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Cong I, Maskara N, Tran MC, Pichler H, Semeghini G, Yelin SF, Choi S, Lukin MD. Enhancing detection of topological order by local error correction. Nat Commun 2024; 15:1527. [PMID: 38378727 PMCID: PMC10879205 DOI: 10.1038/s41467-024-45584-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2023] [Accepted: 01/25/2024] [Indexed: 02/22/2024] Open
Abstract
The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a paradigm for quantifying topological states-locally error-corrected decoration (LED)-by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations. We subsequently apply it to an experimental realization, providing new insights into a quantum spin liquid created on a Rydberg-atom simulator. Finally, we extend LED to generic topological phases, including those with non-abelian order.
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Affiliation(s)
- Iris Cong
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Nishad Maskara
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Minh C Tran
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Hannes Pichler
- Institute for Theoretical Physics, University of Innsbruck, 6020, Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020, Innsbruck, Austria
| | - Giulia Semeghini
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Susanne F Yelin
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Soonwon Choi
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA.
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2
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Bluvstein D, Evered SJ, Geim AA, Li SH, Zhou H, Manovitz T, Ebadi S, Cain M, Kalinowski M, Hangleiter D, Bonilla Ataides JP, Maskara N, Cong I, Gao X, Sales Rodriguez P, Karolyshyn T, Semeghini G, Gullans MJ, Greiner M, Vuletić V, Lukin MD. Logical quantum processor based on reconfigurable atom arrays. Nature 2024; 626:58-65. [PMID: 38056497 PMCID: PMC10830422 DOI: 10.1038/s41586-023-06927-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2023] [Accepted: 12/01/2023] [Indexed: 12/08/2023]
Abstract
Suppressing errors is the central challenge for useful quantum computing1, requiring quantum error correction (QEC)2-6 for large-scale processing. However, the overhead in the realization of error-corrected 'logical' qubits, in which information is encoded across many physical qubits for redundancy2-4, poses substantial challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Using logical-level control and a zoned architecture in reconfigurable neutral-atom arrays7, our system combines high two-qubit gate fidelities8, arbitrary connectivity7,9, as well as fully programmable single-qubit rotations and mid-circuit readout10-15. Operating this logical processor with various types of encoding, we demonstrate improvement of a two-qubit logic gate by scaling surface-code6 distance from d = 3 to d = 7, preparation of colour-code qubits with break-even fidelities5, fault-tolerant creation of logical Greenberger-Horne-Zeilinger (GHZ) states and feedforward entanglement teleportation, as well as operation of 40 colour-code qubits. Finally, using 3D [[8,3,2]] code blocks16,17, we realize computationally complex sampling circuits18 with up to 48 logical qubits entangled with hypercube connectivity19 with 228 logical two-qubit gates and 48 logical CCZ gates20. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical-qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling21,22. These results herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors.
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Affiliation(s)
- Dolev Bluvstein
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Simon J Evered
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Sophie H Li
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Hengyun Zhou
- Department of Physics, Harvard University, Cambridge, MA, USA
- QuEra Computing Inc., Boston, MA, USA
| | - Tom Manovitz
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Sepehr Ebadi
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Madelyn Cain
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Dominik Hangleiter
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD, USA
| | | | - Nishad Maskara
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Iris Cong
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Xun Gao
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | | | - Giulia Semeghini
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
| | - Michael J Gullans
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Vladan Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, MA, USA.
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3
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Evered SJ, Bluvstein D, Kalinowski M, Ebadi S, Manovitz T, Zhou H, Li SH, Geim AA, Wang TT, Maskara N, Levine H, Semeghini G, Greiner M, Vuletić V, Lukin MD. High-fidelity parallel entangling gates on a neutral-atom quantum computer. Nature 2023; 622:268-272. [PMID: 37821591 PMCID: PMC10567572 DOI: 10.1038/s41586-023-06481-y] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 07/25/2023] [Indexed: 10/13/2023]
Abstract
The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing1. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits2,3 and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture4. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions5. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction6,7. Our method uses fast, single-pulse gates based on optimal control8, atomic dark states to reduce scattering9 and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications10,11, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates12,13. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms14, error-corrected circuits7 and digital simulations15.
