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Quantum Nonlinearities in Strong Coupling Circuit

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Quantum Nonlinearities in Strong Coupling Circuit Q u a n t Circuit QED offers the possibility to realize an exceptionally strong coupling u between artificial atoms – individual superconducting qubits – and single m microwave photons in a one dimensional waveguide resonator. This new N o solid state approach to investigate the matter-light interaction on the level n l of individual quanta also represents a promising hardware architecture for i n the realization of a scalable quantum information processor. We first e a summarize and review the important theoretical and experimental r i principles of this rapidely developing field and give an overview of the t i e relevant literature. Here the focus is to provide a detailed discussion of the s i experimental ultra-low temperature measurement setup and the design, n fabrication and characterization of superconducting Josephson junction C i devices. Presented key experimental results include: 1) The first clear r c observation of the Jaynes-Cummings nonlinearity in the vacuum Rabi u i spectrum by measuring both two- and three-photon dressed states. 2) The t observation of strong collective coupling for up to 3 qubits. 3) A Q E quantitative investigation of the quantum to classical transition induced by D an elevated temperature environment. Johannes M. Fink Johannes M. Fink Quantum Nonlinearities in The author is a post doctoral scientist at the Swiss Strong Coupling Circuit QED Federal Institute of Technology Zurich. He studied in Vienna, Sydney and at ETH Zurich where he earned a On-Chip Quantum Optics with Microwave Photons Ph.D. in physics. His research is focused on designing, fabricating and controlling coherent devices for and Superconducting Electronic Circuits quantum optics and quantum information processing applications. J o h a n n e s M . F i 978-3-8454-1971-8 n k QUANTUM NONLINEARITIES IN STRONG COUPLING CIRCUIT QED Johannes M. Fink For Pia and Alwin and for Stephanie CONTENTS Abstract ix List of publications xi I Basic Concepts1 1 Introduction3 1.1 QED in cavities................................... 4 1.2 Outline of the thesis ................................ 5 2 Review and Theory7 2.1 On-chip microwave cavity............................. 9 2.1.1 Coplanar waveguide resonator ..................... 9 2.1.2 Transmission matrix model........................ 11 2.1.3 Circuit quantization............................ 11 2.2 Superconducting quantum bits.......................... 12 2.2.1 Charge qubits ............................... 13 2.2.2 Transmon regime ............................. 15 2.2.3 Spin-1/2 notation ............................. 16 2.3 Matter – light coupling............................... 17 2.3.1 Atom-field interaction........................... 17 2.3.2 Jaynes-Cummings model ........................ 18 2.3.3 Transmon – photon coupling....................... 20 2.3.4 Dispersive limit: Qubit control and readout .............. 22 3 Conclusion 25 II Experimental Principles 27 4 Measurement Setup 31 4.1 Microchip sample.................................. 32 4.1.1 Superconducting circuit.......................... 33 v vi CONTENTS 4.1.2 Printed circuit board............................ 34 4.1.3 Wire bonds................................. 35 4.1.4 Sample mount, coils and shielding................... 35 4.2 Signal synthesis .................................. 36 4.2.1 Microwave generation, control and synchronization ......... 37 4.2.2 Quadrature modulation.......................... 37 4.2.3 Generation of Gaussian noise...................... 38 4.3 Cryogenic setup .................................. 39 4.3.1 Dilution refrigerator............................ 39 4.3.2 Microwave input.............................. 40 4.3.3 Heat loads................................. 41 4.3.4 DC bias input ............................... 43 4.3.5 Microwave output............................. 44 4.4 Data acquisition................................... 46 5 Design and Fabrication of Josephson Junction Devices 49 5.1 Qubit design..................................... 49 5.1.1 Charging energy and voltage division ................. 49 5.1.2 Josephson energy............................. 52 5.2 Fabrication process ................................ 54 5.2.1 Chip preparation.............................. 54 5.2.2 Electron beam lithography........................ 56 5.2.3 Development................................ 62 5.2.4 Shadow evaporation and oxidation................... 63 5.2.5 Resist stripping and liftoff ........................ 65 5.3 Room-temperature characterization....................... 66 5.3.1 DC resistance measurements...................... 66 5.3.2 Junction aging............................... 68 6 Sample Characterization 71 6.1 Resonator spectrum................................ 