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Billaud E, Balembois L, Le Dantec M, Rančić M, Albertinale E, Bertaina S, Chanelière T, Goldner P, Estève D, Vion D, Bertet P, Flurin E. Microwave Fluorescence Detection of Spin Echoes. Phys Rev Lett 2023; 131:100804. [PMID: 37739386 DOI: 10.1103/physrevlett.131.100804] [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: 08/30/2022] [Accepted: 07/19/2023] [Indexed: 09/24/2023]
Abstract
Counting the microwave photons emitted by an ensemble of electron spins when they relax radiatively has recently been proposed as a sensitive method for electron paramagnetic resonance spectroscopy, enabled by the development of operational single microwave photon detectors at millikelvin temperature. Here, we report the detection of spin echoes in the spin fluorescence signal. The echo manifests itself as a coherent modulation of the number of photons spontaneously emitted after a π/2_{X}-τ-π_{Y}-τ-π/2_{Φ} sequence, dependent on the relative phase Φ. We demonstrate experimentally this detection method using an ensemble of Er^{3+} ion spins in a scheelite crystal of CaWO_{4}. We use fluorescence-detected echoes to measure the erbium spin coherence time, as well as the echo envelope modulation due to the coupling to the ^{183}W nuclear spins surrounding each ion. We finally compare the signal-to-noise ratio of inductively detected and fluorescence-detected echoes, and show that it is larger with the fluorescence method.
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Affiliation(s)
- E Billaud
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - L Balembois
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - M Le Dantec
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - M Rančić
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - E Albertinale
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - S Bertaina
- CNRS, Aix-Marseille Université, IM2NP (UMR 7334), Institut Matériaux Microélectronique et Nanosciences de Provence, 13397 Marseille, France
| | - T Chanelière
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - P Goldner
- Chimie ParisTech, PSL University, CNRS, Institut de Recherche de Chimie Paris, 75005 Paris, France
| | - D Estève
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - D Vion
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - P Bertet
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - E Flurin
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
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2
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Wang Z, Balembois L, Rančić M, Billaud E, Le Dantec M, Ferrier A, Goldner P, Bertaina S, Chanelière T, Esteve D, Vion D, Bertet P, Flurin E. Single-electron spin resonance detection by microwave photon counting. Nature 2023; 619:276-281. [PMID: 37438594 DOI: 10.1038/s41586-023-06097-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2022] [Accepted: 04/18/2023] [Indexed: 07/14/2023]
Abstract
Electron spin resonance spectroscopy is the method of choice for characterizing paramagnetic impurities, with applications ranging from chemistry to quantum computing1,2, but it gives access only to ensemble-averaged quantities owing to its limited signal-to-noise ratio. Single-electron spin sensitivity has, however, been reached using spin-dependent photoluminescence3-5, transport measurements6-9 and scanning-probe techniques10-12. These methods are system-specific or sensitive only in a small detection volume13,14, so that practical single-spin detection remains an open challenge. Here, we demonstrate single-electron magnetic resonance by spin fluorescence detection15, using a microwave photon counter at millikelvin temperatures16. We detect individual paramagnetic erbium ions in a scheelite crystal coupled to a high-quality-factor planar superconducting resonator to enhance their radiative decay rate17, with a signal-to-noise ratio of 1.9 in one second integration time. The fluorescence signal shows anti-bunching, proving that it comes from individual emitters. Coherence times up to 3 ms are measured, limited by the spin radiative lifetime. The method has the potential to be applied to arbitrary paramagnetic species with long enough non-radiative relaxation times, and allows single-spin detection in a volume as large as the resonator magnetic mode volume (approximately 10 μm3 in the present experiment), orders of magnitude larger than other single-spin detection techniques. As such, it may find applications in magnetic resonance and quantum computing.
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Affiliation(s)
- Z Wang
- Quantronics group, Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette Cedex, France
- Département de Physique et Institut Quantique, Université de Sherbrooke, Sherbrooke, Québec, Canada
| | - L Balembois
- Quantronics group, Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette Cedex, France
| | - M Rančić
- Quantronics group, Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette Cedex, France
| | - E Billaud
- Quantronics group, Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette Cedex, France
| | - M Le Dantec
- Quantronics group, Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette Cedex, France
| | - A Ferrier
- Chimie ParisTech, PSL University, CNRS, Institut de Recherche de Chimie Paris, Paris, France
| | - P Goldner
- Chimie ParisTech, PSL University, CNRS, Institut de Recherche de Chimie Paris, Paris, France
| | - S Bertaina
- CNRS, Aix-Marseille Université, IM2NP (UMR 7334), Institut Matériaux Microélectronique et Nanosciences de Provence, Marseille, France
| | - T Chanelière
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble, France
| | - D Esteve
- Quantronics group, Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette Cedex, France
| | - D Vion
- Quantronics group, Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette Cedex, France
| | - P Bertet
- Quantronics group, Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette Cedex, France
| | - E Flurin
- Quantronics group, Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette Cedex, France.
