1
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Cao A, Yelin TL, Eckner WJ, Oppong ND, Kaufman AM. Autoionization-Enhanced Rydberg Dressing by Fast Contaminant Removal. PHYSICAL REVIEW LETTERS 2025; 134:133201. [PMID: 40250344 DOI: 10.1103/physrevlett.134.133201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2024] [Accepted: 03/04/2025] [Indexed: 04/20/2025]
Abstract
Rydberg dressing is a powerful tool for entanglement generation in long-lived atomic states. While already employed effectively in several demonstrations, a key challenge for this technique is the collective loss triggered by blackbody-radiation-driven transitions to contaminant Rydberg states of opposite parity. We demonstrate the rapid removal of such contaminants using autoionization (AI) transitions found in alkaline-earth-like atoms. The AI is shown to be compatible with coherent operation of an array of optical clock qubits. By incorporating AI pulses into a stroboscopic Rydberg dressing (SRD) sequence, we enhance lifetimes by an order of magnitude for system sizes of up to 144 atoms, while maintaining an order of magnitude larger duty cycle than previously achieved. To highlight the utility of our approach, we use the AI-enhanced SRD protocol to improve the degree of achieved spin-squeezing during early time dressing dynamics. These results bring Rydberg dressing lifetimes closer to fundamental limits, opening the door to previously infeasible dressing proposals.
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Affiliation(s)
- Alec Cao
- University of Colorado, National Institute of Standards and Technology, JILA, University of Colorado and , and Department of Physics, Boulder, Colorado 80309, USA
| | - Theodor Lukin Yelin
- University of Colorado, National Institute of Standards and Technology, JILA, University of Colorado and , and Department of Physics, Boulder, Colorado 80309, USA
| | - William J Eckner
- University of Colorado, National Institute of Standards and Technology, JILA, University of Colorado and , and Department of Physics, Boulder, Colorado 80309, USA
| | - Nelson Darkwah Oppong
- University of Colorado, National Institute of Standards and Technology, JILA, University of Colorado and , and Department of Physics, Boulder, Colorado 80309, USA
| | - Adam M Kaufman
- University of Colorado, National Institute of Standards and Technology, JILA, University of Colorado and , and Department of Physics, Boulder, Colorado 80309, USA
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2
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Tu HT, Liao KY, Wang HL, Zhu YF, Qiu SY, Jiang H, Huang W, Bian W, Yan H, Zhu SL. Approaching the standard quantum limit of a Rydberg-atom microwave electrometer. SCIENCE ADVANCES 2024; 10:eads0683. [PMID: 39705347 DOI: 10.1126/sciadv.ads0683] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2024] [Accepted: 11/15/2024] [Indexed: 12/22/2024]
Abstract
The development of a microwave electrometer with inherent uncertainty approaching its ultimate limit carries both fundamental and technological significance. However, because of the thermal motion of atoms, the state-of-art Rydberg electrometer falls considerably short of the standard quantum limit by about three orders of magnitude. Here, we use an optically thin medium with approximately 5.2 × 105 laser-cooled atoms to implement the microwave heterodyne detection. By mitigating various noises and strategically optimizing the electrometer parameters, our study reduces the equivalent noise temperature by a factor of 20 and achieves an electric field sensitivity of 10.0 nV cm-1 Hz-1/2, lastly reaching a factor of 2.6 above the standard quantum limit. Our work also provides valuable insights into the inherent capabilities and limitations of Rydberg electrometers, offering superior sensitivity in detecting weak microwave signals for numerous applications.
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Affiliation(s)
- Hai-Tao Tu
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Kai-Yu Liao
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
- Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen, China
| | - Hong-Lei Wang
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Yi-Fei Zhu
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Si-Yuan Qiu
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Hao Jiang
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Wei Huang
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
- GPETR Center for Quantum Precision Measurement, South China Normal University, Guangzhou 510006, China
| | - Wu Bian
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
- Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen, China
- GPETR Center for Quantum Precision Measurement, South China Normal University, Guangzhou 510006, China
| | - Hui Yan
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
- GPETR Center for Quantum Precision Measurement, South China Normal University, Guangzhou 510006, China
| | - Shi-Liang Zhu
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
- Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen, China
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3
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Hines JA, Rajagopal SV, Moreau GL, Wahrman MD, Lewis NA, Marković O, Schleier-Smith M. Spin Squeezing by Rydberg Dressing in an Array of Atomic Ensembles. PHYSICAL REVIEW LETTERS 2023; 131:063401. [PMID: 37625064 DOI: 10.1103/physrevlett.131.063401] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2023] [Revised: 06/08/2023] [Accepted: 06/20/2023] [Indexed: 08/27/2023]
Abstract
We report on the creation of an array of spin-squeezed ensembles of cesium atoms via Rydberg dressing, a technique that offers optical control over local interactions between neutral atoms. We optimize the coherence of the interactions by a stroboscopic dressing sequence that suppresses super-Poissonian loss. We thereby prepare squeezed states of N=200 atoms with a metrological squeezing parameter ξ^{2}=0.77(9) quantifying the reduction in phase variance below the standard quantum limit. We realize metrological gain across three spatially separated ensembles in parallel, with the strength of squeezing controlled by the local intensity of the dressing light. Our method can be applied to enhance the precision of tests of fundamental physics based on arrays of atomic clocks and to enable quantum-enhanced imaging of electromagnetic fields.