71 6.2 Flux periodicity................................... 73 6.3 Dipole coupling strengths............................. 74 6.4 Qubit spectroscopy................................. 76 6.4.1 Charging energy.............................. 77 6.4.2 Flux dependence, dressed states and number splitting . 77 6.4.3 AC-Stark shift photon-number calibration ............... 79 6.5 Rabi oscillations .................................. 79 7 Conclusion 83 III Main Results 85 8 Observation of the Jaynes-Cummings pn Nonlinearity 89 CONTENTS vii 8.1 Introduction..................................... 89 8.1.1 The Jaynes-Cummings model...................... 90 8.1.2 Experimental setup............................ 92 8.2 Coherent dressed states spectroscopy..................... 92 8.2.1 Vacuum Rabi splitting........................... 93 8.2.2 Two photon vacuum Rabi splitting.................... 94 8.3 Weak thermal excitation.............................. 96 8.3.1 Sample parameters............................ 96 8.3.2 Generalized Jaynes-Cummings model................. 97 8.3.3 Thermal background field ........................ 98 8.3.4 Quasi-thermal excitation.........................100 8.4 Three photon pump and probe spectroscopy of dressed states . 103 8.5 Conclusion .....................................104 9 Collective Multi-Qubit Interaction 107 9.1 Introduction.....................................107 9.1.1 Experimental setup............................108 9.1.2 Tavis-Cummings model..........................109 9.2 Collective dipole coupling.............................109 9.3 Summary ......................................113 10 Quantum-to-Classical Transition 115 10.1 Introduction.....................................115 10.1.1 Experimental setup............................116 10.1.2 Vacuum Rabi splitting...........................117 10.2 Strong quasi-thermal excitation..........................117 10.2.1 The high temperature limit........................117 10.2.2 Quantitative model ............................118 10.2.3 Time domain measurements ......................120 10.2.4 Extraction of the effective field temperature . 120 10.3 Conclusion .....................................121 11 Conclusion and Prospects 123 IV Appendices 127 A Aspects of the Cryogenic Setup 129 A.1 Dimensioning He vacuum pumping lines....................129 A.2 Mechanical vibration measurements.......................132 A.3 Double gimbal vibration isolation.........................134 B Nano Fabrication Recipes 137 B.1 Chip preparation ..................................137 viii CONTENTS B.2 Electron beam lithography ............................138 B.3 Development ....................................141 B.4 Shadow evaporation................................141 B.5 Resist stripping...................................142 BibliographyI Acknowledgements XIX ABSTRACT The fundamental interaction between matter and light can be studied in cavity quantum electrodynamics (QED). If a single atom and a single photon interact in a cavity resonator where they are well isolated from the environment, the coherent dipole coupling can dominate over any dissipative effects. In this strong coupling limit the atom repeatedly absorbs and emits a single quantum of energy. The photon and the atom loose their individual character and the new eigenstates are quantum superpositions of matter and light – so called dressed states. Circuit QED is a novel on-chip realization of cavity QED. It offers the possibility to real- ize an exceptionally strong coupling between artificial atoms – individual superconducting qubits – and single microwave photons in a one dimensional waveguide resonator. This new solid state approach to investigate the matter-light interaction enables to carry out novel quantum optics experiments with an unprecedented degree of control. Moreover, multiple superconducting qubits coupled via intra-cavity photons – a quantum bus – are a promising hardware architecture for the realization of a scalable quantum information processor. In this thesis we study in detail a number of important aspects of the resonant in- teraction between microwave photons and superconducting qubits in the context of cav- ity QED: We report the long sought for spectroscopic observation of the pn nonlinearity of the Jaynes-Cummings energy ladder where n is the number of excitations in the resonantly coupled matter-light system. The enhancement of the matter-light coupling by pn in the presence of additional photons was already predicted in the early nineteen sixties. It directly reveals the quantum nature of light. In multi-photon pump and probe and in elevated temperature experiments we controllably populate one or multi-photon / qubit superposition states and probe the resulting vacuum Rabi transmission spectrum. We find that the multi-level
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