Coulomb crystal studies, sympathetic cooling, and mass spectrometry using laser cooled Be_1hn+ ions [Elektronische Ressource] / vorgelegt von Ulf Fröhlich

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• Physik

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• Publié par: heinrich-heine-universitat_dusseldorf
• Publié le: 01 janvier 2008
• Nombre de lectures: 9
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

Coulomb Crystal Studies, Sympathetic Cooling,
and Mass Spectrometry Using
+Laser-Cooled Be Ions
Inaugural-Dissertation
zur Erlangung des Doktorgrades
der Mathematisch-Naturwissenschaftlichen Fakult¨at
der Heinrich-Heine-Universit¨at Du¨sseldorf
vorgelegt von
Ulf Fr¨ohlich
aus Munc¨ hen
D¨ usseldorf, April 2008Aus dem Institut fur¨ Experimentalphysik
der Heinrich-Heine-Universit¨at Du¨sseldorf
Gedruckt mit der Genehmigung der
Mathematisch-Naturwissenschaftlichen Fakult¨at der
Heinrich-Heine-Universit¨at Du¨sseldorf
Referent: Prof. S.Schiller, Ph.D.
Koreferent: Prof. Dr. A.G¨orlitz
Tag der mundlic¨ hen Prufung:¨ 24.06.2008Contents
1 Introduction 1
1.1 OverviewoftheProject......................... 1
+1.2 Laser Spectroscopy of Ultracold HD Ions and Related Topics . . . . 2
1.3 StructureofthePresentThesis..................... 6
2 Theoretical Introduction 7
2.1 Time-AveragedTrapPotential ..................... 7
2.2 Thermal Equilibrium States of Confined Single-Species Plasmas . . . 10
2.2.1 Single-SpeciesPlasmasandtheOCPModel.......... 10
2.2.2 TheChargedFluidModel.................... 12
2.3 Laser-Cooled Fluorescence Mass Spectrometry (LCF-MS) . . . . . . 15
2.3.1 EffectiveTrapPotential..................... 15
2.3.2 SimplifiedModelofLCF-MS.................. 18
3UHVSetup 27
3.1 OverviewoftheCompleteSetup.................... 27
3.2 LinearRFTrap.............................. 29
3.3 Trap Supply Electronics . ........................ 31
3.4 PhotomultiplierTubeandCCDCamera................ 34ii CONTENTS
4 Cooling Laser System 37
4.1 OverviewoftheCompleteSetup.................... 38
4.2 DoublyResonantSFGof313nmLight................. 39
4.2.1 TheoryofDR-SFG........................ 40
4.2.2 NonlinearCrystalandOpticalCavity............. 42
4.2.3 Fundamental Lasers and Stabilization Scheme . . . . . . . . . 44
4.2.4 Output Power, Tunability, and Spectral Purity . . . . . . . . 46
4.3 Absolute Frequency Stabilization .................... 49
4.3.1 Doppler-Free Modulation Transfer Spectroscopy . . . . . . . 50
4.3.2 FrequencyShifter......................... 52
5 Laser-Cooled Fluorescence Mass Spectrometry (LCF-MS) 55
5.1 CoolingLaserDetuning......................... 56
5.2 SecularExcitationofLaser-CooledIons................ 58
+95.2.1 Experimental Results: I. Be –UpwardScans........ 58
9 +5.2.2 Experimental Results: II. Be –DownwardScans...... 60
5.3 LCF-MSofSympatheticalyCooledIons................ 62
14 +5.3.1 Experimental Results: I. N ................ 64
4 +5.3.2 Experimental Results: II. He ................ 6
+ +
5.3.3 Experimental Results: III. HD &D ............ 68
9 +6 Be Ion Crystals 73
6.1 TransitiontotheCrystalizedState................... 73
6.2 Temperature Determination from the Fluorescence Signal . . . . . . 77
+96.3 Ellipsoidal Shaped Be IonCrystals.................. 83
4 +7 Sympathetic Crystallization of He Ions 91
7.1 TheTwo-BodyCoulombSystem.................... 91
9 + 4 +7.2 Two-Species Be - He IonCrystals.................. 93CONTENTS iii
8 Summary and Outlook 97
A Electrostatic Potential within a Constant Density Ellipsoid 100
B Mean Photon Scattering Rate 102
C Alternative RF Trap Setup and Miniature Electron Gun 104
Bibliography 117
Acknowledgment 119iv CONTENTSChapter 1
Introduction
1.1 Overview of the Project
The work described in this thesis is part of a project which may be entitled as
High-Precision Laser Spectroscopy of Ultracold Molecular Hydrogen Ions.Starting
in the year 1999 at the University of Konstanz [1–4] and now being conducted in
the group of Prof. S.Schiller at the University of Du¨sseldorf, progress achieved so
far may be divided into three stages.
I. In a first stage, described in Refs. [1–4], conceptual work was done on the
trapping and cooling of molecular hydrogen ions, leading to the choice of a
linear rf (Paul) trap together with sympathetic cooling, using laser-cooled