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Affiliation(s)
- Simon J Evered
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Dolev Bluvstein
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Sepehr Ebadi
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Tom Manovitz
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Hengyun Zhou
- Department of Physics, Harvard University, Cambridge, MA, USA
- QuEra Computing Inc., Boston, MA, USA
| | - Sophie H Li
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Tout T Wang
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Nishad Maskara
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Harry Levine
- Department of Physics, Harvard University, Cambridge, MA, USA
- AWS Center for Quantum Computing, Pasadena, CA, USA
| | - Giulia Semeghini
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Vladan Vuletić
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, MA, USA.
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4
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Ebadi S, Keesling A, Cain M, Wang TT, Levine H, Bluvstein D, Semeghini G, Omran A, Liu JG, Samajdar R, Luo XZ, Nash B, Gao X, Barak B, Farhi E, Sachdev S, Gemelke N, Zhou L, Choi S, Pichler H, Wang ST, Greiner M, Vuletic V, Lukin MD. Quantum optimization of maximum independent set using Rydberg atom arrays. Science 2022; 376:1209-1215. [PMID: 35511943 DOI: 10.1126/science.abo6587] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find the problem hardness is controlled by the solution degeneracy and number of local minima, and experimentally benchmark the quantum algorithm's performance against classical simulated annealing. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions in the deep circuit regime and analyze its origins.
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Affiliation(s)
- S Ebadi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Keesling
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - M Cain
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - T T Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Levine
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - D Bluvstein
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - G Semeghini
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Omran
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - J-G Liu
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - R Samajdar
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - X-Z Luo
- QuEra Computing Inc., Boston, MA 02135, USA.,Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada.,Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - B Nash
- School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA
| | - X Gao
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - B Barak
- School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA
| | - E Farhi
- Google Quantum AI, Venice, CA 90291, USA.,Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - S Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA
| | - N Gemelke
- QuEra Computing Inc., Boston, MA 02135, USA
| | - L Zhou
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - S Choi
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - H Pichler
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria.,Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - S-T Wang
- QuEra Computing Inc., Boston, MA 02135, USA
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | | | - M D Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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5
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Bluvstein D, Levine H, Semeghini G, Wang TT, Ebadi S, Kalinowski M, Keesling A, Maskara N, Pichler H, Greiner M, Vuletić V, Lukin MD. A quantum processor based on coherent transport of entangled atom arrays. Nature 2022; 604:451-456. [PMID: 35444318 PMCID: PMC9021024 DOI: 10.1038/s41586-022-04592-6] [Citation(s) in RCA: 54] [Impact Index Per Article: 27.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2021] [Accepted: 02/28/2022] [Indexed: 11/23/2022]
Abstract
The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is key for building scalable quantum information systems1,2. In most state-of-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here we demonstrate a quantum processor with dynamic, non-local connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, between layers of single- and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation3–5. We use this architecture to realize programmable generation of entangled graph states, such as cluster states and a seven-qubit Steane code state6,7. Furthermore, we shuttle entangled ancilla arrays to realize a surface code state with thirteen data and six ancillary qubits8 and a toric code state on a torus with sixteen data and eight ancillary qubits9. Finally, we use this architecture to realize a hybrid analogue–digital evolution2 and use it for measuring entanglement entropy in quantum simulations10–12, experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars13,14. Realizing a long-standing goal, these results provide a route towards scalable quantum processing and enable applications ranging from simulation to metrology. A quantum processer is realized using arrays of neutral atoms that are transported in a parallel manner by optical tweezers during computations, and used for quantum error correction and simulations.
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Affiliation(s)
- Dolev Bluvstein
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Harry Levine
- Department of Physics, Harvard University, Cambridge, MA, USA.,AWS Center for Quantum Computing, Pasadena, CA, USA
| | | | - Tout T Wang
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Sepehr Ebadi
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Alexander Keesling
- Department of Physics, Harvard University, Cambridge, MA, USA.,QuEra Computing Inc., Boston, MA, USA
| | - Nishad Maskara
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Hannes Pichler
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck, Austria.,Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Vladan Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, MA, USA.