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Affiliation(s)
- Jacob A Hines
- Department of Physics, Stanford University, Stanford, California 94305, USA
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | | | - Gabriel L Moreau
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Michael D Wahrman
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Neomi A Lewis
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Ognjen Marković
- Department of Physics, Stanford University, Stanford, California 94305, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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4
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Minář J, van Voorden B, Schoutens K. Kink Dynamics and Quantum Simulation of Supersymmetric Lattice Hamiltonians. PHYSICAL REVIEW LETTERS 2022; 128:050504. [PMID: 35179932 DOI: 10.1103/physrevlett.128.050504] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Revised: 09/07/2021] [Accepted: 01/07/2022] [Indexed: 06/14/2023]
Abstract
We propose a quantum simulation of a supersymmetric lattice model using atoms trapped in a 1D configuration and interacting through a Rydberg dressed potential. The elementary excitations in the model are kinks or (in a sector with one extra particle) their superpartners-the skinks. The two are connected by supersymmetry and display identical quantum dynamics. We provide an analytical description of the kink (skink) quench dynamics and propose a protocol to prepare and detect these excitations in the quantum simulator. We make a detailed analysis, based on numerical simulation, of the Rydberg atom simulator and show that it accurately tracks the dynamics of the supersymmetric model.
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Affiliation(s)
- Jiří Minář
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
- QuSoft, Science Park 123, 1098 XG Amsterdam, Netherlands
| | - Bart van Voorden
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Kareljan Schoutens
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
- QuSoft, Science Park 123, 1098 XG Amsterdam, Netherlands
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5
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Young JT, Bienias P, Belyansky R, Kaufman AM, Gorshkov AV. Asymmetric Blockade and Multiqubit Gates via Dipole-Dipole Interactions. PHYSICAL REVIEW LETTERS 2021; 127:120501. [PMID: 34597076 DOI: 10.1103/physrevlett.127.120501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2020] [Revised: 05/11/2021] [Accepted: 07/13/2021] [Indexed: 06/13/2023]
Abstract
Because of their strong and tunable interactions, Rydberg atoms can be used to realize fast two-qubit entangling gates. We propose a generalization of a generic two-qubit Rydberg-blockade gate to multiqubit Rydberg-blockade gates that involve both many control qubits and many target qubits simultaneously. This is achieved by using strong microwave fields to dress nearby Rydberg states, leading to asymmetric blockade in which control-target interactions are much stronger than control-control and target-target interactions. The implementation of these multiqubit gates can drastically simplify both quantum algorithms and state preparation. To illustrate this, we show that a 25-atom Greenberger-Horne-Zeilinger state can be created using only three gates with an error of 5.8%.
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Affiliation(s)
- Jeremy T Young
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742 USA
| | - Przemyslaw Bienias
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742 USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742 USA
| | - Ron Belyansky
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742 USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742 USA
| | - Adam M Kaufman
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742 USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742 USA
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6
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Guardado-Sanchez E, Spar BM, Schauss P, Belyansky R, Young JT, Bienias P, Gorshkov AV, Iadecola T, Bakr WS. Quench Dynamics of a Fermi Gas with Strong Nonlocal Interactions. PHYSICAL REVIEW. X 2021; 11:10.1103/physrevx.11.021036. [PMID: 36451802 PMCID: PMC9706409 DOI: 10.1103/physrevx.11.021036] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
We induce strong nonlocal interactions in a 2D Fermi gas in an optical lattice using Rydberg dressing. The system is approximately described by a t - V model on a square lattice where the fermions experience isotropic nearest-neighbor interactions and are free to hop only along one direction. We measure the interactions using many-body Ramsey interferometry and study the lifetime of the gas in the presence of tunneling, finding that tunneling does not reduce the lifetime. To probe the interplay of nonlocal interactions with tunneling, we investigate the short-time-relaxation dynamics of charge-density waves in the gas. We find that strong nearest-neighbor interactions slow down the relaxation. Our work opens the door for quantum simulations of systems with strong nonlocal interactions such as extended Fermi-Hubbard models.