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3
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Ranjan V, O'Sullivan J, Albertinale E, Albanese B, Chanelière T, Schenkel T, Vion D, Esteve D, Flurin E, Morton JJL, Bertet P. Multimode Storage of Quantum Microwave Fields in Electron Spins over 100 ms. Phys Rev Lett 2020; 125:210505. [PMID: 33274991 DOI: 10.1103/physrevlett.125.210505] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Accepted: 10/19/2020] [Indexed: 06/12/2023]
Abstract
We report long coherence times (up to 300 ms) for near-surface bismuth donor electron spins in silicon coupled to a superconducting microresonator, biased at a clock transition. This enables us to demonstrate the partial absorption of a train of weak microwave fields in the spin ensemble, their storage for 100 ms, and their retrieval, using a Hahn-echo-like protocol. Phase coherence and quantum statistics are preserved in the storage.
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Affiliation(s)
- V Ranjan
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - J O'Sullivan
- London Centre for Nanotechnology, University College London, London WC1H 0AH, United Kingdom
| | - E Albertinale
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - B Albanese
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - T Chanelière
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - T Schenkel
- Accelerator Technology and Applied Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - D Vion
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - D Esteve
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - E Flurin
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
| | - J J L Morton
- London Centre for Nanotechnology, University College London, London WC1H 0AH, United Kingdom
| | - P Bertet
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
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4
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Ranjan V, Probst S, Albanese B, Doll A, Jacquot O, Flurin E, Heeres R, Vion D, Esteve D, Morton JJL, Bertet P. Pulsed electron spin resonance spectroscopy in the Purcell regime. J Magn Reson 2020; 310:106662. [PMID: 31837553 DOI: 10.1016/j.jmr.2019.106662] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2019] [Revised: 11/22/2019] [Accepted: 11/25/2019] [Indexed: 06/10/2023]
Abstract
In EPR, spin relaxation is typically governed by interactions with the lattice or other spins. However, it has recently been shown that given a sufficiently strong spin-resonator coupling and high resonator quality factor, the spontaneous emission of microwave photons from the spins into the resonator can become the main relaxation mechanism, as predicted by Purcell. With increasing attention on the use of microresonators for EPR to achieve high spin-number sensitivity it is important to understand how this novel regime influences measured EPR signals, for example the amplitude and temporal shape of the spin-echo. We study this regime theoretically and experimentally, using donor spins in silicon, under different conditions of spin-linewidth and coupling homogeneity. When the spin-resonator coupling is distributed inhomogeneously, we find that the effective spin-echo relaxation time measured in a saturation recovery sequence strongly depends on the parameters for the detection echo. When the spin linewidth is larger than the resonator bandwidth, the different Fourier components of the spin echo relax with different characteristic times - due to the role of the resonator in driving relaxation - which results in the temporal shape of the echo becoming dependent on the repetition time of the experiment.
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Affiliation(s)
- V Ranjan
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - S Probst
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - B Albanese
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - A Doll
- Laboratoire Nanomagnétisme et Oxydes, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - O Jacquot
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - E Flurin
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - R Heeres
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - D Vion
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - D Esteve
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - J J L Morton
- London Centre for Nanotechnology, University College London, London WC1H 0AH, United Kingdom
| | - P Bertet
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France.
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5
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Rolland C, Peugeot A, Dambach S, Westig M, Kubala B, Mukharsky Y, Altimiras C, le Sueur H, Joyez P, Vion D, Roche P, Esteve D, Ankerhold J, Portier F. Antibunched Photons Emitted by a dc-Biased Josephson Junction. Phys Rev Lett 2019; 122:186804. [PMID: 31144884 DOI: 10.1103/physrevlett.122.186804] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2018] [Revised: 02/20/2019] [Indexed: 06/09/2023]
Abstract
We show experimentally that a dc biased Josephson junction in series with a high-enough-impedance microwave resonator emits antibunched photons. Our resonator is made of a simple microfabricated spiral coil that resonates at 4.4 GHz and reaches a 1.97 kΩ characteristic impedance. The second order correlation function of the power leaking out of the resonator drops down to 0.3 at zero delay, which demonstrates the antibunching of the photons emitted by the circuit at a rate of 6×10^{7} photons per second. Results are found in quantitative agreement with our theoretical predictions. This simple scheme could offer an efficient and bright single-photon source in the microwave domain.
