Electrical Control and Quantum Chaos with a High-Spin Nucleus in Silicon (Springer Theses)

✍ Scribed by Serwan Asaad

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 212
• Category: Library

✦ Synopsis

Nuclear spins are highly coherent quantum objects that were featured in early ideas and demonstrations of quantum information processing. In silicon, the high-fidelity coherent control of a single phosphorus (31-P) nuclear spin I=1/2 has demonstrated record-breaking coherence times, entanglement, and weak measurements. In this thesis, we demonstrate the coherent quantum control of a single antimony (123-Sb) donor atom, whose higher nuclear spin I = 7/2 corresponds to eight nuclear spin states. However, rather than conventional nuclear magnetic resonance (NMR), we employ nuclear electric resonance (NER) to drive nuclear spin transitions using localized electric fields produced within a silicon nanoelectronic device. This method exploits an idea first proposed in 1961 but never realized experimentally with a single nucleus, nor in a non-polar crystal such as silicon. We then present a realistic proposal to construct a chaotic driven top from the nuclear spin of 123-Sb. Signatures of chaos are expected to arise for experimentally realizable parameters of the system, allowing the study of the relation between quantum decoherence and classical chaos, and the observation of dynamical tunneling. These results show that high-spin quadrupolar nuclei could be deployed as chaotic models, strain sensors, hybrid spin-mechanical quantum systems, and quantum-computing elements using all-electrical controls.

