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Ion Traps A gentle introduction Online at: https://doi.org/10.1088/978-0-7503-5472-1 Ion Traps A gentle introduction Masatoshi Kajita Terahertz Technology Research Center, National Institute of Information and Communications Technology, Tokyo, Japan IOP Publishing, Bristol, UK ªIOPPublishingLtd2022 Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording orotherwise,withoutthepriorpermissionofthepublisher,orasexpresslypermittedbylawor undertermsagreedwiththeappropriaterightsorganization.Multiplecopyingispermittedin accordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgency,theCopyright ClearanceCentreandotherreproductionrightsorganizations. PermissiontomakeuseofIOPPublishingcontentotherthanassetoutabovemaybesought [email protected]. MasatoshiKajitahasassertedhisrighttobeidentifiedastheauthorofthisworkinaccordance withsections77and78oftheCopyright,DesignsandPatentsAct1988. ISBN 978-0-7503-5472-1(ebook) ISBN 978-0-7503-5470-7(print) ISBN 978-0-7503-5473-8(myPrint) ISBN 978-0-7503-5471-4(mobi) DOI 10.1088/978-0-7503-5472-1 Version:20221201 IOPebooks BritishLibraryCataloguing-in-PublicationData:Acataloguerecordforthisbookisavailable fromtheBritishLibrary. PublishedbyIOPPublishing,whollyownedbyTheInstituteofPhysics,London IOPPublishing,No.2TheDistillery,Glassfields,AvonStreet,Bristol,BS20GR,UK USOffice:IOPPublishing,Inc.,190NorthIndependenceMallWest,Suite601,Philadelphia, PA19106,USA Contents Preface viii Acknowledgement ix Author biography x 1 What is an ion trap? 1-1 1.1 Introduction 1-1 1.2 Equation of motion of ions and Maxwell’s equation 1-2 1.3 Can we trap ions using only a DC electric field? 1-3 1.4 Trap using DC magnetic field and DC electric field (Penning trap) 1-4 1.5 Fundamentals of an RF trap 1-6 1.6 Different configurations of electrodes to give inhomogeneous 1-8 electric field 1.6.1 Electrodes for three-dimensional trapping 1-9 1.6.2 Two-dimensional RF trapping + DC electric trapping 1-11 1.7 Frequency of the AC electric field trap 1-14 1.8 Production of ions 1-15 References 1-16 2 Optical treatments of ions 2-1 2.1 Energy structure of ions 2-1 2.2 Optical pumping 2-8 2.3 Monitoring the quantum state by the quantum jump 2-9 2.4 Laser cooling of trapped ions 2-10 2.4.1 Doppler cooling 2-11 2.4.2 Sideband cooling 2-14 2.4.3 Sideband Raman cooling 2-15 2.4.4 EIT cooling 2-15 2.4.5 Sympathetic cooling 2-17 2.5 Crystalization of laser cooled ions 2-17 2.6 Trapping of ions by optical dipole force 2-21 2.7 Optical manipulation and entropy 2-22 References 2-23 3 Quantum characteristics of trapped ion 3-1 3.1 Coupling between multi eigenstates 3-1 v IonTraps 3.2 Schrödinger’s cat 3-3 3.3 Entangled state 3-7 3.4 Interaction between a single trapped ion and a single photon 3-8 in a cavity 3.5 Quantum computer 3-10 References 3-12 4 Chemical reaction of trapped ions 4-1 4.1 The motivation to study the chemical reaction of trapped ions 4-1 4.2 Mass spectrum of RF-trapped ions 4-2 4.3 Reaction with H molecules 4-3 2 4.4 The reaction between Ca+ ions and molecules at room temperature 4-4 4.5 Chemical reaction between polar molecular ions and polar molecules 4-6 4.6 Prospect to search for the rate of collision between ultra-cold ions 4-8 and atoms (or molecules) References 4-10 5 Atomic clocks using trapped ions 5-1 5.1 What is an atomic clock? 