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Affiliation(s)
- C Rolland
- DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA, Université Paris-Saclay, 91190 Gif sur Yvette, France
| | - A Peugeot
- DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA, Université Paris-Saclay, 91190 Gif sur Yvette, France
| | - S Dambach
- Institute for Complex Quantum Systems and IQST, University of Ulm, 89069 Ulm, Germany
| | - M Westig
- DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA, Université Paris-Saclay, 91190 Gif sur Yvette, France
| | - B Kubala
- Institute for Complex Quantum Systems and IQST, University of Ulm, 89069 Ulm, Germany
| | - Y Mukharsky
- DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA, Université Paris-Saclay, 91190 Gif sur Yvette, France
| | - C Altimiras
- DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA, Université Paris-Saclay, 91190 Gif sur Yvette, France
| | - H le Sueur
- DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA, Université Paris-Saclay, 91190 Gif sur Yvette, France
| | - P Joyez
- DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA, Université Paris-Saclay, 91190 Gif sur Yvette, France
| | - D Vion
- DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA, Université Paris-Saclay, 91190 Gif sur Yvette, France
| | - P Roche
- DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA, Université Paris-Saclay, 91190 Gif sur Yvette, France
| | - D Esteve
- DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA, Université Paris-Saclay, 91190 Gif sur Yvette, France
| | - J Ankerhold
- Institute for Complex Quantum Systems and IQST, University of Ulm, 89069 Ulm, Germany
| | - F Portier
- DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA, Université Paris-Saclay, 91190 Gif sur Yvette, France
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6
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Parlavecchio O, Altimiras C, Souquet JR, Simon P, Safi I, Joyez P, Vion D, Roche P, Esteve D, Portier F. Erratum: Fluctuation-Dissipation Relations of a Tunnel Junction Driven by a Quantum Circuit [Phys. Rev. Lett. 114, 126801 (2015)]. Phys Rev Lett 2018; 120:049901. [PMID: 29437444 DOI: 10.1103/physrevlett.120.049901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Indexed: 06/08/2023]
Abstract
This corrects the article DOI: 10.1103/PhysRevLett.114.126801.
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7
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Westig M, Kubala B, Parlavecchio O, Mukharsky Y, Altimiras C, Joyez P, Vion D, Roche P, Esteve D, Hofheinz M, Trif M, Simon P, Ankerhold J, Portier F. Emission of Nonclassical Radiation by Inelastic Cooper Pair Tunneling. Phys Rev Lett 2017; 119:137001. [PMID: 29341699 DOI: 10.1103/physrevlett.119.137001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2017] [Indexed: 06/07/2023]
Abstract
We show that a properly dc-biased Josephson junction in series with two microwave resonators of different frequencies emits photon pairs in the resonators. By measuring auto- and intercorrelations of the power leaking out of the resonators, we demonstrate two-mode amplitude squeezing below the classical limit. This nonclassical microwave light emission is found to be in quantitative agreement with our theoretical predictions, up to an emission rate of 2 billion photon pairs per second.