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6
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Semeghini G, Levine H, Keesling A, Ebadi S, Wang TT, Bluvstein D, Verresen R, Pichler H, Kalinowski M, Samajdar R, Omran A, Sachdev S, Vishwanath A, Greiner M, Vuletić V, Lukin MD. Probing topological spin liquids on a programmable quantum simulator. Science 2021; 374:1242-1247. [PMID: 34855494 DOI: 10.1126/science.abi8794] [Citation(s) in RCA: 64] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
[Figure: see text].
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Affiliation(s)
- G Semeghini
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Levine
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Keesling
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing, Boston, MA 02135, USA
| | - S Ebadi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - T T Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - D Bluvstein
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - R Verresen
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Pichler
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria.,Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - M Kalinowski
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - R Samajdar
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Omran
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing, Boston, MA 02135, USA
| | - S Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA
| | - A Vishwanath
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - V Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - M D Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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7
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Masi L, Petrucciani T, Ferioli G, Semeghini G, Modugno G, Inguscio M, Fattori M. Spatial Bloch Oscillations of a Quantum Gas in a "Beat-Note" Superlattice. Phys Rev Lett 2021; 127:020601. [PMID: 34296908 DOI: 10.1103/physrevlett.127.020601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Revised: 03/17/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
We report the experimental realization of a new kind of optical lattice for ultracold atoms where arbitrarily large separation between the sites can be achieved without renouncing to the stability of ordinary lattices. Two collinear lasers, with slightly different commensurate wavelengths and retroreflected on a mirror, generate a superlattice potential with a periodic "beat-note" profile where the regions with large amplitude modulation provide the effective potential minima for the atoms. To prove the analogy with a standard large spacing optical lattice we study Bloch oscillations of a Bose Einstein condensate with negligible interactions in the presence of a small force. The observed dynamics between sites separated by ten microns for times exceeding one second proves the high stability of the potential. This novel lattice is the ideal candidate for the coherent manipulation of atomic samples at large spatial separations and might find direct application in atom-based technologies like trapped-atom interferometers and quantum simulators.
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Affiliation(s)
- L Masi
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - T Petrucciani
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
| | - G Ferioli
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - G Semeghini
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - G Modugno
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Department of Physics and Astronomy, University of Florence, 50019 Sesto Fiorentino, Italy
| | - M Inguscio
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy
| | - M Fattori
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Department of Physics and Astronomy, University of Florence, 50019 Sesto Fiorentino, Italy
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8
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Bluvstein D, Omran A, Levine H, Keesling A, Semeghini G, Ebadi S, Wang TT, Michailidis AA, Maskara N, Ho WW, Choi S, Serbyn M, Greiner M, Vuletić V, Lukin MD. Controlling quantum many-body dynamics in driven Rydberg atom arrays. Science 2021; 371:1355-1359. [PMID: 33632894 DOI: 10.1126/science.abg2530] [Citation(s) in RCA: 46] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Accepted: 02/12/2021] [Indexed: 11/02/2022]
Abstract
The control of nonequilibrium quantum dynamics in many-body systems is challenging because interactions typically lead to thermalization and a chaotic spreading throughout Hilbert space. We investigate nonequilibrium dynamics after rapid quenches in a many-body system composed of 3 to 200 strongly interacting qubits in one and two spatial dimensions. Using a programmable quantum simulator based on Rydberg atom arrays, we show that coherent revivals associated with so-called quantum many-body scars can be stabilized by periodic driving, which generates a robust subharmonic response akin to discrete time-crystalline order. We map Hilbert space dynamics, geometry dependence, phase diagrams, and system-size dependence of this emergent phenomenon, demonstrating new ways to steer complex dynamics in many-body systems and enabling potential applications in quantum information science.
