Optical preparation and detection of spin coherence in molecules and crystal defects Lof, Gerrit
DOI:
10.33612/diss.109567350
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Publication date: 2020
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Lof, G. (2020). Optical preparation and detection of spin coherence in molecules and crystal defects. University of Groningen. https://doi.org/10.33612/diss.109567350
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Optical preparation and detection
of spin coherence in molecules
ISBN: 978-94-034-2203-9 (electronic version)
The work described in this thesis was performed in the research groups Physics of Nanodevices and Theoretical Chemistry of the Zernike Institute for
Advanced Materials at the University of Groningen, the Netherlands. The project was funded by the Zernike Institute.
Optical preparation and detection
of spin coherence in molecules
and crystal defects
PhD thesis
to obtain the degree of PhD at the University of Groningen
on the authority of the
Rector Magnificus Prof. C. Wijmenga and in accordance with
the decision by the College of Deans. This thesis will be defended in public on
Friday 10 January 2020 at 14.30 hours
by
Gerrit Jan Jacob Lof
born on 30 March 1988
Co-supervisor Dr. R. W. A. Havenith Assessment committee Prof. H. B. Braam Prof. M. Orrit Prof. J. Koehler
Contents
1 Introduction 1
1.1 Coherence and polarization of electron spins and photons . . . 1
1.2 Optical orientation . . . 2
1.3 Spin precession . . . 3
1.4 Coherent population trapping . . . 5
1.5 Jones calculus . . . 5
1.6 Theoretical chemistry methods . . . 7
1.7 Scope of this research and thesis outline . . . 8
1.8 SI: Change of basis . . . 11
1.9 SI: Jones calculus applied to a waveplate . . . 13
2 Evolution of atomic optical selection rules upon gradual sym-metry lowering 15 2.1 Introduction . . . 16
2.2 The resonance lines of the hydrogen atom without spin . . . 17
2.2.1 The hydrogen atom in the absence of a magnetic field . . . 17
2.2.2 The hydrogen atom in the presence of a magnetic field . . 19
2.2.3 Electric dipole radiation . . . 19
2.3 The resonance lines of the hydrogen atom including spin . . . 20
2.4 Evolution of optical selection rules for the hydrogen atom in a C2v arrangement of point charges . . . 22
2.4.1 The hydrogen atom in the presence of a weak magnetic field 25 2.4.2 The hydrogen atom in the presence of a C2v arrangement of point charges and a weak magnetic field . . . 27
2.5 Summary and Outlook . . . 31
2.6 Author contributions . . . 32
2.7 SI: Energy levels of the hydrogen atom in a magnetic field . . . . 33
2.8 SI: Electric dipole oscillations . . . 34
2.9 SI: Spin-orbit coupling . . . 36 v
2.11 SI: Transition dipole moment and oscillator strength . . . 40
2.12 SI: Jones calculus applied to the oscillation of an atomic electric dipole . . . 41
2.13 SI: Perturbation-theory description of distortion by extra charges 43 3 Proposal for time-resolved optical preparation and detection of triplet-exciton spin coherence in organic molecules 45 3.1 Introduction . . . 46
3.2 Theoretical proof of principle for a molecular TRFR experiment . 46 3.3 Feasibility analysis . . . 53
3.3.1 TRFR experiment with an ensemble of randomly oriented molecules . . . 53
3.3.2 Single molecule TRFR experiment . . . 54
3.3.3 Franck-Condon suppression of optical transitions . . . 54
3.3.4 Persistence of spin-orientation effects for symmetries lower than C2v . . . 55
3.4 Summary and Outlook . . . 55
3.5 Author contributions . . . 56
3.6 SI: Principles of the TRFR technique for an idealized Π−system . 57 3.7 SI: Fundamentals of a molecular TRFR experiment . . . 64
3.8 SI: Polarization rotation for a TRFR experiment applied to a V -system . . . 66
3.9 SI: Idealized TRFR scenario for a V -system . . . 73
3.10 SI: TRFR model results and discussion . . . 75
3.11 SI: Computational details and methods . . . 78
3.12 SI: Symmetry analysis . . . 83
3.13 SI: Franck-Condon factors . . . 85
3.14 SI: Optical selection rules of platinum porphyrins . . . 86
3.15 SI: Ensemble of randomly oriented molecules . . . 91
4 Proposal for time-resolved optical probing of electronic spin coherence in divacancy defects in SiC 97 4.1 Introduction . . . 98
4.2 Fundamentals for a TRFR experiment with a homogeneous en-semble of c-axis divacancies in SiC . . . 99
4.3 Estimating the polarization rotation of a linear probe for a TRFR experiment with c-axis divacancies in SiC . . . 106
CONTENTS vii
4.3.1 Assumptions and parameters . . . 106
4.3.2 Results and discussion . . . 108
4.4 Summary and Outlook . . . 109
4.5 Author contributions . . . 110
4.6 SI: Estimating the transition dipole moment of divacancies in SiC 111 4.7 SI: Dependency on the magnetic field angle for the optical selection rules of c-axis divacancies in SiC . . . 112
5 Identification and tunable optical coherent control of transition-metal spins in silicon carbide 115 5.1 Introduction . . . 116
5.2 Materials and experimental methods . . . 118
5.3 Single-laser characterization . . . 120
5.4 Two-laser characterization . . . 122
5.5 Analysis . . . 123
5.6 Coherent Population Trapping . . . 126
5.7 Further discussion . . . 129
5.8 Summary and Outlook . . . 129
5.9 Methods . . . 130
5.10 Author contributions . . . 131
5.11 SI: Single-laser spectroscopy . . . 132
5.12 SI: Additional two-laser spectroscopy for Mo in 6H-SiC . . . 133
5.13 SI: Two-laser spectroscopy for Mo in 4H-SiC . . . 135
5.14 SI: Franck-Condon principle with respect to spin . . . 138
5.15 SI: V-scheme dip . . . 140
5.16 SI: Modeling of coherent population trapping . . . 143
5.17 SI: Anisotropic g-factor in the effective spin-Hamiltonian . . . 144
5.17.1 Relationship between effective spin Hamiltonian and local configuration of the defect . . . 144
5.17.2 Ion in 4d1 configuration in the presence of crystal field of C3v symmetry and spin-orbit coupling . . . 146
5.17.3 Validity of our assumptions . . . 150
5.17.4 Summary . . . 152
References 153
Acknowledgements 173
Curriculum Vitae 175
