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Uribe AJ, Cridland Mathad A, Lacy JH, Pinder J, Willetts R, Verdú J. High frequency properties of a planar ion trap fabricated on a chip. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:083202. [PMID: 36050058 DOI: 10.1063/5.0091745] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 07/16/2022] [Indexed: 06/15/2023]
Abstract
We report on the measurement of the high frequency properties of a planar Penning ion trap fabricated on a chip. Two types of chips have been measured: the first manufactured by photolithographic metal deposition on a p-doped silicon substrate and the second made with printed circuit board technology on an alumina substrate. The input capacitances and the admittances between the different trap's electrodes play a critical role in the electronic detection of the trapped particles. The measured input capacitances of the photolithographic chip amount to 65-76 pF, while the values for the printed circuit board chips are in the range of 3-5 pF. The latter are small enough for detecting non-destructively a single trapped electron or ion with a specifically tuned LC resonator. We have also measured a mutual capacitance of ∼85 fF between two of the trap's electrodes in the printed circuit board chip. This enables the detection of single, or very few, trapped particles in a broader range of charge-to-mass ratios with a simple resistor on the chip. We provide analytic calculations of the capacitances and discuss their origin and possible further reduction.
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Affiliation(s)
- A J Uribe
- Department of Physics and Astronomy, University of Sussex, Falmer BN1 9QH, United Kingdom
| | - A Cridland Mathad
- Department of Physics and Astronomy, University of Sussex, Falmer BN1 9QH, United Kingdom
| | - J H Lacy
- Department of Physics and Astronomy, University of Sussex, Falmer BN1 9QH, United Kingdom
| | - J Pinder
- Department of Physics and Astronomy, University of Sussex, Falmer BN1 9QH, United Kingdom
| | - R Willetts
- Department of Physics and Astronomy, University of Sussex, Falmer BN1 9QH, United Kingdom
| | - J Verdú
- Department of Physics and Astronomy, University of Sussex, Falmer BN1 9QH, United Kingdom
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Nandi J, Sikdar AK, Das P, Ray A. Design of a helical resonator with improved figure of merit. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:014706. [PMID: 35104962 DOI: 10.1063/5.0065422] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 01/03/2022] [Indexed: 06/14/2023]
Abstract
A helical resonator serves as a key element for the detection of the trapped charged particles in a Penning trap. In order to compare the performance of the helical resonators, the concept of figure of merit (FOM) was introduced by Ulmer et al. [Nucl. Instrum. Methods Phys. Res., Sect. A 705, 55-60 (2013)]. In this work, we optimized the geometrical parameters of a resonator by numerical simulations keeping its outer dimensions and the diameter of the copper wire fixed and obtained the best possible value of FOM under these constraints. The corresponding 95 MHz helical resonator has been designed and fabricated, and its measured value of FOM is in good agreement with the simulated values. An empirical relationship between the total length of the wire to make the helical coil and the resonance frequency has been obtained. The simulations show that the FOM increases considerably with the increase in the conductivity of the building material, and this would be useful in detecting the feeble trap signal in cryogenic environment.
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Affiliation(s)
- J Nandi
- Variable Energy Cyclotron Centre, 1/AF Bidhannagar, Kolkata 700064, India
| | - A K Sikdar
- Variable Energy Cyclotron Centre, 1/AF Bidhannagar, Kolkata 700064, India
| | - P Das
- Variable Energy Cyclotron Centre, 1/AF Bidhannagar, Kolkata 700064, India
| | - A Ray
- Variable Energy Cyclotron Centre, 1/AF Bidhannagar, Kolkata 700064, India
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Andrews B, Conduit G. Absence of diagonal force constants in cubic Coulomb crystals. Proc Math Phys Eng Sci 2020; 476:20200518. [PMID: 33402875 PMCID: PMC7776971 DOI: 10.1098/rspa.2020.0518] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Accepted: 11/25/2020] [Indexed: 11/20/2022] Open
Abstract
The quasi-harmonic model proposes that a crystal can be modelled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss’s law shows that the ion–ion potential for a cubic Coulomb system can have no diagonal harmonic contribution and so cannot necessarily be modelled by springs. We investigate the repercussions of this observation by examining three illustrative regimes: the bare ionic, density tight-binding and density nearly-free electron models. For the bare ionic model, we demonstrate the zero elements in the force constants matrix and explain this phenomenon as a natural consequence of Poisson’s law. In the density tight-binding model, we confirm that the inclusion of localized electrons stabilizes all major crystal structures at harmonic order and we construct a phase diagram of preferred structures with respect to core and valence electron radii. In the density nearly-free electron model, we verify that the inclusion of delocalized electrons, in the form of a background jellium, is enough to counterbalance the diagonal force constants matrix from the ion–ion potential in all cases and we show that a first-order perturbation to the jellium does not have a destabilizing effect. We discuss our results in connection to Wigner crystals in condensed matter, Yukawa crystals in plasma physics, as well as the elemental solids.
