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Wiesinger M, Stuhlmann F, Bohman M, Micke P, Will C, Yildiz H, Abbass F, Arndt BP, Devlin JA, Erlewein S, Fleck M, Jäger JI, Latacz BM, Schweitzer D, Umbrazunas G, Wursten E, Blaum K, Matsuda Y, Mooser A, Quint W, Soter A, Walz J, Smorra C, Ulmer S. Trap-integrated fluorescence detection with silicon photomultipliers for sympathetic laser cooling in a cryogenic Penning trap. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2023; 94:123202. [PMID: 38109470 DOI: 10.1063/5.0170629] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Accepted: 11/23/2023] [Indexed: 12/20/2023]
Abstract
We present a fluorescence-detection system for laser-cooled 9Be+ ions based on silicon photomultipliers (SiPMs) operated at 4 K and integrated into our cryogenic 1.9 T multi-Penning-trap system. Our approach enables fluorescence detection in a hermetically sealed cryogenic Penning-trap chamber with limited optical access, where state-of-the-art detection using a telescope and photomultipliers at room temperature would be extremely difficult. We characterize the properties of the SiPM in a cryocooler at 4 K, where we measure a dark count rate below 1 s-1 and a detection efficiency of 2.5(3)%. We further discuss the design of our cryogenic fluorescence-detection trap and analyze the performance of our detection system by fluorescence spectroscopy of 9Be+ ion clouds during several runs of our sympathetic laser-cooling experiment.
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Affiliation(s)
- M Wiesinger
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
| | - F Stuhlmann
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - M Bohman
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
| | - P Micke
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
- CERN, Esplanade des Particules 1, 1217 Meyrin, Switzerland
| | - C Will
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
| | - H Yildiz
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - F Abbass
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - B P Arndt
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstraße 1, 64291 Darmstadt, Germany
- RIKEN, Fundamental Symmetries Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - J A Devlin
- CERN, Esplanade des Particules 1, 1217 Meyrin, Switzerland
- RIKEN, Fundamental Symmetries Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - S Erlewein
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
- RIKEN, Fundamental Symmetries Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - M Fleck
- RIKEN, Fundamental Symmetries Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- Graduate School of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan
| | - J I Jäger
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
- CERN, Esplanade des Particules 1, 1217 Meyrin, Switzerland
- RIKEN, Fundamental Symmetries Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - B M Latacz
- CERN, Esplanade des Particules 1, 1217 Meyrin, Switzerland
- RIKEN, Fundamental Symmetries Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - D Schweitzer
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - G Umbrazunas
- RIKEN, Fundamental Symmetries Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- Eidgenössische Technische Hochschule Zürich, John-von-Neumann-Weg 9, 8093 Zürich, Switzerland
| | - E Wursten
- CERN, Esplanade des Particules 1, 1217 Meyrin, Switzerland
- RIKEN, Fundamental Symmetries Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - K Blaum
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
| | - Y Matsuda
- Graduate School of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan
| | - A Mooser
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
| | - W Quint
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstraße 1, 64291 Darmstadt, Germany
| | - A Soter
- Eidgenössische Technische Hochschule Zürich, John-von-Neumann-Weg 9, 8093 Zürich, Switzerland
| | - J Walz
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
- Helmholtz-Institut Mainz, Staudingerweg 18, 55128 Mainz, Germany
| | - C Smorra
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
- RIKEN, Fundamental Symmetries Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - S Ulmer
- RIKEN, Fundamental Symmetries Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany
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Propp TB, van Enk SJ. On nonlinear amplification: improved quantum limits for photon counting. OPTICS EXPRESS 2019; 27:23454-23463. [PMID: 31510621 DOI: 10.1364/oe.27.023454] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2019] [Accepted: 07/24/2019] [Indexed: 06/10/2023]
Abstract
We show that detection of single photons is not subject to the fundamental limitations that accompany quantum linear amplification of bosonic mode amplitudes, even though a photodetector does amplify a few-photon input signal to a macroscopic output signal. Alternative limits are derived for nonlinear photon-number amplification schemes with optimistic implications for single-photon detection. Four commutator-preserving transformations are presented: one idealized (which is optimal) and three more realistic (less than optimal). Our description makes clear that nonlinear amplification takes place, in general, at a different frequency ω' than the frequency ω of the input photons. This can be exploited to suppress thermal noise and dark counts past what is possible with linear amplification up to a fundamental limit imposed by nonlinear amplification into a single bosonic mode.
