Ultralong-range Diatomic Molecules in External Electric and Magnetic Fields Dissertation zur Erlangung des Doktorgrades des Department Physik der Universit¨at Hamburg vorgelegt von Markus Kurz aus N¨urnberg Hamburg 2014 a Gutachter der Dissertation: Prof. Dr. Peter Schmelcher Prof. Dr. Hossein Sadeghpour Gutachter der Disputation: Prof. Dr. Peter Schmelcher Prof. Dr. Henning Moritz Datum der Disputation: 19.01.2015 VorsitzenderderPr¨ufungskommission: Prof.Dr.LudwigMathey VorsitzenderdesPromotionsausschusses: Prof. Dr. JanLouis Dekan der Fakult¨at f¨ur Mathematik, Informatik und Naturwissenschaften: Prof. Dr. Heinrich Graener a 1 “Per aspera ad astra.“ -Seneca1 1Lucius Annaeus Seneca (c. 4BC-AD65): Roman statesman, philosopher and dramatist [1]. a Zusammenfassung Ultralangreichweitige diatomare Molek¨ule in externen Feldern Gegenstand dieser Arbeit − ist die theoretische Untersuchung der Quanteneigenschaften von ultralangreichweitigen diatomaren Molek¨ulen in Anwesenheit externer elektrischer und magnetischer Felder. Im Rahmen dieser Dis- sertation werden sowohl die elektronischen Born-Oppenheimer Potentialfl¨achen als auch die durch diese induzierte Dynamik der Rotations- und Vibrationsfreiheitsgrade analysiert. Neben analytis- chen N¨aherungen wird hierzu auf etablierte numerischen Diagonalisierungsverfahren zur¨uckgegrif- fen. Im ersten Teil dieser Arbeit untersuchen wir ultralangreichweitige Rydbergmolek¨ule. In Abh¨angigkeit vom adressierten elektronischen Zustand erh¨alt man Molek¨ule mit einer spezifischen Ausrichtung und Orientierung bez¨uglich der angelegten Felder. Reine elektrische Felder stabil- isieren die untersuchten Molek¨ule, welche dann antiparallel zum Feld orientiert sind. Aufgrund der starken elektrischen Polarisierbarkeit gen¨ugen bereits kleine Feldst¨arken, um verschiedene moleku- lare Parameter wie den internuklearen Abstand als auch das elektrische Dipolmoment zu variieren. F¨ur reine Magnetfelder erh¨alt man Molek¨ule unterschiedlicher Ausrichtungen. Die berechneten Bindungsenergien verschiedener molekularer Zust¨ande werden mit experimentellen Werten ver- glichen. Hierbei wird eine gute Ubereinstimmung¨ festgestellt. Im Falle parallel oder auch senkrecht zueinander angeordneter Feldkonfigurationen ergeben sich eine F¨ulle von M¨oglichkeiten, molekulare Eigenschaften wie das elektrische Dipolmoment sowie die spezifische Ausrichtung und Orientierung als zweiparametrige Gr¨oßen der angelegten Feldst¨arken zu steuern. Abschließend pr¨asentieren wir den neuartigen Bindungszustand eines Grundzustandatoms mit einem sogenannten giant dipole ” atom“. Diese Spezies ist von ultralangreichweitigem Charakater und geh¨ort mit zu den gr¨oßten bisher bekannten diatomaren Molek¨ulen. Abstract Ultralong-range diatomic molecules in external fields In this thesis, the quantum me- − chanical properties of ultralong-range diatomic molecules in external electric and magnetic fields are studied theoretically. Both the electronic Born-Oppenheimer potential surfaces and the rovi- brational dynamics are analyzed. Besides analytic approximations, we apply standard numerical diagonalization routines. In the first part of the thesis, we study the properties of ultralong-range Rydberg molecules. Depending on the considered electronic state, one obtains molecular states pos- sessing a specific degree of alignment and orientation with respect to the applied field. In the case of pure electric fields, the considered molecules are stabilized and oriented antiparallel to the field. Because of the high electronic polarizability, already very weak electric field strengths are sufficient to control molecular properties such as the internuclear separation and the electric dipole moment. For a pure magnetic field configuration, the molecular states are either aligned or antialigned. The molecular binding energies are calculated and confirmed to agree well with experimental data. In the case of parallel and perpendicular electric and magnetic field configurations different molecular properties such as the electric dipole moment and the molecular alignment and orientation can be tuned by varying both the electric and magnetic field strengths. Finally, we discuss the properties of a novel diatomic species where a ground state atom is bound to a giant dipole atom. These molecular species are of ultralong-range character and belong to the largest diatomic molecules known so far. Publications In the framework of this thesis, the following articles have been published: [2] M. Kurz, M. Mayle, P. Schmelcher: Ultra-long-range giant dipole molecules in crossed electric and magnetic fields , EPL 97, 77, 43001 (2012) (Editor’s choice) [3] M. Kurz, P. Schmelcher: Electrically dressed ultra-long-range polar Rydberg molecules, Phys. Rev. A 88, 022501 (2013) [4] A. T. Krupp, A. Gaj, J. B. Balewski, P. Ilzh¨ofer, S. Hofferberth, R. L¨ow, M. Kurz, P. Schmelcher, T. Pfau: Alignment of D-State Rydberg Molecules, Phys. Rev. Letters 112, 143008 (2014) [5] M. Kurz, P. Schmelcher: Ultralong-range Rydberg molecules in combined electric and magnetic fields, J. Phys. B 47, 165101 (2014) (featured by J. Phys. B in their LabTalk) Contents Introduction i I Theoretical foundations 1 1 Rydberg atoms 3 1.1 Historicalremarks ............................... ...... 