✦ Table of Contents

Supervisor’s Foreword
Abstract
Acknowledgements
Contents
Acronyms
1 Introduction
1.1 Coherent Control of a Quantum Spin
1.2 Manipulating a High-Spin Nucleus
1.3 Thesis Outline
References
2 High-Dimensional Spins
2.1 The Discovery of Spin
2.2 Nuclear Spin
2.3 Nuclear Spin States
2.4 Spin Operators
2.5 Spin Coherent States
2.6 Spin Visualization with the Husimi Q Distribution
2.7 Generalized Rotating Frame
2.7.1 Description of the Generalized Rotating Frame
2.7.2 Derivation of the Generalized Rotating Frame
2.8 Basis Comparison
2.9 Arbitrary State Preparation
References
3 Theory of Donors in Silicon
3.1 Solid State Physics of Donors in Silicon
3.2 Donor Spin Hamiltonian
3.2.1 Neutral Donor Spin Hamiltonian
3.2.2 Zeeman Interaction
3.2.3 Hyperfine Interaction
3.2.4 Low-Field Versus High-Field Limit
3.2.5 Resonant Driving
3.2.6 Ionized Donor Hamiltonian
3.3 Nuclear Quadrupole Interaction
3.3.1 Nuclear Quadrupole Hamiltonian
3.3.2 Estimates of Nuclear Quadrupole Interaction
3.3.3 Nuclear Spectrum
3.3.4 Extraction of Quadrupole Parameters
References
4 Experimental Setup
4.1 Architecture of an 123123-Sb-Implanted Silicon Nanodevice
4.2 The Single Electron Transistor (SET)
4.2.1 Electrostatics of the SET
4.2.2 SET Modes of Operation
4.3 Fabrication Protocol
4.4 123123-Sb Implantation Parameters
4.5 Device Packaging and Cooling
4.6 Instrumentation and Connectivity
4.7 Phase-Coherent DDS
4.8 SilQ Measurement Software
References
5 123-Sb Donor Device Characterization
5.1 Charge Sensing with an SET
5.1.1 Calibration of the SET
5.1.2 Charge Stability Diagram
5.2 Donor Triangulation
5.3 Electron Spin Control and Readout
5.3.1 Donor Electrochemical Potential Regimes
5.3.2 Electron Readout and Initialization Fidelity
5.4 ESR Spectrum
5.5 Flip-Flop Transition
5.5.1 Flip-Flop Rabi Oscillations
5.5.2 Flip-Flop Driven Nuclear-Spin Initialization
5.6 Continuous Tuning via a Neural-Network
References
6 Nuclear Electric Resonance
6.1 Initial Nuclear Resonance Measurements
6.1.1 Nuclear Spin Initialization, Manipulation, and Readout
6.1.2 First Nuclear Transition and Rabi Oscillations
6.1.3 Measurements of Subsequent Transitions
6.2 Nuclear Electric Resonance (NER)
6.2.1 Properties of NER
6.2.2 Delta m = 1 Nuclear Spectrum and Rabi Oscillations
6.2.3 Delta m = 2 Nuclear Spectrum and Rabi Oscillations
6.2.4 Power Dependence of Rabi Frequencies
6.3 Antenna-Driven NER
6.3.1 Enhanced Electric Fields from a Melted Antenna
6.3.2 Gate-Driven Versus Antenna-Driven NER
6.4 Linear Quadrupole Stark Effect
6.5 Nuclear Coherence Times
6.6 Possible Quadrupole Orientations
6.7 Conclusion
References
7 Microscopic Crystalline Origins of the Quadrupole Interaction
7.1 Microscopic Origins of the Electric Field Gradient
7.2 Finite-Element Model of the Nanostructure Device
7.3 Electric-Field-Induced Quadrupole Splitting and NER
7.3.1 The Linear Quadrupole Stark Effect (LQSE)
7.3.2 The Electric-Field Response Tensor
7.3.3 Electric-Field Response-Tensor Estimate
7.3.4 Comparison to LQSE Measurements and Empirical Theory
7.4 Strain-Induced Quadrupole Splitting
7.4.1 The Gradient-Elastic Tensor
7.4.2 Gradient-Elastic Tensor Calculations
7.4.3 Calculation of Quadrupole Splitting Due to Strain
7.5 Alternative (Unlikely) Sources of NER
7.5.1 Direct Effect of Electric Gate Potentials
7.5.2 Mechanical Driving Through SiO2 Piezoelectricity
7.6 Conclusion
References
8 Exploring Quantum Chaos with a Single High-Spin Nucleus
8.1 Background of Quantum Chaos
8.1.1 Introduction
8.1.2 Chaos Theory
8.1.3 Quantum Chaos
8.1.4 Experimental Tests of Quantum Chaos
8.2 The Classical Chaotic Driven Top
8.3 The Quantum Driven Top
8.3.1 Experimental Platform
8.3.2 Comparison Between Classical and Quantum Hamiltonian Parameters
8.3.3 Realizing a Quantum Driven Top in the Laboratory Frame
8.3.4 Eigenbasis Mismatch
8.3.5 Realizing a Quantum Driven Top in the Rotating Frame
8.3.6 Summary
8.4 Quantum Dynamics and the Floquet Formalism
8.5 Quantum Versus Classical Dynamics: A Comparison
8.5.1 Decoherence as a Precursor of Chaos
8.5.2 Dynamical Tunneling
8.5.3 Dependence of Dynamical Tunneling Rate on System Parameters
8.6 Conclusion and Outlook
References
9 Conclusions and Outlook
9.1 Summary
9.2 Comparison with Other High-Dimensional Quantum Systems
9.3 Further Characterization of the Quadrupole Coupling to Strain and Electric Fields
9.4 Strain Sensing
9.5 Quantum Computation
9.6 Mutual Coupling of High-Dimensional Spins
9.7 Quantum Chaos
9.8 Quantum Metrology
9.9 Spin-Mechanical Coupling
References
Appendix A Finite Element Model Parameters
Appendix B Hyperfine-Coupled 123-Sb Nucleus
Appendix C Slope in Delta m = 2 Rabi Frequencies
Appendix D Spectral Shift at Charge Transition
Appendix E DFT Simulation Details
Appendix F Classical Equations of Motion for the Driven Top
F.1 Derivation of Classical Equations of Motion
F.2 Equations of Motion for the Classical Driven Top
Appendix G Quantum Driven Top in the Rotating Frame and the Rotating Wave Approximation
G.1 Transforming Spin Operators to the Rotating Frame
G.2 Hamiltonian Under the Rotating Wave Approximation
G.3 Relative Angle Between Quadrupole Interaction and Periodic Drive
Appendix H Simulation Details for Chaotic Dynamics
H.1 Classical Simulations
H.2 Quantum Simulations
Appendix About the Author
Appendix References