An Introduction to Cold and Ultracold Chemistry: Atoms, Molecules, Ions and Rydbergs

278 Pages·2020·12.986 MB·English

by  Jesús Pérez Ríos

Jesús Pérez Ríos
An Introduction
to Cold and
Ultracold
Chemistry
Atoms, Molecules, Ions and Rydbergs
An Introduction to Cold and Ultracold
Chemistry
Jesús Pérez Ríos
An Introduction to Cold
and Ultracold Chemistry
Atoms, Molecules, Ions and Rydbergs
JesúsPérezRíos
DepartmentofMolecularPhysics
FritzHaberInstituteoftheMaxPlanckSociety
Berlin,Germany
ISBN978-3-030-55935-9 ISBN978-3-030-55936-6 (eBook)
https://doi.org/10.1007/978-3-030-55936-6
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TomynephewDimas
Preface
This book is devoted to master’s and graduate students interested in the most
intimate nature of chemical reactions at very low collision energies where the
inherent quantum mechanical nature of chemical processes emerges and becomes
tangible. My approach to the subject in this book revolves around presenting
novelandinterestingtheoreticalmethodsforstudyingcoldandultracoldchemistry
reactions,goingbeyondtheconventionaltechniquesinthefield.Moreover,Itryto
showthereaderthebroadnessofthefieldthroughthestudyofRydbergatoms,ions,
andphysicsbeyondthestandardmodelwithultracoldatomsandmolecules.
In general, cold and ultracold chemistry are assumed to be disciplines focused
on the control of chemical reactions involving atoms and molecules. However, in
this book, it is shown that there is a lot more to cold and ultracold chemistry! For
instance, we will see that ion–neutral collision leads to a new realm of chemical
reactions that require the development of a chemical intuition different than that
required for theneutral–neutral collision.Inthesamevein, the studyof Rydberg–
neutral collisions leads to a new set of chemical reactions that have acute effects
on the different applications of Rydberg atoms for the development of quantum
technologies. Moreover, throughout this book, the reader will see how cold and
ultracold molecules are useful systems for understanding the Standard Model of
particle physics and even the exploration of physics beyond the Standard Model.
Finally, I want to make a statement: no matter what you are working on, if it
involvesatomsandmolecules,chemistrywillalwaysbethere.Therefore,betterwe
understandthechemistrytodesignbettermachinesandbetterquantumsimulators.
This book is not just the result of my work, there are contributions from many
people in different ways. First, I would like to thank all those who contributed or
contribute to the field of cold and ultracold chemistry. Next, I would like to thank
Prof.SherwinLoveforhissupportduringthedevelopmentofthisbookandforhis
valuable comments on Chap.6, and Prof. Dr. Gerard Meijer for his understanding
andsupport.Also,IwouldliketothankDr.ChristianScheweforhishelpinsome
parts of this book, Dr. Rene Gerritsma for reading Chap.9, Dr. David Cassidy for
readingandcommentingonChap.12,Dr.MarjanMirahmadiforreadingChap.10,
Dr. Stefan Truppe for reading Chap.3, Dr. Matthew T. Eiles for reading Chaps. 7
and 8, and Simon Hofsäss for reading Chaps.1, 2, 3, and 4 of the book. Last but
notleast,Iwouldliketoexpressmygratitudetomyfamilyfortheirunconditional
vii
viii Preface
support, especially to my wife Anne for her constant help and motivation, to my
sisters for the support, to my dad for being my number one fan, to my nephew
Dimas,becausewithoutnoticing,hemakeseverythingfunnierandmorebeautiful,
andmymotherMaríaTeresaforherinsistentattitudeandforalwaysbeingtherefor
me.
Berlin,Germany JesúsPérezRíos
Contents
1 TheRealmofColdandUltracold ........................................ 1
1.1 WhyUltracoldTemperatures?....................................... 1
1.2 ColdandUltracoldChemistry....................................... 3
1.2.1 TheStandardApproach .................................... 3
1.2.2 AMorePhysicalApproach ................................ 3
1.3 UltracoldPhysicsandFundamentalPhysics........................ 5
References.................................................................... 6
2 QuantumScatteringTheory .............................................. 9
2.1 Collisions............................................................. 9
2.1.1 WhenDoesaCollisionOccur? ............................ 9
2.1.2 ExperimentalApproach:TheMeanFreePath............ 10
2.1.3 QuantumMechanicalCrossSection....................... 11
2.1.4 ClassicalCrossSection..................................... 12
2.2 ElasticCrossSection................................................. 14
2.2.1 Definition ................................................... 14
2.2.2 WignerThresholdLawfortheElasticCrossSection..... 17
2.2.3 CollisionBetweenTwoIdenticalParticles................ 19
2.3 TheScatteringLength................................................ 21
2.4 InelasticCrossSection............................................... 24
2.4.1 UnitarityoftheS-Matrix................................... 26
2.4.2 WignerThresholdLawforInelasticScattering........... 26
2.5 ScatteringResonances ............................................... 28
2.5.1 ShapeResonancesorOrbiting............................. 28
2.5.2 Fano–FeshbachResonances................................ 29
2.5.3 TheGloryEffect............................................ 31
References.................................................................... 33
3 UltracoldGases............................................................. 37
3.1 Bose–EinsteinCondensation ........................................ 37
3.1.1 TheIdealBoseGas......................................... 37
3.2 InteractingBoseGas................................................. 41
3.2.1 Gross–PitaevskiiEquation ................................. 42
ix
x Contents
3.2.2 Thomas–FermiApproximation............................ 44