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Affiliation(s)
- Bartholomew Andrews
- TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
- Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Gareth Conduit
- TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
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Ruiz-García A, Alonso D. Spatial configurations and temperature profiles in nonequilibrium steady state of two-species trapped ion systems. Phys Rev E 2020; 101:012129. [PMID: 32069590 DOI: 10.1103/physreve.101.012129] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2019] [Indexed: 11/07/2022]
Abstract
We study Coulomb crystals containing two ion species simultaneously confined in radio frequency traps and coupled to different thermal reservoirs located in two separate regions. We use a three-dimensional model to simulate the trapped bicrystal and show in a numerically rigorous manner the effects of the mass dependence of the trapping frequencies on the underlying nonequilibrium dynamics and the temperature profiles. By solving the classical Langevin equations of motion, we obtain the spatial probability densities of the two ion species and the kinetic temperature profiles across the axial direction of the trap in the nonequilibrium steady state. We analyze trapping conditions leading to bicrystals that exhibit ion conformations ranging from a linear chain of alternating ion species to two- and three-dimensional configurations. The results evidence the spatial segregation of the two ion species due to the mass dependence of the trapping frequencies and the increase of ion delocalization for heavier ion species and/or weaker trapping confinements. We also show the correlation between the increase of the temperature gradient in the bulk and this enhancement of ion delocalization through the trap.
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Affiliation(s)
- A Ruiz-García
- Departamento de Física, Universidad de La Laguna, La Laguna 38203, Spain and IUdEA Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, La Laguna 38203, Spain
| | - D Alonso
- Departamento de Física, Universidad de La Laguna, La Laguna 38203, Spain and IUdEA Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, La Laguna 38203, Spain
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Ruiz-García A, Fernández JJ, Alonso D. Delocalization and heat transport in multidimensional trapped ion systems. Phys Rev E 2019; 99:062105. [PMID: 31330614 DOI: 10.1103/physreve.99.062105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2019] [Indexed: 11/07/2022]
Abstract
We study the connection between heat transport properties of systems coupled to different thermal baths in two separate regions and their underlying nonequilibrium dynamics. We consider classical systems of interacting particles that may exhibit a certain degree of delocalization and whose effective dimensionality can be modified through the controlled variation of a global trapping potential. We focus on Coulomb crystals of trapped ions, which offer a versatile playground to shed light on the role that spatial constraints play on heat transport. We use a three-dimensional model to simulate the trapped ion system and show in a numerically rigorous manner to what extent heat transport properties could be feasibly tuned across the structural phase transitions among the linear, planar zigzag, and helical configurations. By solving the classical Langevin equations of motion, we analyze the steady state spatial distributions of the particles, the temperature profiles, and total heat flux through the various structural phase transitions that the system may experience. The results evidence a clear correlation between the degree of delocalization of the internal ions and the emergence of a nonzero gradient in the temperature profiles. The signatures of the phase transitions in the total heat flux as well as the optimal spatial configuration for heat transport are shown.