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Affiliation(s)
- D Bluvstein
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Omran
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - H Levine
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Keesling
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - G Semeghini
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - S Ebadi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - T T Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | | | - N Maskara
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - W W Ho
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,Department of Physics, Stanford University, Stanford, CA 94305, USA
| | - S Choi
- Department of Physics, University of California Berkeley, Berkeley, CA 94720, USA
| | - M Serbyn
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - V Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - M D Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.
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9
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Omran A, Levine H, Keesling A, Semeghini G, Wang TT, Ebadi S, Bernien H, Zibrov AS, Pichler H, Choi S, Cui J, Rossignolo M, Rembold P, Montangero S, Calarco T, Endres M, Greiner M, Vuletić V, Lukin MD. Generation and manipulation of Schrödinger cat states in Rydberg atom arrays. Science 2020; 365:570-574. [PMID: 31395778 DOI: 10.1126/science.aax9743] [Citation(s) in RCA: 88] [Impact Index Per Article: 22.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2019] [Accepted: 07/08/2019] [Indexed: 11/03/2022]
Abstract
Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging because such states are extremely fragile. Using a programmable quantum simulator based on neutral atom arrays with interactions mediated by Rydberg states, we demonstrate the creation of "Schrödinger cat" states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 20 qubits. Our approach is based on engineering the energy spectrum and using optimal control of the many-body system. We further demonstrate entanglement manipulation by using GHZ states to distribute entanglement to distant sites in the array, establishing important ingredients for quantum information processing and quantum metrology.
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Affiliation(s)
- A Omran
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Levine
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Keesling
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - G Semeghini
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - T T Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,Department of Physics, Gordon College, Wenham, MA 01984, USA
| | - S Ebadi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Bernien
- Institute for Molecular Engineering, University of Chicago, Chicago, IL 60637, USA
| | - A S Zibrov
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Pichler
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,Institute for Theoretical Atomic Molecular and Optical Physics (ITAMP), Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA
| | - S Choi
- Department of Physics, University of California, Berkeley, Berkeley, CA 94720, USA
| | - J Cui
- Forschungszentrum Jülich, Institute of Quantum Control (PGI-8), D-52425 Jülich, Germany
| | - M Rossignolo
- Institute for Quantum Optics and Center of Integrated Quantum Science and Technology (IQST), Universität Ulm, D-89081 Ulm, Germany
| | - P Rembold
- Forschungszentrum Jülich, Institute of Quantum Control (PGI-8), D-52425 Jülich, Germany
| | - S Montangero
- Dipartimento di Fisica e Astronomia "G. Galilei," Università degli Studi di Padova and Istituto Nazionale di Fisica Nucleare (INFN), I-35131 Padova, Italy
| | - T Calarco
- Forschungszentrum Jülich, Institute of Quantum Control (PGI-8), D-52425 Jülich, Germany.,Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
| | - M Endres
- Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - V Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - M D Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.
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10
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Levine H, Keesling A, Semeghini G, Omran A, Wang TT, Ebadi S, Bernien H, Greiner M, Vuletić V, Pichler H, Lukin MD. Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms. Phys Rev Lett 2019; 123:170503. [PMID: 31702233 DOI: 10.1103/physrevlett.123.170503] [Citation(s) in RCA: 64] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2019] [Indexed: 06/10/2023]
Abstract
We report the implementation of universal two- and three-qubit entangling gates on neutral-atom qubits encoded in long-lived hyperfine ground states. The gates are mediated by excitation to strongly interacting Rydberg states and are implemented in parallel on several clusters of atoms in a one-dimensional array of optical tweezers. Specifically, we realize the controlled-phase gate, enacted by a novel, fast protocol involving only global coupling of two qubits to Rydberg states. We benchmark this operation by preparing Bell states with fidelity F≥95.0(2)%, and extract gate fidelity ≥97.4(3)%, averaged across five atom pairs. In addition, we report a proof-of-principle implementation of the three-qubit Toffoli gate, in which two control atoms simultaneously constrain the behavior of one target atom. These experiments demonstrate key ingredients for high-fidelity quantum information processing in a scalable neutral-atom platform.