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Affiliation(s)
- M Westig
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - B Kubala
- Institute for Complex Quantum Systems and IQST, University of Ulm, 89069 Ulm, Germany
| | - O Parlavecchio
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - Y Mukharsky
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - C Altimiras
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - P Joyez
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - D Vion
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - P Roche
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - D Esteve
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - M Hofheinz
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - M Trif
- Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France
| | - P Simon
- Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France
| | - J Ankerhold
- Institute for Complex Quantum Systems and IQST, University of Ulm, 89069 Ulm, Germany
| | - F Portier
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
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8
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Bienfait A, Pla JJ, Kubo Y, Stern M, Zhou X, Lo CC, Weis CD, Schenkel T, Thewalt MLW, Vion D, Esteve D, Julsgaard B, Mølmer K, Morton JJL, Bertet P. Reaching the quantum limit of sensitivity in electron spin resonance. Nat Nanotechnol 2016; 11:253-257. [PMID: 26657787 DOI: 10.1038/nnano.2015.282] [Citation(s) in RCA: 58] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2015] [Accepted: 10/29/2015] [Indexed: 06/05/2023]
Abstract
The detection and characterization of paramagnetic species by electron spin resonance (ESR) spectroscopy is widely used throughout chemistry, biology and materials science, from in vivo imaging to distance measurements in spin-labelled proteins. ESR relies on the inductive detection of microwave signals emitted by the spins into a coupled microwave resonator during their Larmor precession. However, such signals can be very small, prohibiting the application of ESR at the nanoscale (for example, at the single-cell level or on individual nanoparticles). Here, using a Josephson parametric microwave amplifier combined with high-quality-factor superconducting microresonators cooled at millikelvin temperatures, we improve the state-of-the-art sensitivity of inductive ESR detection by nearly four orders of magnitude. We demonstrate the detection of 1,700 bismuth donor spins in silicon within a single Hahn echo with unit signal-to-noise ratio, reduced to 150 spins by averaging a single Carr-Purcell-Meiboom-Gill sequence. This unprecedented sensitivity reaches the limit set by quantum fluctuations of the electromagnetic field instead of thermal or technical noise, which constitutes a novel regime for magnetic resonance. The detection volume of our resonator is ∼ 0.02 nl, and our approach can be readily scaled down further to improve sensitivity, providing a new versatile toolbox for ESR at the nanoscale.
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Affiliation(s)
- A Bienfait
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - J J Pla
- London Centre for Nanotechnology, University College London, London WC1H 0AH, UK
| | - Y Kubo
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - M Stern
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
- Quantum Nanoelectronics Laboratory, BINA, Bar Ilan University, Ramat Gan, Israel
| | - X Zhou
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
- ISEN Department, Institute of Electronics Microelectronics and Nanotechnology, CNRS UMR 8520, Avenue Poincaré, CS 60069, Villeneuve d'Ascq Cedex 59652, France
| | - C C Lo
- London Centre for Nanotechnology, University College London, London WC1H 0AH, UK
| | - C D Weis
- Accelerator Technology and Applied Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - T Schenkel
- Accelerator Technology and Applied Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - M L W Thewalt
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - D Vion
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - D Esteve
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - B Julsgaard
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, Aarhus C DK-8000, Denmark
| | - K Mølmer
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, Aarhus C DK-8000, Denmark
| | - J J L Morton
- London Centre for Nanotechnology, University College London, London WC1H 0AH, UK
| | - P Bertet
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
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9
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Janvier C, Tosi L, Bretheau L, Girit ÇÖ, Stern M, Bertet P, Joyez P, Vion D, Esteve D, Goffman MF, Pothier H, Urbina C. Coherent manipulation of Andreev states in superconducting atomic contacts. Science 2015; 349:1199-202. [DOI: 10.1126/science.aab2179] [Citation(s) in RCA: 127] [Impact Index Per Article: 14.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- C. Janvier
- Quantronics Group, Service de Physique de l’État Condensé, CNRS UMR 3680, IRAMIS, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - L. Tosi
- Quantronics Group, Service de Physique de l’État Condensé, CNRS UMR 3680, IRAMIS, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica, 8400 Bariloche, Argentina
| | - L. Bretheau
- Quantronics Group, Service de Physique de l’État Condensé, CNRS UMR 3680, IRAMIS, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - Ç. Ö. Girit
- Quantronics Group, Service de Physique de l’État Condensé, CNRS UMR 3680, IRAMIS, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - M. Stern
- Quantronics Group, Service de Physique de l’État Condensé, CNRS UMR 3680, IRAMIS, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - P. Bertet
- Quantronics Group, Service de Physique de l’État Condensé, CNRS UMR 3680, IRAMIS, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - P. Joyez
- Quantronics Group, Service de Physique de l’État Condensé, CNRS UMR 3680, IRAMIS, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - D. Vion
- Quantronics Group, Service de Physique de l’État Condensé, CNRS UMR 3680, IRAMIS, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - D. Esteve
- Quantronics Group, Service de Physique de l’État Condensé, CNRS UMR 3680, IRAMIS, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - M. F. Goffman
- Quantronics Group, Service de Physique de l’État Condensé, CNRS UMR 3680, IRAMIS, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - H. Pothier
- Quantronics Group, Service de Physique de l’État Condensé, CNRS UMR 3680, IRAMIS, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - C. Urbina
- Quantronics Group, Service de Physique de l’État Condensé, CNRS UMR 3680, IRAMIS, CEA-Saclay, 91191 Gif-sur-Yvette, France
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10
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Parlavecchio O, Altimiras C, Souquet JR, Simon P, Safi I, Joyez P, Vion D, Roche P, Esteve D, Portier F. Fluctuation-dissipation relations of a tunnel junction driven by a quantum circuit. Phys Rev Lett 2015; 114:126801. [PMID: 25860764 DOI: 10.1103/physrevlett.114.126801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2014] [Indexed: 06/04/2023]
Abstract
We derive fluctuation-dissipation relations for a tunnel junction driven through a resonator displaying strong quantum fluctuations. We find that the fluctuation-dissipation relations derived for classical external drives hold, provided the effect of the circuit's quantum fluctuations is incorporated into the modified nonlinear current voltage characteristics. We also demonstrate that all quantities measured under a time dependent bias can be reconstructed from their values measured under a dc bias using photoassisted tunneling relations. We confirm these predictions by implementing the circuit and measuring the dc current through the junction, its high frequency admittance, and its current noise at the frequency of the resonator.
