[Springer Theses] Fast Gates and Mixed-Species Entanglement with Trapped Ions ||

Quantum logic gates are the crucial information-processing operation of quantum computers. Two crucial performance metrics for logic gates are their precision and speed. Quantum processors based on trapped ions have always been the touchstone for gate precision, but have suffered from slow speed relative to other quantum logic platforms such as solid state systems. This thesis shows that it is possible to accelerate the logic "clock speed" from kHz to MHz speeds, whilst maintaining a precision of 99.8%. This is almost as high as the world record for conventional trapped-ion gates, but more than 20 times faster. It also demonstrates entanglement generation in a time (480ns) shorter than the natural timescale of the ions' motion in the trap, which starts to probe an interesting new regime of ion trap physics. In separate experiments, some of the first "mixed-species" quantum logic gates are performed, both between two different elements, and between different isotopes. The mixed-isotope gate is used to make the first test of the quantum-mechanical Bell inequality between two different species of isolated atoms. 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