+9Be ions. A two-photon, ro-vibrational transition in the electronic ground
+state of the HD molecular ion was selected, suitable for high precision laser
spectroscopy. Furthermore, a detection scheme was worked out, employing
+selective photodissociation of the HD molecular ions in the excited state. In
addition to conceptual work, an ultra-high vacuum (UHV) chamber for the
linear rf trap was set up together with a first version of the 313nm cooling
9 +laser system, required for Doppler laser cooling of the Be ions.
II. In a second stage, described in this thesis as well as Refs. [4–8], the experimen-
tal setup was completed and first results were obtained. In particular, laser
9 + 9 +cooling and crystallization of Be ions was demonstrated, the Be ion crys-
tals being characterized with respect to their crystal structure, outer shape,
14 + + +and temperature. Furthermore, sympathetic cooling of N ,BeD,BeH,
+ + +4He ,HD,andD ions was demonstrated with both the sympathetically
cooled (SC) and the laser-cooled (LC) ions in a cloud-like state. Accordingly,
sympathetic cooling down to a mass ratio of m /m =0.22 was shown to beSC LC
possible as was later confirmed for the crystalline state [9]. Finally, sympa-
+4thetic crystallization of He ions was demonstrated by preparing two-species
9 + 4 +Be - He ion crystals of different size, each with a core of crystallized non-
4 +fluorescent He ions.2 Introduction
III. Subsequent experimental work performed in the group of Prof. S.Schiller up
to the present time is described in Refs.[9–15], a short summary of which is
found at the end of this thesis. In particular, sympathetic crystallization of
+ + +H ,HD ,andD as well as many other atomic and molecular ion species was
2 2
demonstrated, culminating in the first laser spectroscopic measurements of
+ 9 +ro-vibrational transitions in ultracold HD ions, embedded into a Be ion
crystal.
1.2 High-Precision Laser Spectroscopy of Ultracold
+HD Ions and Related Topics
In the following, various topics will be described, all related in some respect to the
+ultimate goal of high-precision laser spectroscopy of ultracold HD molecular ions.
Laser Spectroscopy of the Molecular Hydrogen Ion
Among numerous motivations [1,2,6,14,16] for high-precision laser spectroscopy
+ + +of the molecular hydrogen ion, i.e. H and its isotopomers HD and D ,ameasure-
2 2
ment of the fundamental mass ratios m /m and m /m is regarded as the maine p p d
motivation for the project described in Sect. 1.1. So far, the most accurate values
−10of m /m and m /m are specified with relative uncertainties of 4.6· 10 [17,18]e p p d
−10and 2.0· 10 [17], respectively, obtained by Penning trap mass spectrometry and
electron spin resonance of hydrogen-like ions in a Penning trap. Alternatively, a
measurement of m /m and m /m by laser spectroscopy of ro-vibrational tran-e p p d
+sitions in HD should be feasible as well. This is due to the dependencies of the
vibrational and rotational level energies on the mass ratio m /μ,whichinafirste
1/2approximation are given by E ∼R (m /μ) and E ∼R (m /μ)[14].Here,vib ∞ e rot ∞ e
μ = m m /(m +m ) is the reduced mass of the two nuclei. Expectations withp d p d
regards to accuracy, surpassing those achieved by Penning trap mass spectrometry,
are based on two facts: (i) by taking appropriate measures against line-shifting
and broadening effects such as collision, Doppler, and transit time broadening, a
spectroscopic resolution at the level of the relative linewidth due to spontaneous
−13decay δν/ν ≤ 10 should be possible. In particular, spatial confinement of the
+HD molecular ions, cooling to the milli-Kelvin range and/or use of two-photon
+ +spectroscopy [1,19] will be required. (ii) the molecular hydrogen ions H ,HD,
2
+
and D are the simplest molecules of all, each representing a fundamental three-
2
body system. Accordingly, high-precision ab initio molecular calculations of the
ro-vibrational level energies and transition rates are possible [16,20–22]. Thus, by
+
comparing the measured ro-vibrational transition frequencies in HD with the cor-
responding molecular calculations, determination of the fundamental mass ratios
m /m and m /m should be possible with an accuracy similar to those of the ex-e p p d