WASHINGTON UNIVERSITY IN ST.LOUIS Department of Physics Dissertation Examination Committee: Kater Murch, Chair James Buckley Erik Henriksen Zohar Nussinov Jung-Tsung Shen Partial Measurements of Quantum Systems by Jonathan Tyler Monroe A dissertation presented to The Graduate School of Washington University in partial fulfillment of the requirements for the degree of Doctor of Philosophy May 2021 St. Louis, Missouri © 2021, Jonathan Tyler Monroe Table of Contents List of Figures........................................................................................... v List of Tables ............................................................................................ vii Acknowledgments...................................................................................... viii Abstract ................................................................................................... xi Chapter 1: Introduction............................................................................ 1 1.1 Motivation....................................................................................... 1 1.2 Quantum Mechanics with Circuits ........................................................ 4 1.2.1 Quantizing the cavity............................................................... 4 1.2.2 Quantizing the LC Circuit ........................................................ 7 1.2.3 Quantizing the Nonlinear LC ..................................................... 8 1.3 Readout Physics ............................................................................... 9 1.3.1 Jaynes-Cummings Interaction .................................................... 10 1.3.2 Partial Measurements............................................................... 14 Chapter 2: Direct-Write Qubits ................................................................ 18 2.1 Introduction..................................................................................... 18 2.2 Fabrication Theory............................................................................ 20 2.2.1 Josephson Junction Nonlinearity ................................................ 20 2.2.2 Josephson Relations from BCS Theory ........................................ 22 2.2.3 Cabrera-Mott Oxidation Model .................................................. 23 2.3 Recipe Development .......................................................................... 28 2.3.1 Design-of-Experiment Philosophy ............................................... 28 2.3.2 Resist Exposure Tuning............................................................ 29 2.3.3 Junction Consistency Tests ....................................................... 35 ii 2.3.4 Full Recipe ............................................................................ 39 2.4 Devices........................................................................................... 43 2.4.1 Structure of Large-Area Junctions .............................................. 44 2.4.2 Circuit Spectroscopy ................................................................ 48 2.4.3 Time Domain Measurements ..................................................... 52 2.4.4 Additional Noise Sources .......................................................... 56 2.4.5 Limits on Loss Tangents ........................................................... 57 Chapter 3: Entropic Uncertainty Relations ............................................... 58 3.1 Introduction..................................................................................... 58 3.1.1 Problems with Variance-based Uncertainty Relations ...................... 59 3.1.2 Entropic Uncertainty Relations .................................................. 60 3.2 Theory............................................................................................ 63 3.2.1 Trivial Bound ......................................................................... 64 3.2.2 Deutsch Bound ....................................................................... 65 3.2.3 Maassen-Uffink Bound ............................................................. 66 3.2.4 Tomamichel Bound.................................................................. 67 3.2.5 Weak Measurement Bound ........................................................ 67 3.3 Experiment...................................................................................... 70 3.3.1 Entropies of the Entropic Uncertainty Relation ............................. 71 3.3.2 Bound of the Entropic Uncertainty Relation ................................. 81 3.3.3 Combing Elements of the RHS ................................................... 85 Chapter 4: Time-Reversed Feedback ......................................................... 88 4.1 Introduction..................................................................................... 88 4.2 Stochastic Thermodynamics ................................................................ 90 4.2.1 Classical Fluctuation Theorems.................................................. 90 4.2.2 Thermodynamics of Quantum Trajectories ................................... 96 4.3 Experiment...................................................................................... 98 4.3.1 Setup.................................................................................... 98 4.3.2 Trajectory probabilities ............................................................ 101 4.3.3 Fluctuation Theorems .............................................................. 103 iii 4.4 Conclusion....................................................................................... 107 Bibliography ............................................................................................. 108 iv List of Figures Figure 1.1: Jaynes-Cummings Hamiltonian Eigenenergies ............................... 12 Figure 2.1: Cabrera Theory...................................................................... 26 Figure 2.2: Exposure Test for S1805........................................................... 30 Figure 2.3: Resist Stack Imaging ............................................................... 32 Figure 2.4: Codename Sandwich Factorial Design ......................................... 33 Figure 2.5: Resistance Variation from Area Variation .................................... 35 Figure 2.6: Variation in Manhattan Evaporation .......................................... 36 Figure 2.7: Wafer Variation with Improved Softbaking................................... 38 Figure 2.8: SEM image of a Large-area Junction .......................................... 44 Figure 2.9: Preparing TEM Sample ........................................................... 45 Figure 2.10: EDXS Data for Multi-layer Junction........................................... 46 Figure 2.11: Resistance Scaling with Oxide Thickness ..................................... 47 Figure 2.12: High Power Spectroscopy ......................................................... 49 Figure 2.13: TLS in Spectroscopy ............................................................... 51 Figure 2.14: T1 vs Flux and Time ............................................................... 53 Figure 2.15: Quality Factor Histograms........................................................ 55 Figure 2.16: Quality Factor Aging............................................................... 56 Figure 3.1: Pulse sequence for measuring entropies........................................ 71 Figure 3.2: Measurement Angles ............................................................... 72 Figure 3.3: Projective measurement entropies .............................................. 74 Figure 3.4: Entropy in the Presence of Weak Measurement ............................. 76 v Figure 3.5: Entropy Under the Influence of Weak Measurement ....................... 78 Figure 3.6: Entropies of the Entropic Uncertainty Relation ............................. 80 Figure 3.7: RHS Components ................................................................... 82 Figure 3.8: Weak Value Measurement Protocol ............................................ 83 Figure 3.9: Weak Values.......................................................................... 84 Figure 3.10: RHS of Entropic Uncertainty Relation ........................................ 87 Figure 4.1: Readout Distributions ............................................................. 99 Figure 4.2: Correlated Tomography ........................................................... 101 Figure 4.3: Feedback Protocol .................................................................. 105 Figure 4.4: Entropy Histograms ................................................................ 106 vi List of Tables Table 3.1: Select values of H(AF )ρ ........................................................... 81 vii Acknowledgments I am delighted to thank the many people who have guided and supported me during my graduate studies. The bountiful support of those close to me filled my experience with joy. I begin with the central driver of my success: Kater Murch. I count myself exceptionally fortunate to have been mentored by such a personable and passionate advisor as Kater. Kater’s example has instilled the virtue of clear explanations. I feel honored to have worked among such great colleagues in the Murch lab. I thank Dian Tan for his patient tutelage of fabrication techniques and Mahdi Naghiloo for his willing explanation of every aspect of our lab, especially as codified in his dissertation. Patrick Harrington has been