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Affiliation(s)
- O Parlavecchio
- SPEC (UMR 3680 CEA-CNRS), CEA Saclay, 91191 Gif-sur-Yvette, France
| | - C Altimiras
- SPEC (UMR 3680 CEA-CNRS), CEA Saclay, 91191 Gif-sur-Yvette, France
| | - J-R Souquet
- Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France
| | - P Simon
- Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France
| | - I Safi
- Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France
| | - P Joyez
- SPEC (UMR 3680 CEA-CNRS), CEA Saclay, 91191 Gif-sur-Yvette, France
| | - D Vion
- SPEC (UMR 3680 CEA-CNRS), CEA Saclay, 91191 Gif-sur-Yvette, France
| | - P Roche
- SPEC (UMR 3680 CEA-CNRS), CEA Saclay, 91191 Gif-sur-Yvette, France
| | - D Esteve
- SPEC (UMR 3680 CEA-CNRS), CEA Saclay, 91191 Gif-sur-Yvette, France
| | - F Portier
- SPEC (UMR 3680 CEA-CNRS), CEA Saclay, 91191 Gif-sur-Yvette, France
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11
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Stern M, Catelani G, Kubo Y, Grezes C, Bienfait A, Vion D, Esteve D, Bertet P. Flux qubits with long coherence times for hybrid quantum circuits. Phys Rev Lett 2014; 113:123601. [PMID: 25279628 DOI: 10.1103/physrevlett.113.123601] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2014] [Indexed: 06/03/2023]
Abstract
We present measurements of superconducting flux qubits embedded in a three dimensional copper cavity. The qubits are fabricated on a sapphire substrate and are measured by coupling them inductively to an on-chip superconducting resonator located in the middle of the cavity. At their flux-insensitive point, all measured qubits reach an intrinsic energy relaxation time in the 6-20 μs range and a pure dephasing time comprised between 3 and 10 μs. This significant improvement over previous works opens the way to the coherent coupling of a flux qubit to individual spins.
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Affiliation(s)
- M Stern
- Quantronics Group, SPEC, IRAMIS, DSM, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - G Catelani
- Forschungszentrum Jülich, Peter Grünberg Institut (PGI-2), 52425 Jülich, Germany
| | - Y Kubo
- Quantronics Group, SPEC, IRAMIS, DSM, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - C Grezes
- Quantronics Group, SPEC, IRAMIS, DSM, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - A Bienfait
- Quantronics Group, SPEC, IRAMIS, DSM, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - D Vion
- Quantronics Group, SPEC, IRAMIS, DSM, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - D Esteve
- Quantronics Group, SPEC, IRAMIS, DSM, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - P Bertet
- Quantronics Group, SPEC, IRAMIS, DSM, CEA Saclay, 91191 Gif-sur-Yvette, France
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12
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Ong FR, Boissonneault M, Mallet F, Doherty AC, Blais A, Vion D, Esteve D, Bertet P. Quantum heating of a nonlinear resonator probed by a superconducting qubit. Phys Rev Lett 2013; 110:047001. [PMID: 25166193 DOI: 10.1103/physrevlett.110.047001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2012] [Indexed: 06/03/2023]
Abstract
We measure the quantum fluctuations of a pumped nonlinear resonator using a superconducting artificial atom as an in situ probe. The qubit excitation spectrum gives access to the frequency and amount of excitation of the intracavity field fluctuations, from which we infer its effective temperature. These quantities are found to be in agreement with theoretical predictions; in particular, we experimentally observe the phenomenon of quantum heating.