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Affiliation(s)
- A Ruiz-García
- Departamento de Física, Universidad de La Laguna, La Laguna 38203, Spain.,IUdEA Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, La Laguna 38203, Spain
| | - J J Fernández
- Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, United Kingdom
| | - D Alonso
- Departamento de Física, Universidad de La Laguna, La Laguna 38203, Spain.,IUdEA Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, La Laguna 38203, Spain
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Ball H, Marciniak CD, Wolf RN, Hung ATH, Pyka K, Biercuk MJ. Site-resolved imaging of beryllium ion crystals in a high-optical-access Penning trap with inbore optomechanics. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2019; 90:053103. [PMID: 31153278 DOI: 10.1063/1.5049506] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2018] [Accepted: 04/13/2019] [Indexed: 06/09/2023]
Abstract
We present the design, construction, and characterization of an experimental system capable of supporting a broad class of quantum simulation experiments with hundreds of spin qubits using 9Be+ ions in a Penning trap. This article provides a detailed overview of the core optical and trapping subsystems and their integration. We begin with a description of a dual-trap design separating loading and experimental zones and associated vacuum infrastructure design. The experimental-zone trap electrodes are designed for wide-angle optical access (e.g., for lasers used to engineer spin-motional coupling across large ion crystals) while simultaneously providing a harmonic trapping potential. We describe a near-zero-loss liquid-cryogen-based superconducting magnet, employed in both trapping and establishing a quantization field for ion spin-states and equipped with a dual-stage remote-motor LN2/LHe recondenser. Experimental measurements using a nuclear magnetic resonance (NMR) probe demonstrate part-per-million homogeneity over 7 mm-diameter cylindrical volume, with no discernible effect on the measured NMR linewidth from pulse-tube operation. Next, we describe a custom-engineered inbore optomechanical system which delivers ultraviolet (UV) laser light to the trap and supports multiple aligned optical objectives for topview and sideview imaging in the experimental trap region. We describe design choices including the use of nonmagnetic goniometers and translation stages for precision alignment. Furthermore, the optomechanical system integrates UV-compatible fiber optics which decouple the system's alignment from remote light sources. Using this system, we present site-resolved images of ion crystals and demonstrate the ability to realize both planar and three-dimensional ion arrays via control of rotating wall electrodes and radial laser beams. Looking to future work, we include interferometric vibration measurements demonstrating root-mean-square trap motion of ∼33 nm (∼117 nm) in the axial (transverse) direction; both values can be reduced when operating the magnet in free-running mode. The paper concludes with an outlook toward extensions of the experimental setup, areas for improvement, and future experimental studies.
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Affiliation(s)
- H Ball
- ARC Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia
| | - Ch D Marciniak
- ARC Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia
| | - R N Wolf
- ARC Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia
| | - A T-H Hung
- ARC Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia
| | - K Pyka
- ARC Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia
| | - M J Biercuk
- ARC Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia
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McDermott D, Olson Reichhardt CJ, Reichhardt C. Structural transitions and hysteresis in clump- and stripe-forming systems under dynamic compression. SOFT MATTER 2016; 12:9549-9560. [PMID: 27834430 DOI: 10.1039/c6sm01939k] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Using numerical simulations, we study the dynamical evolution of particles interacting via competing long-range repulsion and short-range attraction in two dimensions. The particles are compressed using a time-dependent quasi-one dimensional trough potential that controls the local density, causing the system to undergo a series of structural phase transitions from a low density clump lattice to stripes, voids, and a high density uniform state. The compression proceeds via slow elastic motion that is interrupted with avalanche-like bursts of activity as the system collapses to progressively higher densities via plastic rearrangements. The plastic events vary in magnitude from small rearrangements of particles, including the formation of quadrupole-like defects, to large-scale vorticity and structural phase transitions. In the dense uniform phase, the system compresses through row reduction transitions mediated by a disorder-order process. We characterize the rearrangement events by measuring changes in the potential energy, the fraction of sixfold coordinated particles, the local density, and the velocity distribution. At high confinements, we find power law scaling of the velocity distribution during row reduction transitions. We observe hysteresis under a reversal of the compression when relatively few plastic rearrangements occur. The decompressing system exhibits distinct phase morphologies, and the phase transitions occur at lower compression forces as the system expands compared to when it is compressed.
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Affiliation(s)
- Danielle McDermott
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. and Department of Physics, Wabash College, Crawfordsville, Indiana 47933, USA.
| | | | - Charles Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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Goodwin JF, Stutter G, Thompson RC, Segal DM. Resolved-Sideband Laser Cooling in a Penning Trap. PHYSICAL REVIEW LETTERS 2016; 116:143002. [PMID: 27104702 DOI: 10.1103/physrevlett.116.143002] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2014] [Indexed: 06/05/2023]
Abstract
We report the laser cooling of a single ^{40}Ca^{+} ion in a Penning trap to the motional ground state in one dimension. Cooling is performed in the strong binding limit on the 729-nm electric quadrupole S_{1/2}↔D_{5/2} transition, broadened by a quench laser coupling the D_{5/2} and P_{3/2} levels. We find the final ground-state occupation to be 98(1)%. We measure the heating rate of the trap to be very low with n[over ¯][over ˙]≈0.3(2) s^{-1} for trap frequencies from 150-400 kHz, consistent with the large ion-electrode distance.