3 1.2 Rydbergstatesinbasicatomicmodels . .......... 4 1.3 Rydbergstatesofalkaliatoms . ........ 7 1.3.1 Thequantumdefect .............................. 7 1.3.2 ElectronicRydbergwavefunctions . ........ 8 1.3.3 RadiativelifetimesofRydbergatoms. ......... 12 1.4 Rydbergatomsinexternalfields . ........ 13 1.4.1 Rydbergatomsinelectricfields. ....... 13 1.4.2 Rydbergatomsinmagneticfields. ...... 14 2 Interaction of Rydberg atoms and ground state atoms 17 2.1 Electron-atominteraction . ......... 17 2.1.1 Fermi-pseudopotential . ...... 18 2.1.2 Higherordercontributions. ....... 20 2.2 Energy dependence of the scattering phase shifts . .............. 22 3 Basic concepts of molecular physics 25 3.1 The generic Hamiltonian of molecular physics . ............. 25 3.2 Adiabatic and Born-Oppenheimer approximations . ............. 27 3.3 Diabaticpotentialsurfaces. .......... 28 3.4 Diatomicmolecules............................... ...... 29 3.4.1 Diatomicpotentialcurves . ...... 29 3.4.2 Labelingofdiatomicelectronicstates . .......... 29 II Ultralong-range molecules in external fields 31 4 The molecular system 33 4.1 TheworkingHamiltonian . ...... 33 4.2 Thefield-freesystem .............................. ...... 35 4.2.1 Trilobitestates ............................... 35 4.2.2 Two-stateanalysis ............................. 40 4.2.3 TheBorodin-Kazanskymodel. ..... 41 4.2.4 Inclusionofadditionalbasisstates . .......... 43 5 Electrically dressed ultralong-range Rydberg molecules 47 5.1 Introduction.................................... ..... 47 5.2 Thesetup........................................ 47 5.3 Methodologyandsymmetries . ....... 48 Contents 5.4 Potentialenergysurfaces. ......... 49 5.4.1 Two-stateanalysis ............................. 49 5.4.2 Perturbation theory and exact diagonalization . ............ 52 5.5 Electricdipolemoment. ....... 55 5.6 Rovibrationalstates ............................. ....... 57 5.7 Conclusion ...................................... 60 6 Ultralong-range Rydberg molecules in combined electric and magnetic fields 63 6.1 Introduction.................................... ..... 63 6.2 Thesetup........................................ 63 6.3 Methodology ..................................... 65 6.4 Thepuremagneticfieldconfiguration . ......... 65 6.4.1 P -waveinteractioneffects . 66 6.4.2 Three-stateanalysis . ..... 67 6.4.3 Two-dimensional potential energy surfaces . ............ 69 6.5 Potential energy surfaces for combined field configurations............... 70 6.5.1 Parallelfieldconfiguration. ....... 70 6.5.2 Perpendicularfieldconfiguration . ........ 71 6.6 Rovibrationalstates ............................. ....... 73 6.6.1 Parallelfieldconfiguration. ....... 73 6.6.2 Perpendicularfieldconfiguration . ........ 74 6.7 Molecularalignmentandorientation . ........... 77 6.8 Electricdipolemoment ............................ ...... 78 6.9 conclusion...................................... 80 7 Alignment of ultracold D5/2-stateRydbergmolecules 81 7.1 Introduction.................................... ..... 81 7.2 Experimentalsetup............................... ...... 81 7.2.1 Preparation of samples of ultracold rubidium atoms . ............ 81 7.2.2 Rydbergexcitation. 83 7.2.3 Iondetectionmethod ............................ 83 7.3 The molecular Hamiltonian in a magnetic field . ........... 84 7.4 Potentialenergysurfaces. ......... 86 7.5 Rovibrational states and binding energies . ............. 89 7.6 Experimentalspectra. ....... 93 7.7 Alignment of D5/2-stateRydbergmolecules . 95 7.8 Conclusion ...................................... 98 8 Polarizability and susceptibility of ultralong-range Rydberg molecules 99 8.1 Molecular response properties in the adiabatic approximation ............. 99 8.2 Magnetically dressed Rydberg molecules . ............100 8.3 Electrically dressed Rydberg molecules . .............101 9 Giant dipole states 103 9.1 Introduction.................................... 103 9.2 ThemodelHamiltonian ............................. 103 9.3 Methodology ..................................... 105 9.4 Convergencestudies .............................. 105 9.5 Molecular ground state potential surfaces . .............107 9.6 Potentialsurfacesofexcitedstates . ............109 9.7 Avoidedcrossingsofpotential surfaces . .............111 9.8 Conclusion