Fast Gates and Mixed-Species Entanglement With Trapped Ions

Supervisor’s Foreword
Abstract
Acknowledgements
Contents
1 Introduction
	1.1 Mixed-Species Entanglement
	1.2 Fast Gates
	1.3 Outline
	References
2 The Ions
	2.1 Ion Species Criteria
		2.1.1 Fundamental Limits for Errors
		2.1.2 Technical Constraints
		2.1.3 Compatibility of Species
	2.2 Our Ions
		2.2.1 Photo Ionization
	2.3 Calcium 43
		2.3.1 State Preparation and Readout
		2.3.2 Logic Operations
		2.3.3 Cooling
	2.4 Strontium
		2.4.1 State Preparation and Readout
		2.4.2 Logic Operations
		2.4.3 Cooling
	2.5 Calcium 40
	References
3 Theory
	3.1 Linear Paul Trap
	3.2 Ion-Light Interactions
		3.2.1 Electric Dipole Interactions
		3.2.2 Magnetic Dipole Interactions
		3.2.3 Raman Interactions
		3.2.4 Scattering
	3.3 Transition Elements
		3.3.1 Intermediate Field
	3.4 Geometric Phase Gate
		3.4.1 Creating a Spin-Dependent Force
		3.4.2 Two Ion Geometric Phase Gate
	3.5 Mixed Species Gate
	3.6 Fast Geometric Phase Gate
		3.6.1 Gate Dynamics
		3.6.2 Estimating Errors
		3.6.3 Finding Appropriate Gate Sequences
	3.7 Two-Qubit Gate Errors
		3.7.1 Photon Scattering
		3.7.2 Motional Errors
		3.7.3 Gate Parameter Imprecision
		3.7.4 Off-Resonant Excitation
		3.7.5 Phase Chirps
		3.7.6 Radial Mode Coupling
		3.7.7 Out-of-Lamb-Dicke Effects
	References
4 Apparatus
	4.1 The Ion Trap
		4.1.1 Trap Voltages
		4.1.2 Imaging System
	4.2 Lasers and Beam Geometry
		4.2.1 Laser Table
		4.2.2 Trap Table
	4.3 Raman Lasers
		4.3.1 Phase Lock
		4.3.2 AOM Network
		4.3.3 AOM Control
	4.4 Microwaves and RF
	4.5 Magnetic Field
	4.6 Experimental Control System
	References
5 Experiment Characterisation
	5.1 Trap Characterisation
		5.1.1 Compensation
		5.1.2 Heating Rate
		5.1.3 Ion Order
		5.1.4 Magnetic Field Gradient
	5.2 Cooling and Fluorescence
		5.2.1 Calcium
		5.2.2 Strontium
		5.2.3 Recrystallisation
	5.3 State Preparation and Readout
		5.3.1 Calcium
		5.3.2 Strontium
	5.4 Magnetic Field
		5.4.1 B-Field Servo
		5.4.2 Field Stability
	5.5 Raman Lasers
	5.6 Motional Coupling to Raman Lasers
		5.6.1 Ion Spacing
		5.6.2 Motional Coherence
	References
6 Mixed Species Gates
	6.1 40Ca+–43Ca+ Gate Results
		6.1.1 Cooling
		6.1.2 State Preparation and Readout
		6.1.3 Ion Order
		6.1.4 Gate Implementation
		6.1.5 Bell Test
	6.2 43Ca+–88Sr+ Gate Results
		6.2.1 Choosing the Raman Detuning
		6.2.2 Preliminary Results
	References
7 Fast Gates
	7.1 Experimental Details
		7.1.1 Experiment Setup
		7.1.2 Measuring Gate Fidelities
	7.2 Gate Sequences
		7.2.1 Single Rectangular Pulses
		7.2.2 Binary Pulse Sequences
		7.2.3 Stepped Pulse Sequences
	7.3 Error Analysis
		7.3.1 Pulse Control
		7.3.2 Phase Chirp
		7.3.3 Coupling to Radial Modes
		7.3.4 Out-of-Lamb-Dicke Effects
		7.3.5 Micro-Motion
	7.4 Fast Gate Results
		7.4.1 Multiple Gates
		7.4.2 Outlook
	References
8 Conclusion
	8.1 Comparison with Other Trapped-Ion Results
		8.1.1 Mixed-Species Entanglement
		8.1.2 Fast Gates
	8.2 Comparison with Other Qubit Platforms
	8.3 Outlook
	References
Appendix A Useful Identities and Definitions
A.1 Spin Operators
A.2 Motion Operators
Appendix B Matrix Elements
B.1 Calcium 43
B.2 Strontium 88
Appendix C Two Qubit Gates
C.1 Magnus Expansion
C.1.1 Geometric Phase Gate
C.2 Unequal Force Amplitudes
C.3 Fast Gate Thermal Error
C.4 Phases
Appendix D 88Sr+Properties
D.1 Einstein A Coefficients
D.2 Energies Relative to 4S1/2
D.3 Wavelengths
D.4 Lifetimes
D.5 Branching Ratios