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Affiliation(s)
- J F Goodwin
- Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
| | - G Stutter
- Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
| | - R C Thompson
- Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
| | - D M Segal
- Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
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Yan LL, Wan W, Chen L, Zhou F, Gong SJ, Tong X, Feng M. Exploring structural phase transitions of ion crystals. Sci Rep 2016; 6:21547. [PMID: 26865229 PMCID: PMC4749997 DOI: 10.1038/srep21547] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2015] [Accepted: 01/27/2016] [Indexed: 11/09/2022] Open
Abstract
Phase transitions have been a research focus in many-body physics over past decades. Cold ions, under strong Coulomb repulsion, provide a repealing paradigm of exploring phase transitions in stable confinement by electromagnetic field. We demonstrate various conformations of up to sixteen laser-cooled (40)Ca(+) ion crystals in a home-built surface-electrode trap, where besides the usually mentioned structural phase transition from the linear to the zigzag, two additional phase transitions to more complicated two-dimensional configurations are identified. The experimental observation agrees well with the numerical simulation. Heating due to micromotion of the ions is analysed by comparison of the numerical simulation with the experimental observation. Our investigation implies very rich and complicated many-body behaviour in the trapped-ion systems and provides effective mechanism for further exploring quantum phase transitions and quantum information processing with ultracold trapped ions.
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Affiliation(s)
- L. L. Yan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
- University of the Chinese Academy of Sciences, Beijing 100049, China
| | - W. Wan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
- University of the Chinese Academy of Sciences, Beijing 100049, China
| | - L. Chen
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
| | - F. Zhou
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
| | - S. J. Gong
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
- University of the Chinese Academy of Sciences, Beijing 100049, China
| | - X. Tong
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
| | - M. Feng
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
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Cornejo JM, Colombano M, Doménech J, Block M, Delahaye P, Rodríguez D. Extending the applicability of an open-ring trap to perform experiments with a single laser-cooled ion. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2015; 86:103104. [PMID: 26520937 DOI: 10.1063/1.4932310] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
A special ion trap was initially built up to perform β-ν correlation experiments with radioactive ions. The trap geometry is also well suited to perform experiments with laser-cooled ions, serving for the development of a new type of Penning trap, in the framework of the project TRAPSENSOR at the University of Granada. The goal of this project is to use a single (40)Ca(+) ion as detector for single-ion mass spectrometry. Within this project and without any modification to the initial electrode configuration, it was possible to perform Doppler cooling on (40)Ca(+) ions, starting from large clouds and reaching single ion sensitivity. This new feature of the trap might be important also for other experiments with ions produced at radioactive ion beam facilities. In this publication, the trap and the laser system will be described, together with their performance with respect to laser cooling applied to large ion clouds down to a single ion.
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Affiliation(s)
- J M Cornejo
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain
| | - M Colombano
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain
| | - J Doménech
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain
| | - M Block
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
| | - P Delahaye
- Grand Accélérateur National d'Ions Lourds, 14000 Caen, France
| | - D Rodríguez
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain
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Abstract
Coulomb crystals-as a source of translationally cold, highly localized ions-are being increasingly utilized in the investigation of ion-molecule reaction dynamics in the cold regime. To develop a fundamental understanding of ion-molecule reactions, and to challenge existing models that describe the rates, product branching ratios, and temperature dependence of such processes, investigators need to exercise full control over the experimental reaction parameters. This requires not only state selection of the reactants, but also control over the collision process (e.g., the collisional energy and angular momentum) and state-selective product detection. The combination of Coulomb crystals in ion traps with cold neutral-molecule sources is enabling the measurement of state-selective reaction rates in a diverse range of systems. With the development of appropriate product detection techniques, we are moving toward the ultimate goal of examining low-energy, state-to-state ion-molecule reaction dynamics.
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