers give the mean and standard deviation for each data set. Measured and reconstructed occupation of lattice for exemplary initial states is depicted above the respective histograms; see the schematic pictograms in (a). The Poissonian distribution with the same mean atom number is shown as a reference (dashed green line). (c) Averaged initial ground-state atom distributions for the respective histograms above. The size of blockade radius $R_{b}$ is shown by the blue bar. (d) Rabi oscillation data (blue points) and sinusoidal fits with exponentially decaying contrast (solid gray line) for $N = 7.7 (2.2)$ and $N = 131 (7)$ . The red line shows the same fit on an axis scaled to the number of ground-state atoms $N$ (right axis). All error bars denote the standard error of the mean (s.e.m.).
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Figure 2
Collective Rabi oscillations. (a) Collective Rabi oscillation data of the mean Rydberg atom number $N_{e}$ (blue points) for different numbers of ground-state atoms $N = 185 (8)$ , 84(6), 42(4), 20(3), 0.74(0.60) (top to bottom) with exponentially decaying sinusoidal fits (gray). All error bars are s.e.m. (b) Density of detected Rydberg atoms for the data sets in (a) with normalized vertically or horizontally averaged density (solid blue line) compared to the initial state atom distributions (solid red line). (c) Histograms of the Rydberg excitation number integrated over the total oscillation (blue bars) and at the position of the first maximum [orange bars, position in (a) marked by solid orange line].
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Figure 3
Scaling of the Rabi frequency and entanglement. (a) Extracted values of $Ω_{N}$ (blue points) versus average initial atom number $N$ for the data shown in Figs. 1 and 2 with a power-law fit (green line). The inset shows the exponential decay time of the Rabi oscillations (blue points). The expected decay based on the reference sample atom-number fluctuations (dark green shading) and additionally taking into account noise in the pulse area (light green shading) are shown for comparison. (b) Extracted oscillation amplitude $C$ of the collective Rabi oscillation versus atom number $N$ after one, three, and five half cycles of oscillation (red data points with increasing lightness, shifted slightly horizontally for better visibility). The gray points show the oscillation amplitude after one half cycle corrected for the measured detection efficiency. The blue shaded area bounded by the lowest blue line includes all classical states with fully separable density matrices. Different bounds for $k$ -particle separability are additionally shown by the blue lines. Error bars in (a) take experimental day-to-day variations of the single-atom Rabi frequency $Ω$ (10%) and the detuning ( $\pm 200 kHz$ ) into account. All error bars in (b) are $1 σ$ statistical uncertainty from the fits.
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Figure 4
Superatom Ramsey spectroscopy. Evolution of the mean Rydberg atom number $N_{e}$ (blue points) versus hold time $T_{R}$ between the two $π / 2$ pulses (schematic in the inset) and sinusoidal fit with Gaussian decay (gray line) for an initial sample size of $N = 38 (3)$ atoms. All error bars are s.e.m.
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Figure 5
Breakdown of the blockade. Measurement of the collective Rabi oscillation in a sample with $N = 185 (8)$ atoms. (a) The contribution of states with $n_{e} = 1$ (blue points) and $n_{e} = 2$ (red points, shifted slightly horizontally for better visibility) agrees with the theoretical calculation (green and orange solid lines, scaled by extracted detection efficiency $η$ ). For comparison, we show the fit (gray line) to the mean (see Fig. 2), which shows twice faster dephasing than the $n_{e} = 1$ subspace alone. We have chosen the simplest possible fitting model with a constant offset such that the increasing fraction of double excitation results in a upward shift of the fit for small times. The inset shows two exemplary single shots with $n_{e} = 2$ (field of view $14 \times 14 μ m^{2}$ , indicated by gray bar) and the two-dimensional pair-correlation function $C_{i, j}$ of all $n_{e} = 2$ events. Color scale: red (anticorrelation) to blue (correlation). Data binned $4 \times 4$ sites. All error bars are s.e.m.
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