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Affiliation(s)
- F R Ong
- Quantronics group, Service de Physique de l'État Condensé (CNRS URA 2464), IRAMIS, DSM, CEA-Saclay, 91191 Gif-sur-Yvette, France and Institute for Quantum Computing, Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
| | - M Boissonneault
- Département de Physique, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1 and Calcul Québec, Université Laval, Québec, Québec, Canada G1V 0A6
| | - F Mallet
- Laboratoire Pierre Aigrain, Ecole Normale Supérieure, CNRS (UMR 8551), Université Pierre et Marie Curie, 24, rue Lhomond, 75005 Paris, France
| | - A C Doherty
- Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia
| | - A Blais
- Département de Physique, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1
| | - D Vion
- Quantronics group, Service de Physique de l'État Condensé (CNRS URA 2464), IRAMIS, DSM, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - D Esteve
- Quantronics group, Service de Physique de l'État Condensé (CNRS URA 2464), IRAMIS, DSM, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - P Bertet
- Quantronics group, Service de Physique de l'État Condensé (CNRS URA 2464), IRAMIS, DSM, CEA-Saclay, 91191 Gif-sur-Yvette, France
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13
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Dewes A, Ong FR, Schmitt V, Lauro R, Boulant N, Bertet P, Vion D, Esteve D. Characterization of a two-transmon processor with individual single-shot qubit readout. Phys Rev Lett 2012; 108:057002. [PMID: 22400953 DOI: 10.1103/physrevlett.108.057002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2011] [Indexed: 05/31/2023]
Abstract
We report the characterization of a two-qubit processor implemented with two capacitively coupled tunable superconducting qubits of the transmon type, each qubit having its own nondestructive single-shot readout. The fixed capacitive coupling yields the sqrt[iSWAP] two-qubit gate for a suitable interaction time. We reconstruct by state tomography the coherent dynamics of the two-bit register as a function of the interaction time, observe a violation of the Bell inequality by 22 standard deviations after correcting readout errors, and measure by quantum process tomography a gate fidelity of 90%.
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Affiliation(s)
- A Dewes
- Quantronics group, Service de Physique de l'État Condensé (CNRS URA 2464), IRAMIS, DSM, CEA-Saclay, 91191 Gif-sur-Yvette, France
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14
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Kubo Y, Grezes C, Dewes A, Umeda T, Isoya J, Sumiya H, Morishita N, Abe H, Onoda S, Ohshima T, Jacques V, Dréau A, Roch JF, Diniz I, Auffeves A, Vion D, Esteve D, Bertet P. Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble. Phys Rev Lett 2011; 107:220501. [PMID: 22182018 DOI: 10.1103/physrevlett.107.220501] [Citation(s) in RCA: 80] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2011] [Indexed: 05/31/2023]
Abstract
We report the experimental realization of a hybrid quantum circuit combining a superconducting qubit and an ensemble of electronic spins. The qubit, of the transmon type, is coherently coupled to the spin ensemble consisting of nitrogen-vacancy centers in a diamond crystal via a frequency-tunable superconducting resonator acting as a quantum bus. Using this circuit, we prepare a superposition of the qubit states that we store into collective excitations of the spin ensemble and retrieve back into the qubit later on. These results constitute a proof of concept of spin-ensemble based quantum memory for superconducting qubits.
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Affiliation(s)
- Y Kubo
- Quantronics group, SPEC (CNRS URA 2464), IRAMIS, DSM, CEA-Saclay, 91191 Gif-sur-Yvette, France
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15
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Hofheinz M, Portier F, Baudouin Q, Joyez P, Vion D, Bertet P, Roche P, Esteve D. Bright side of the Coulomb blockade. Phys Rev Lett 2011; 106:217005. [PMID: 21699333 DOI: 10.1103/physrevlett.106.217005] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2011] [Indexed: 05/31/2023]
Abstract
We explore the photonic (bright) side of the dynamical Coulomb blockade (DCB) by measuring the radiation emitted by a dc voltage-biased Josephson junction embedded in a microwave resonator. In this regime Cooper pair tunneling is inelastic and associated with the transfer of an energy 2eV into the resonator modes. We have measured simultaneously the Cooper pair current and the photon emission rate at the resonance frequency of the resonator. Our results show two regimes, in which each tunneling Cooper pair emits either one or two photons into the resonator. The spectral properties of the emitted radiation are accounted for by an extension to DCB theory.