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Noek R, Vrijsen G, Gaultney D, Mount E, Kim T, Maunz P, Kim J. High speed, high fidelity detection of an atomic hyperfine qubit. OPTICS LETTERS 2013; 38:4735-4738. [PMID: 24322119 DOI: 10.1364/ol.38.004735] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Fast and efficient detection of the qubit state in trapped ion systems is critical for implementing quantum error correction and performing fundamental tests such as a loophole-free Bell test. In this work we present a simple qubit state detection protocol for a (171)Yb+ hyperfine atomic qubit trapped in a microfabricated surface trap, enabled by high collection efficiency of the scattered photons and low background photon count rate. We demonstrate average detection times of 10.5, 28.1, and 99.8 μs, corresponding to state detection fidelities of 99%, 99.856(8)%, and 99.915(7)%, respectively.
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Schneider C, Porras D, Schaetz T. Experimental quantum simulations of many-body physics with trapped ions. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:024401. [PMID: 22790343 DOI: 10.1088/0034-4885/75/2/024401] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.
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Affiliation(s)
- Ch Schneider
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
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Fuhrmanek A, Bourgain R, Sortais YRP, Browaeys A. Free-space lossless state detection of a single trapped atom. PHYSICAL REVIEW LETTERS 2011; 106:133003. [PMID: 21517380 DOI: 10.1103/physrevlett.106.133003] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2010] [Indexed: 05/30/2023]
Abstract
We demonstrate the lossless state-selective detection of a single rubidium 87 atom trapped in an optical tweezer. This detection is analogous to the one used on trapped ions. After preparation in either a dark or a bright state, we probe the atom internal state by sending laser light that couples an excited state to the bright state only. The laser-induced fluorescence is collected by a high numerical aperture lens. The single-shot fidelity of the detection is 98.6±0.2% and is presently limited by the dark count noise of the detector. The simplicity of this method opens new perspectives in view of applications to quantum manipulations of neutral atoms.
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Affiliation(s)
- A Fuhrmanek
- Laboratoire Charles Fabry, Institut d'Optique, CNRS, Univ. Paris-Sud, Campus Polytechnique, 2 avenue Augustin Fresnel, RD 128, 91127 Palaiseau cedex, France
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6
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Thompson R, Barwood G, Gill P. Laser Cooling of Magnesium Ions Confined in a Penning Trap. ACTA ACUST UNITED AC 2010. [DOI: 10.1080/713821957] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- R.C. Thompson
- a National Physical Laboratory, Division of Mechanical and Optical Metrology, Queens Road, Teddington, Middlesex, England
| | - G.P. Barwood
- a National Physical Laboratory, Division of Mechanical and Optical Metrology, Queens Road, Teddington, Middlesex, England
| | - P. Gill
- a National Physical Laboratory, Division of Mechanical and Optical Metrology, Queens Road, Teddington, Middlesex, England
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Herdman CM, Young KC, Scarola VW, Sarovar M, Whaley KB. Stroboscopic generation of topological protection. PHYSICAL REVIEW LETTERS 2010; 104:230501. [PMID: 20867218 DOI: 10.1103/physrevlett.104.230501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2009] [Indexed: 05/29/2023]
Abstract
Trapped neutral atoms offer a powerful route to robust simulation of complex quantum systems. We present here a stroboscopic scheme for realization of a Hamiltonian with n-body interactions on a set of neutral atoms trapped in an addressable optical lattice, using only 1- and 2-body physical operations together with a dissipative mechanism that allows thermalization to finite temperature or cooling to the ground state. We demonstrate this scheme with application to the toric code Hamiltonian, ground states of which can be used to robustly store quantum information when coupled to a low temperature reservoir.