3.2.3 HealingLength ............................................. 45
3.3 UltracoldDipolarGases ............................................. 46
3.3.1 Dipole–DipoleInteractions ................................ 47
3.3.2 TheoryoftheDipolarBose–EinsteinCondensation...... 48
3.4 SpinorBose–EinsteinCondensates.................................. 50
References.................................................................... 51
4 CoolingandTrappingofMolecules ...................................... 55
4.1 StarkDeceleration.................................................... 56
4.2 OpticalStarkDeceleration........................................... 58
4.3 ZeemanDecelerator.................................................. 61
4.4 LaserCooling......................................................... 63
4.5 BufferGasCooling................................................... 67
4.5.1 LoadingoftheTargetMolecules .......................... 67
4.5.2 Thermalization.............................................. 68
4.5.3 DiffusionoftheColdTargetMolecules................... 69
4.6 OpticalTrapping:DipoleTraps...................................... 70
4.7 MagneticTrapping................................................... 72
4.8 EvaporativeCooling.................................................. 73
4.9 AssemblyofMoleculesatUltracoldTemperatures ................ 75
4.9.1 Photoassociation............................................ 75
4.9.2 Magnetoassociation......................................... 76
References.................................................................... 77
5 UltracoldMolecularCollisions............................................ 83
5.1 Introduction........................................................... 83
5.2 ScatteringMolecularTheory:RigidRotor–RigidRotor
Scattering............................................................. 83
5.2.1 DistinguishableMolecule–MoleculeScattering .......... 83
5.2.2 IdenticalMolecule–MoleculeScattering.................. 90
5.2.3 The Role of Indistinguishability in
Molecule–MoleculeCollisions ............................ 93
5.3 MolecularCollisionsinanExternalField .......................... 93
5.3.1 DistinguishableMolecules................................. 94
5.3.2 IndistinguishableMolecules ............................... 96
5.4 UltracoldCollisionsofOxygenMoleculesinthePresence
ofanExternalMagneticField....................................... 98
5.4.1 ZeemanHamiltonianfor3(cid:2)Molecules................... 98
5.4.2 SpinRelaxationandZeemanSuppression ................ 101
5.4.3 MolecularScatteringTheoryinAction.................... 104
5.4.4 Fano–Feshbach Resonances in Ultracold
Molecule–MoleculeCollisions ............................ 109
5.4.5 Cross Section as a Function of the Collision
Energy:TheWignerThresholdLaws ..................... 110
Contents xi
5.4.6 Do Short-Range Interactions Play a Role in
UltracoldCollisions?....................................... 112
5.5 ComputationalTechniques........................................... 112
5.5.1 Single-ChannelScattering.................................. 113
5.5.2 Multi-channelScattering:ElasticandInelastic
Channels .................................................... 116
References.................................................................... 117
6 Three-Body Collisions at Ultracold Temperatures: An
EffectiveFieldTheoryApproach......................................... 119
6.1 TheRenormalizationGroup......................................... 119
6.2 Effective Field Theory Approach for Low-Energy
Two-BodyCollisions................................................. 122
6.3 EffectiveFieldTheoryforThree-BodyBosonicCollisions
InvolvingShort-RangedInteractions................................ 126
6.4 UniversalityontheThreeBosonProblem:EfimovStates
fromaRenormalizationGroupApproach........................... 131
6.5 ConcludingRemarks................................................. 133
References.................................................................... 134
7 UltracoldRydbergAtomsandUltralong-RangeRydberg
Molecules.................................................................... 137
7.1 RydbergAtoms....................................................... 137
7.1.1 SommerfeldOrbits ......................................... 139
7.1.2 PropertiesofRydbergAtoms.............................. 142
7.2 RydbergBlockade.................................................... 143
7.3 Ultralong-RangeRydbergMolecules ............................... 144
7.4 PotentialEnergyCurvesforUltralong-RangeRydberg
Molecules............................................................. 146
7.4.1 Low-lUltralong-RangeRydbergMolecules.............. 148
7.4.2 TrilobiteMolecules......................................... 149
7.4.3 ButterflyMolecules......................................... 151
References.................................................................... 152
8 Rydberg-NeutralUltracoldChemicalReactions........................ 155
8.1 Rydberg-NeutralElasticCollisions ................................. 155
8.2 Rydberg-NeutralInelasticandReactiveCollisions................. 157
8.2.1 L-MixingCollisions........................................ 159
8.2.2 Chemi-Ionization........................................... 163
8.2.3 CollisionTimeforChemi-IonizationandL-Mixing
Collisions:amoleculardynamicsapproach............... 166
8.2.4 SomeOpenQuestions...................................... 169
References.................................................................... 169
9 HybridAtom–IonSystems ................................................ 171
9.1 WhatIsaHybridSystem?........................................... 172
9.2 IonTraps.............................................................. 173