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Affiliation(s)
- M Hofheinz
- Service de Physique de l'Etat Condensé (CNRS URA 2464), IRAMIS, CEA Saclay, 91191 Gif-sur-Yvette, France
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16
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Ong FR, Boissonneault M, Mallet F, Palacios-Laloy A, Dewes A, Doherty AC, Blais A, Bertet P, Vion D, Esteve D. Circuit QED with a nonlinear resonator: ac-Stark shift and dephasing. Phys Rev Lett 2011; 106:167002. [PMID: 21599402 DOI: 10.1103/physrevlett.106.167002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2010] [Indexed: 05/30/2023]
Abstract
We have performed spectroscopic measurements of a superconducting qubit dispersively coupled to a nonlinear resonator driven by a pump microwave field. Measurements of the qubit frequency shift provide a sensitive probe of the intracavity field, yielding a precise characterization of the resonator nonlinearity. The qubit linewidth has a complex dependence on the pump frequency and amplitude, which is correlated with the gain of the nonlinear resonator operated as a small-signal amplifier. The corresponding dephasing rate is found to be close to the quantum limit in the low-gain limit of the amplifier.
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Affiliation(s)
- F R Ong
- Service de Physique de l'État Condensé (CNRS URA 2464), IRAMIS, DSM, CEA-Saclay, Gif-sur-Yvette, France
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17
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Kubo Y, Ong FR, Bertet P, Vion D, Jacques V, Zheng D, Dréau A, Roch JF, Auffeves A, Jelezko F, Wrachtrup J, Barthe MF, Bergonzo P, Esteve D. Strong coupling of a spin ensemble to a superconducting resonator. Phys Rev Lett 2010; 105:140502. [PMID: 21230818 DOI: 10.1103/physrevlett.105.140502] [Citation(s) in RCA: 144] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2010] [Indexed: 05/23/2023]
Abstract
We report the realization of a quantum circuit in which an ensemble of electronic spins is coupled to a frequency tunable superconducting resonator. The spins are nitrogen-vacancy centers in a diamond crystal. The achievement of strong coupling is manifested by the appearance of a vacuum Rabi splitting in the transmission spectrum of the resonator when its frequency is tuned through the nitrogen-vacancy center electron spin resonance.
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Affiliation(s)
- Y Kubo
- Quantronics group, SPEC (CNRS URA 2464), IRAMIS, DSM, CEA, 91191 Gif-sur-Yvette, France
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18
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Schmidt V, Firpo L, Vion D, Oliván MEDC, Casella L, Cuenya L, Blum GD, Pedrón V. Modelo Psicobiológico de Personalidad de Eysenck: una historia proyectada hacia el futuro. Rev int psicol 2010. [DOI: 10.33670/18181023.v11i02.63] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
En el presente artículo, se revisan las circunstancias particulares, autores e ideas que influyeron en la generación de uno de los modelos de personalidad más sólidos con que cuenta la Psicología hasta nuestros días: el ModeloPsicobiológico de Eysenck. Se presentan las características principales del mismo, las cuales lo definen como un modelo disposicional, dimensional, jerárquico y psicobiológico. El intento de mejorar la descripción, explicación y medición de las dimensiones llevó a este autor a proponer modificaciones a su teoría original y a sus instrumentos. Se analizan de este modo las distintas etapas de su modelo. A pesar de la proliferación de teorías de personalidad, el modelo de Eysenck tienen una validez empírica que pocos poseen. Disponemos en Psicología de la Personalidad de un cuerpo de conocimientos que representa el Paradigma dentro del cual con mucha probabilidad nos moveremos en los próximos años.
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19
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Nguyen F, Boulant N, Ithier G, Bertet P, Pothier H, Vion D, Esteve D. Current to frequency conversion in a Josephson circuit. Phys Rev Lett 2007; 99:187005. [PMID: 17995431 DOI: 10.1103/physrevlett.99.187005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2007] [Indexed: 05/25/2023]
Abstract
The voltage oscillations which occur in an ideally current-biased Josephson junction were proposed to make a current standard for metrology. We demonstrate similar oscillations in a more complex Josephson circuit derived from the Cooper pair box: the quantronium. When a constant current I is injected in the gate capacitor of this device, oscillations develop at the frequency f(B)=I/2e, with e the electron charge. We detect these oscillations through the sidebands induced at multiples of f(B) in the spectrum of a microwave signal reflected on the circuit, up to currents I exceeding 100 pA. We discuss the potential interest of this current-to-frequency conversion experiment for metrology.