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Affiliation(s)
- C M Herdman
- Department of Physics, Berkeley Center for Quantum Information and Computation, University of California, Berkeley, California 94720, USA
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8
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9
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Myerson AH, Szwer DJ, Webster SC, Allcock DTC, Curtis MJ, Imreh G, Sherman JA, Stacey DN, Steane AM, Lucas DM. High-fidelity readout of trapped-ion qubits. PHYSICAL REVIEW LETTERS 2008; 100:200502. [PMID: 18518518 DOI: 10.1103/physrevlett.100.200502] [Citation(s) in RCA: 70] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2008] [Indexed: 05/26/2023]
Abstract
We demonstrate single-shot qubit readout with a fidelity sufficient for fault-tolerant quantum computation. For an optical qubit stored in 40Ca+ we achieve 99.991(1)% average readout fidelity in 10(6) trials, using time-resolved photon counting. An adaptive measurement technique allows 99.99% fidelity to be reached in 145 micros average detection time. For 43Ca+, we propose and implement an optical pumping scheme to transfer a long-lived hyperfine qubit to the optical qubit, capable of a theoretical fidelity of 99.95% in 10 micros. We achieve 99.87(4)% transfer fidelity and 99.77(3)% net readout fidelity.
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Affiliation(s)
- A H Myerson
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
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Diddams SA, Bergquist JC, Jefferts SR, Oates CW. Standards of Time and Frequency at the Outset of the 21st Century. Science 2004; 306:1318-24. [PMID: 15550659 DOI: 10.1126/science.1102330] [Citation(s) in RCA: 189] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
After 50 years of development, microwave atomic clocks based on cesium have achieved fractional uncertainties below 1 part in 10(15), a level unequaled in all of metrology. The past 5 years have seen the accelerated development of optical atomic clocks, which may enable even greater improvements in timekeeping. Time and frequency standards with various levels of performance are ubiquitous in our society, with applications in many technological fields as well as in the continued exploration of the frontiers of basic science. We review state-of-the-art atomic time and frequency standards and discuss some of their uses in science and technology.
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Affiliation(s)
- S A Diddams
- Time & Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA.
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11
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Wineland D, Itano W, Bergquist J, Bollinger J, Prestage J. Optical pumping of stored atomic ions. ACTA ACUST UNITED AC 2004. [DOI: 10.1051/anphys:01985001006073700] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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12
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Beige A, Hegerfeldt GC. Projection postulate and atomic quantum Zeno effect. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 53:53-65. [PMID: 9912860 DOI: 10.1103/physreva.53.53] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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13
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Bollinger JJ, Heinzen DJ, Moore FL, Itano WM, Wineland DJ, Dubin DH. Electrostatic modes of ion-trap plasmas. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 48:525-545. [PMID: 9909626 DOI: 10.1103/physreva.48.525] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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14
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Itano WM, Bergquist JC, Bollinger JJ, Gilligan JM, Heinzen DJ, Moore FL, Raizen MG, Wineland DJ. Quantum projection noise: Population fluctuations in two-level systems. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 47:3554-3570. [PMID: 9909363 DOI: 10.1103/physreva.47.3554] [Citation(s) in RCA: 131] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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15
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Heinzen DJ, Bollinger JJ, Moore FL, Itano WM, Wineland DJ. Rotational equilibria and low-order modes of a non-neutral ion plasma. PHYSICAL REVIEW LETTERS 1991; 66:2080-2083. [PMID: 10043386 DOI: 10.1103/physrevlett.66.2080] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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16
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Yu FQ, Zhang CP, Zhang GY. Transmission spectrum of a system composed of one-dimensional chains of small metallic spheres. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 42:11003-11007. [PMID: 9995378 DOI: 10.1103/physrevb.42.11003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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17