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Affiliation(s)
| | - Benjamin M. Spar
- Department of Physics, Princeton University, Princeton, New Jersey 08544 USA
| | - Peter Schauss
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904 USA
| | - Ron Belyansky
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742 USA
| | - Jeremy T. Young
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- JILA, NIST, and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Przemyslaw Bienias
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742 USA
| | - Alexey V. Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742 USA
| | - Thomas Iadecola
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
| | - Waseem S. Bakr
- Department of Physics, Princeton University, Princeton, New Jersey 08544 USA
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7
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Borish V, Marković O, Hines JA, Rajagopal SV, Schleier-Smith M. Transverse-Field Ising Dynamics in a Rydberg-Dressed Atomic Gas. PHYSICAL REVIEW LETTERS 2020; 124:063601. [PMID: 32109106 DOI: 10.1103/physrevlett.124.063601] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2019] [Accepted: 01/09/2020] [Indexed: 06/10/2023]
Abstract
We report on the realization of long-range Ising interactions in a cold gas of cesium atoms by Rydberg dressing. The interactions are enhanced by coupling to Rydberg states in the vicinity of a Förster resonance. We characterize the interactions by measuring the mean-field shift of the clock transition via Ramsey spectroscopy, observing one-axis twisting dynamics. We furthermore emulate a transverse-field Ising model by periodic application of a microwave field and detect dynamical signatures of the paramagnetic-ferromagnetic phase transition. Our results highlight the power of optical addressing for achieving local and dynamical control of interactions, enabling prospects ranging from investigating Floquet quantum criticality to producing tunable-range spin squeezing.
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Affiliation(s)
- V Borish
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - O Marković
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - J A Hines
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - S V Rajagopal
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - M Schleier-Smith
- Department of Physics, Stanford University, Stanford, California 94305, USA
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8
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Masella G, Angelone A, Mezzacapo F, Pupillo G, Prokof'ev NV. Supersolid Stripe Crystal from Finite-Range Interactions on a Lattice. PHYSICAL REVIEW LETTERS 2019; 123:045301. [PMID: 31491241 DOI: 10.1103/physrevlett.123.045301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2018] [Revised: 05/21/2019] [Indexed: 06/10/2023]
Abstract
Strong, long-range interactions present a unique challenge for the theoretical investigation of quantum many-body lattice models, due to the generation of large numbers of competing states at low energy. Here, we investigate a class of extended bosonic Hubbard models with off-site terms interpolating between short and infinite range, thus allowing for an exact numerical solution for all interaction strengths. We predict a novel type of stripe crystal at strong coupling. Most interestingly, for intermediate interaction strengths we demonstrate that the stripes can turn superfluid, thus leading to a self-assembled array of quasi-one-dimensional superfluids. These bosonic superstripes turn into an isotropic supersolid with decreasing the interaction strength. The mechanism for stripe formation is based on cluster self-assembling in the corresponding classical ground state, reminiscent of classical soft-matter models of polymers, different from recently proposed mechanisms for cold gases of alkali or dipolar magnetic atoms.
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Affiliation(s)
- Guido Masella
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
| | - Adriano Angelone
- Abdus Salam International Centre for Theoretical Physics, strada Costiera 11, 34151 Trieste, Italy
- SISSA, via Bonomea 265, 34136 Trieste, Italy
| | - Fabio Mezzacapo
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
- Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Guido Pupillo
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
| | - Nikolay V Prokof'ev
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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9
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Bounds AD, Jackson NC, Hanley RK, Faoro R, Bridge EM, Huillery P, Jones MPA. Rydberg-Dressed Magneto-optical Trap. PHYSICAL REVIEW LETTERS 2018; 120:183401. [PMID: 29775327 DOI: 10.1103/physrevlett.120.183401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2018] [Revised: 03/05/2018] [Indexed: 06/08/2023]
Abstract
We propose and demonstrate the laser cooling and trapping of Rydberg-dressed Sr atoms. By off-resonantly coupling the excited state of a narrow (7 kHz) cooling transition to a high-lying Rydberg state, we transfer Rydberg properties such as enhanced electric polarizability to a stable magneto-optical trap operating at <1 μK. Simulations show that it is possible to reach a regime where the long-range interaction between Rydberg-dressed atoms becomes comparable to the kinetic energy, opening a route to combining laser cooling with tunable long-range interactions.
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Affiliation(s)
- A D Bounds
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - N C Jackson
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - R K Hanley
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - R Faoro
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - E M Bridge
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - P Huillery
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - M P A Jones
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
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