5-1 5.2 Measurement uncertainty 5-2 5.2.1 Statistical uncertainty 5-2 5.2.2 Systematic uncertainty 5-4 5.2.3 Concepts of accuracy and stability 5-4 5.3 Special characteristics of atomic clocks using trapped ions 5-5 5.4 Precision measurement of hyperfine transition frequencies of 5-6 alkali-like ions 5.5 Precision measurement of the optical transition frequencies of 5-10 atomic ions 5.5.1 Measurement with alkali-like ions 5-12 5.5.2 Measurement with alkali earth-like ions 5-16 5.5.3 Measurement with highly charged ions 5-18 5.6 Measurement of transition frequencies of molecular ions 5-19 5.6.1 Experimental results of the molecular ion spectrum 5-20 5.6.2 Prospect for the precision measurements of transition 5-22 frequencies of molecular ions 5.6.3 The vibrational transition frequencies of diatomic polar 5-23 molecular ions 5.6.4 The vibrational transition frequencies of homonuclear 5-25 diatomic molecular ions vi IonTraps 5.7 Precision measurement of frequency in the THz region 5-28 5.8 Search for the variation in fundamental constants by precision 5-30 frequency measurement 5.9 Precision measurement of the mass of an ion using a Penning trap 5-32 References 5-33 6 Conclusion 6-1 Appendix A: Transition between two or three states A-1 Appendix B: Stark and Zeeman energy shift B-1 Appendix C: Motion mode of two cold ions in a string crystal C-1 Appendix D: Bose–Einstein condensation D-1 Appendix E: Feshbach resonance E-1 Appendix F: Dark matter F-1 vii Preface Detailed research into particles (atoms, molecules, etc) is possible by observing the sameparticlescontinuouslyforalongperiod.Forthispurpose,weneedsomeforce fortrappingwithoutchangingthepropertiesofthetrappedparticles.Themotionof ions can be manipulated by the electric or magnetic field. Three-dimensional trapping of an ion is possible using a combination of the DC magnetic field and theinhomogeneousDCelectricfield(Penningtrap).APenningtrapisusefulforthe precision measurement of mass ratios between different charged particles. UsinganinhomogeneousRFelectricfield,ionsaretightlytrappedinasmallarea foralongperiodoftime(RFtrap,Paultrap).Themotionenergyofthetrappedion is reduced to the lowest eigen states by laser cooling. The internal quantum energy state of the trapped ion can be also manipulated. Therefore, we can observe the phenomena of one or a few ions with a deterministic quantum state (eigen state or coupled state). For example, a single ion was observed at two positions simulta- neously(Schroedinger’scat).Theprecisionmeasurementoftransitionfrequenciesof RF trapped ions has been performed and the fractional uncertainty of 10−18 was obtained with a few transitions. This book introduces the fundamentals of ion trap technology and their use for the development of new physics, chemistry, or engineering and is targetted at graduate course students. The development of the ion trap was the subject of the Nobel prizes: 1989 H G Dehmelt and W Paul 2012 D J Wineland viii Acknowledgement The research activity of the author is supported by a Grant-in-Aid for Scientific Research (B) (Grant Nos. JP17H02881 and JP20H01920), and a Grant-in-Aid for Scientific Research (C) (Grant Nos. JP17K06483 and 16K05500) from the Japan Society for the Promotion of Science (JSPS). The author is highly appreciative of discussions with Y Yano, T Ido, N Ohtsubo, A Shinjo-Kihara, H Hachisu, S Nagano, M Kumagai, S Hayashi, N Sekine, and M Hara, all from the NICT, Japan, as well as K Okada (Sophia University), T Aoki (the University of Tokyo),andNKimura(RIKEN).TheauthorisgratefultoKKametaandJNavas (IOP, UK) for the opportunity to write this book. ix