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Heinzen DJ, Wineland DJ. Quantum-limited cooling and detection of radio-frequency oscillations by laser-cooled ions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 42:2977-2994. [PMID: 9904368 DOI: 10.1103/physreva.42.2977] [Citation(s) in RCA: 54] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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18
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Itano WM, Heinzen DJ, Bollinger JJ, Wineland DJ. Quantum Zeno effect. PHYSICAL REVIEW A 1990; 41:2295-2300. [PMID: 9903355 DOI: 10.1103/physreva.41.2295] [Citation(s) in RCA: 208] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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19
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Brewer LR, Prestage JD, Bollinger JJ, Itano WM, Larson DJ, Wineland DJ. Static properties of a non-neutral 9Be. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 38:859-873. [PMID: 9900451 DOI: 10.1103/physreva.38.859] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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20
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Thompson RC, Barwood GP, Gill P. Progress towards an optical frequency standard based on ion traps. ACTA ACUST UNITED AC 1988. [DOI: 10.1007/bf00698657] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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21
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Hulet RG, Wineland DJ. Quantum jumps via spontaneous Raman scattering. PHYSICAL REVIEW. A, GENERAL PHYSICS 1987; 36:2758-2762. [PMID: 9899180 DOI: 10.1103/physreva.36.2758] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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22
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Bergquist JC, Itano WM, Wineland DJ. Recoilless optical absorption and Doppler sidebands of a single trapped ion. PHYSICAL REVIEW. A, GENERAL PHYSICS 1987; 36:428-430. [PMID: 9898712 DOI: 10.1103/physreva.36.428] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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23
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Bergquist JC, Hulet RG, Itano WM, Wineland DJ. Observation of quantum jumps in a single atom. PHYSICAL REVIEW LETTERS 1986; 57:1699-1702. [PMID: 10033522 DOI: 10.1103/physrevlett.57.1699] [Citation(s) in RCA: 163] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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24
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Nagourney W, Sandberg J, Dehmelt H. Shelved optical electron amplifier: Observation of quantum jumps. PHYSICAL REVIEW LETTERS 1986; 56:2797-2799. [PMID: 10033097 DOI: 10.1103/physrevlett.56.2797] [Citation(s) in RCA: 200] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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25
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Bergquist JC, Wineland DJ, Itano WM, Hemmati H, Daniel H, Leuchs G. Energy and radiative lifetime of the 5d96s2 2D5/2 state in Hg II by Doppler-free two-photon laser spectroscopy. PHYSICAL REVIEW LETTERS 1985; 55:1567-1570. [PMID: 10031858 DOI: 10.1103/physrevlett.55.1567] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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26
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Bollinger JJ, Wells JS, Wineland DJ, Itano WM. Hyperfine structure of the 2p sup2Psub1/2 state in sup9Besup+. PHYSICAL REVIEW. A, GENERAL PHYSICS 1985; 31:2711-2714. [PMID: 9895812 DOI: 10.1103/physreva.31.2711] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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27
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Abstract
Ions that are stored in electromagnetic "traps" provid the basis for extremely high resolution spectroscopy. By using lasers, the kinetic energy of the ions can be cooled to millikelvin temperatures, thereby suppressing Doppler frequency shifts. Potential accuracies of frequency standards and clocks based on such experiments are anticipated to be better than one part in 10(15).
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Abstract
The history of atomic and molecular standards of time and frequency is traced from the earliest work on molecular and atomic beam resonance techniques to more recent developments that promise improved standards in the future. The various devices currently used as standards are discussed in detail from an historical prospective. The latter part of the article is devoted to a discussion of prospective developments which hold promise for major improvements in accuracy, stability and reproducibility.
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Affiliation(s)
- Norman F Ramsey
- Mount Holyoke College, South Hadley, MA 01075 and Harvard University, Cambridge, MA 02138
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29
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