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Affiliation(s)
- Harry Levine
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Alexander Keesling
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Giulia Semeghini
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Ahmed Omran
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Tout T Wang
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Physics, Gordon College, Wenham, Massachusetts 01984, USA
| | - Sepehr Ebadi
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Hannes Bernien
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Vladan Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Hannes Pichler
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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11
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Ferioli G, Semeghini G, Masi L, Giusti G, Modugno G, Inguscio M, Gallemí A, Recati A, Fattori M. Collisions of Self-Bound Quantum Droplets. Phys Rev Lett 2019; 122:090401. [PMID: 30932536 DOI: 10.1103/physrevlett.122.090401] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2018] [Indexed: 06/09/2023]
Abstract
We report on the study of binary collisions between quantum droplets formed by an attractive mixture of ultracold atoms. We distinguish two main outcomes of the collision, i.e., merging and separation, depending on the velocity of the colliding pair. The critical velocity v_{c} that discriminates between the two cases displays a different dependence on the atom number N for small and large droplets. By comparing our experimental results with numerical simulations, we show that the nonmonotonic behavior of v_{c}(N) is due to the crossover from a compressible to an incompressible regime, where the collisional dynamics is governed by different energy scales, i.e., the droplet binding energy and the surface tension. These results also provide the first evidence of the liquidlike nature of quantum droplets in the large N limit, where their behavior closely resembles that of classical liquid droplets.
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Affiliation(s)
- Giovanni Ferioli
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - Giulia Semeghini
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - Leonardo Masi
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - Giovanni Giusti
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - Giovanni Modugno
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - Massimo Inguscio
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - Albert Gallemí
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
- Trento Institute for Fundamental Physics and Applications, INFN, 38123, Trento, Italy
| | - Alessio Recati
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
- Trento Institute for Fundamental Physics and Applications, INFN, 38123, Trento, Italy
| | - Marco Fattori
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
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12
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Semeghini G, Ferioli G, Masi L, Mazzinghi C, Wolswijk L, Minardi F, Modugno M, Modugno G, Inguscio M, Fattori M. Self-Bound Quantum Droplets of Atomic Mixtures in Free Space. Phys Rev Lett 2018; 120:235301. [PMID: 29932719 DOI: 10.1103/physrevlett.120.235301] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2017] [Indexed: 06/08/2023]
Abstract
Self-bound quantum droplets are a newly discovered phase in the context of ultracold atoms. In this Letter, we report their experimental realization following the original proposal by Petrov [Phys. Rev. Lett. 115, 155302 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.155302], using an attractive bosonic mixture. In this system, spherical droplets form due to the balance of competing attractive and repulsive forces, provided by the mean-field energy close to the collapse threshold and the first-order correction due to quantum fluctuations. Thanks to an optical levitating potential with negligible residual confinement, we observe self-bound droplets in free space, and we characterize the conditions for their formation as well as their size and composition. This work sets the stage for future studies on quantum droplets, from the measurement of their peculiar excitation spectrum to the exploration of their superfluid nature.