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Affiliation(s)
- F Nguyen
- Quantronics Group, Service de Physique de l'Etat Condensé (CNRS URA 2464), DSM/DRECAM/SPEC, CEA-Saclay, 91191 Gif-sur-Yvette, France
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20
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Ithier G, Collin E, Joyez P, Vion D, Esteve D, Ankerhold J, Grabert H. Zener enhancement of quantum tunneling in a two-level superconducting circuit. Phys Rev Lett 2005; 94:057004. [PMID: 15783681 DOI: 10.1103/physrevlett.94.057004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2004] [Indexed: 05/24/2023]
Abstract
We have investigated the macroscopic quantum tunneling (MQT) of the phase across a Josephson junction embedded in a superconducting circuit. This system is equivalent to a spin 1/2 particle in a potential energy well. The MQT escape rate of such a particle was recently predicted to be strongly modified when a crossing of its inner Zeeman levels occurs while tunneling. In this regime, we observe a significant enhancement of the MQT rate and compare it to theory.
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Affiliation(s)
- G Ithier
- Quantronics group, Service de Physique de l'Etat Condensé, DSM/DRECAM, CEA Saclay, 91191 Gif-sur-Yvette, France
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21
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Siddiqi I, Vijay R, Pierre F, Wilson CM, Frunzio L, Metcalfe M, Rigetti C, Schoelkopf RJ, Devoret MH, Vion D, Esteve D. Direct observation of dynamical bifurcation between two driven oscillation states of a Josephson junction. Phys Rev Lett 2005; 94:027005. [PMID: 15698220 DOI: 10.1103/physrevlett.94.027005] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2003] [Indexed: 05/24/2023]
Abstract
We performed a novel phase-sensitive microwave reflection experiment which directly probes the dynamics of the Josephson plasma resonance in both the linear and the nonlinear regime. When the junction was driven below the plasma frequency into the nonlinear regime, we observed for the first time the transition between two different dynamical states predicted for nonlinear systems. In our experiment, this transition appears as an abrupt change in the reflected signal phase at a critical excitation power. This controlled dynamical switching can form the basis of a sensitive amplifier, in particular, for the readout of superconducting qubits.
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Affiliation(s)
- I Siddiqi
- Departments of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520-8284, USA
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22
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Collin E, Ithier G, Aassime A, Joyez P, Vion D, Esteve D. NMR-like control of a quantum bit superconducting circuit. Phys Rev Lett 2004; 93:157005. [PMID: 15524928 DOI: 10.1103/physrevlett.93.157005] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2004] [Indexed: 05/24/2023]
Abstract
Coherent superpositions of quantum states have already been demonstrated in different superconducting circuits based on Josephson junctions. These circuits are now considered for implementing quantum bits. We report on experiments in which the state of a qubit circuit, the quantronium, is efficiently manipulated using methods inspired from nuclear magnetic resonance (NMR): multipulse sequences are used to perform arbitrary operations, to improve their accuracy, and to fight decoherence.
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Affiliation(s)
- E Collin
- Quantronics group, Service de Physique de l'Etat Condensé, DSM/DRECAM, CEA Saclay, 91191 Gif-sur-Yvette, France
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Abstract
We have designed and operated a superconducting tunnel junction circuit that behaves as a two-level atom: the "quantronium." An arbitrary evolution of its quantum state can be programmed with a series of microwave pulses, and a projective measurement of the state can be performed by a pulsed readout subcircuit. The measured quality factor of quantum coherence Qphi approximately 25,000 is sufficiently high that a solid-state quantum processor based on this type of circuit can be envisioned.
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Affiliation(s)
- D Vion
- Quantronics Group, Service de Physique de l'Etat Condensé, Direction des Sciences de la Matière, Commissariat à l'Energie Atomique-Saclay, 91191 Gif-sur-Yvette, France.
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Vion D, Götz M, Joyez P, Esteve D, Devoret MH. Thermal Activation above a Dissipation Barrier: Switching of a Small Josephson Junction. Phys Rev Lett 1996; 77:3435-3438. [PMID: 10062219 DOI: 10.1103/physrevlett.77.3435] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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