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Affiliation(s)
- G Semeghini
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - G Ferioli
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - L Masi
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - C Mazzinghi
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - L Wolswijk
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - F Minardi
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
- Dipartimento di Fisica e Astronomia, Università di Bologna, 40127 Bologna, Italy
| | - M Modugno
- Departamento de Física Teórica e Historia de la Ciencia, Universidad del Pais Vasco UPV/EHU, 48080 Bilbao, Spain
- IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
| | - G Modugno
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - M Inguscio
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - M Fattori
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
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13
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Trenkwalder A, Spagnolli G, Semeghini G, Coop S, Landini M, Castilho P, Pezzè L, Modugno G, Inguscio M, Smerzi A, Fattori M. Quantum Phase Transitions with Parity-Symmetry Breaking and Hysteresis. Nat Phys 2016; 12:826-829. [PMID: 27610189 PMCID: PMC5011422 DOI: 10.1038/nphys3743] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2015] [Accepted: 03/24/2016] [Indexed: 06/02/2023]
Abstract
Symmetry-breaking quantum phase transitions play a key role in several condensed matter, cosmology and nuclear physics theoretical models1-3. Its observation in real systems is often hampered by finite temperatures and limited control of the system parameters. In this work we report for the first time the experimental observation of the full quantum phase diagram across a transition where the spatial parity symmetry is broken. Our system is made of an ultra-cold gas with tunable attractive interactions trapped in a spatially symmetric double-well potential. At a critical value of the interaction strength, we observe a continuous quantum phase transition where the gas spontaneously localizes in one well or the other, thus breaking the underlying symmetry of the system. Furthermore, we show the robustness of the asymmetric state against controlled energy mismatch between the two wells. This is the result of hysteresis associated with an additional discontinuous quantum phase transition that we fully characterize. Our results pave the way to the study of quantum critical phenomena at finite temperature4, the investigation of macroscopic quantum tunneling of the order parameter in the hysteretic regime and the production of strongly quantum entangled states at critical points5.
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Affiliation(s)
- A Trenkwalder
- Istituto Nazionale di Ottica-CNR, 50019 Sesto Fiorentino, Italy
| | - G Spagnolli
- LENS European Laboratory for Nonlinear Spectroscopy, and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - G Semeghini
- LENS European Laboratory for Nonlinear Spectroscopy, and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - S Coop
- LENS European Laboratory for Nonlinear Spectroscopy, and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy; ICFO-Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - M Landini
- Istituto Nazionale di Ottica-CNR, 50019 Sesto Fiorentino, Italy
| | - P Castilho
- Istituto Nazionale di Ottica-CNR, 50019 Sesto Fiorentino, Italy; Instituto de Física de São Carlos, Universidade de São Paulo, C.P. 369, 13560-970, São Carlos, São Paulo, Brazil
| | - L Pezzè
- Istituto Nazionale di Ottica-CNR, 50019 Sesto Fiorentino, Italy; LENS European Laboratory for Nonlinear Spectroscopy, and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy; Quantum Science and Technology in Arcetri, QSTAR, 50125 Firenze, Italy
| | - G Modugno
- LENS European Laboratory for Nonlinear Spectroscopy, and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - M Inguscio
- Istituto Nazionale di Ottica-CNR, 50019 Sesto Fiorentino, Italy; LENS European Laboratory for Nonlinear Spectroscopy, and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - A Smerzi
- Istituto Nazionale di Ottica-CNR, 50019 Sesto Fiorentino, Italy; LENS European Laboratory for Nonlinear Spectroscopy, and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy; Quantum Science and Technology in Arcetri, QSTAR, 50125 Firenze, Italy
| | - M Fattori
- Istituto Nazionale di Ottica-CNR, 50019 Sesto Fiorentino, Italy; LENS European Laboratory for Nonlinear Spectroscopy, and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
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14
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Roy S, Landini M, Trenkwalder A, Semeghini G, Spagnolli G, Simoni A, Fattori M, Inguscio M, Modugno G. Test of the universality of the three-body Efimov parameter at narrow Feshbach resonances. Phys Rev Lett 2013; 111:053202. [PMID: 23952396 DOI: 10.1103/physrevlett.111.053202] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2013] [Indexed: 06/02/2023]
Abstract
We measure the critical scattering length for the appearance of the first three-body bound state, or Efimov three-body parameter, at seven different Feshbach resonances in ultracold ^{39}K atoms. We study both intermediate and narrow resonances, where the three-body spectrum is expected to be determined by the nonuniversal coupling of two scattering channels. Instead, our observed ratio of the three-body parameter with the van der Waals radius is approximately the same universal ratio as for broader resonances. This unexpected observation suggests the presence of a new regime for three-body scattering at narrow resonances.
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Affiliation(s)
- Sanjukta Roy
- LENS and Dipartimento di Fisica e Astronomia, Universitá di Firenze, and Istituto Nazionale di Ottica, CNR, 50019 Sesto Fiorentino, Italy
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