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Controlling Photons in Superconducting Electrical Circuits Blakerobertjohnson 2011

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Controlling Photons in Superconducting Electrical Circuits Blakerobertjohnson 2011 Abstract Controlling Photons in Superconducting Electrical Circuits BlakeRobertJohnson 2011 Circuit quantum electrodynamics (circuit QED) is a system that allows for strong coupling between microwave photons in transmission line cavities and superconducting qubits or artificial atoms. While circuit QED is often studied in the context of quantum information processing, it also provides an attractive platform for performing quantum optics experiments on-a-chip, because the level of control and coupling strengths available in circuit QED opens a vast array of possibilities for the creation, manipulation, and detection of quantum states of light. In this thesis, the extension of circuit QED to two cavities is examined, including design issues for cavities with very different Q-factors, and a new qubit design is proposed that couples to both cavities. The qubit-cavity interaction, while providing much of the utility of circuit QED, also introduces additional qubit relaxation. A powerful formalism for calculating this energy decay due to the classical admittance of the electromagnetic environment is presented in the context of circuit QED. Measurements of a wide range of samples validate this theory as providing an effective model for relaxation. A new circuit element, called the ‘Purcell filter’,is introduced and demonstrated to decouple the relationship between cavity Q and qubit relaxation. Finally, a new method for performing quantum non- demolition measurements of microwave photons is demonstrated. Controlling Photons in Superconducting Electrical Circuits A Dissertation PresentedtotheFacultyoftheGraduateSchool of Yale University in Candidacy for the Degree of Doctor of Philosophy by BlakeRobertJohnson Dissertation Director: Professor Robert J. Schoelkopf May 2011 ©byBlakeRobertJohnson All rights reserved. Contents Contents iv List of Figures vii Acknowledgements xi Publication list xiii Introduction . Overview of thesis ................................... Circuit QED and Quantum Optics . Cooper-pair Box and Transmon .......................... . Circuit Quantum Electrodynamics ......................... .. Resonant regime ............................... .. Dispersive regime .............................. .. Generalized Jaynes-Cummings Hamiltonian .............. .. Quasi-dispersive regime .......................... . QND measurements ................................. . Quantum Optics Background ............................ .. Representations of cavity modes ...................... . Creating and measuring quantum states of light ................. .. Rapid Adiabatic Passage .......................... Theory of Two-Cavity Architecture . The Two Cavity Hamiltonian ............................ . Separation of Cavity Modes ............................. iv CONTENTS v . Qubit-mediated cavity relaxation .......................... . The Sarantapede Qubit ................................ . Self- and Cross-Kerr Effects ............................. The Electromagnetic Environment and Fast Qubit Control . Multi-mode Purcell Effect .............................. .. Balanced Transmons ............................ .. Purcell Filter ................................. . Flux Bias Lines ..................................... . Classical Control Theory (Deconvolution) .................... Device Fabrication and Experiment Setup . Circuit QED devices ................................. .. Transmon zoo ................................ .. Qubit fabrication on sapphire substrates ................. . Measurement setup .................................. .. Sample holders ................................ .. Eccosorb filters ................................ .. Pulse Generation ............................... Purcell Effect, Purcell Filter, and Qubit Reset . Multi-mode Purcell Effect .............................. Purcell Filter and Qubit Reset ............................ Chapter Summary ................................... Measurement of the Self- and Cross-Kerr Effects in Two-Cavity Circuit QED Quantum Non-Demolition Detection of Single Microwave Photons in a Circuit .. Measured Voltage Scaling ......................... .. Error Estimate ................................ Conclusions and Outlook Bibliography Appendices A Mathematica code for Landau-Zener simulations B Mathematica code for pulse sequence generation C Fabrication recipes CONTENTS vi Copyright Permissions List of Figures Introduction . Viewing light on an oscilloscope. .......................... Circuit QED and Quantum Optics . The Cooper-pair box. ................................. . Charge dispersion. .................................. . Resonant and Dispersive Jaynes-Cummings Regimes. .............. . AC-Stark effect. .................................... . Number splitting. ................................... . Energy levels of a transmon qubit coupled to a cavity. .............. . Extension of the AC-Stark Shift in the Quasi-dispersive Regime. ....... . Phase space representation of cavity states. .................... . Wigner tomography by resonant Rabi interaction. ................ . Wigner tomography by dispersive Ramsey interferometry. ........... . Numerical Simulation of Rapid Adiabatic Passage for Preparing ∣, д⟩. .... . Numerical Simulation of Rapid Adiabatic Passage for Preparing ∣, д⟩. .... Theory of Two Cavity Architecture . Coupling Geometries ................................. . Coupled Cavities Schematic ............................. . Reducing the coupled cavities circuit to calculate Qcouple forcavity1. ..... . Coupled Q vs Inter-cavity Coupling ........................ . Qubit-mediated cavity-cavity hybridization. ................... . Capacitance network for a transmon qubit coupled to two cavities. ...... . Relevant capacitance network for a sarantapede-style transmon qubit. .... vii LIST OF FIGURES viii The Electromagnetic Environment and Fast Qubit Control . Quantum LC oscillator with an environment Y(ω). ............... . Single cavity multi-mode Purcell effect. ...................... . Two cavity multi-mode Purcell effect. ....................... . Capacitance network for transmon coupled to a CPW transmission line. .. . Balanced transmon designs. ............................. . Purcell filter. ...................................... . Flux bias line setup. .................................. . Relaxation from inductive coupling to SQUID loop. ............... . Relaxation from charge coupling to transmon. .................. . Tϕ duetofluxnoise................................... . Correcting the output of the Tektronix AWG5014. ................ . Flux bias line response. ................................ . Flux balancing. ..................................... Device Fabrication and Experiment Setup . Optical images of transmon designs. ........................ . Josephson junction aging on silicon and corundum. ............... . Schematic of cryogenic measurement setup. ................... . Directional coupler. .................................. . Octobox sample holder. ............................... . Eccosorb filter. ..................................... . Microwave pulse generation setup. ......................... Custom electronics for IQ mixer calibration. ................... Single sideband modulation. ............................. Purcell Effect, Purcell Filter, and Qubit Reset . Circuit model of qubit relaxation .......................... Comparison of circuit and single-mode models of relaxation ......... Relaxation times for seven superconducting qubits. ............... Dephasing times for four sapphire qubits. ..................... Design, realization, and diagnostic transmission data of the Purcell filter .. Qubit T as a function of frequency measured with two methods, and com- parisontovariousmodels .............................. Fast qubit reset ..................................... Self- and Cross-Kerr Effects in Two-Cavity Circuit QED . Optical image of cQED274. ............................. Spectroscopy of cQED274. .............................. Cavity response vs self- and cross-power. ..................... Self- and cross-Kerr effect. .............................. Comparison of measured self- and cross-Kerr effect with theory. ....... LIST OF FIGURES ix QNDDetectionofSingleMicrowavePhotonsinaCircuit . Circuit schematic and cQED291 device ...................... Pulsed spectroscopy with coherent state in storage cavity vs. qubit-cavity detuning ........................................ Single photon preparation and CNOT selectivity ................. Repeated measurements of photons ........................ Conclusions and Outlook . Transmission readout geometries. ......................... Single shot histograms of photon readout. ..................... Quasi-dispersive spectroscopy of ∣ψ⟩≃∣, д⟩. ................... Coherent state minus a Fock state. ......................... State transfer with tunable mirrors. ......................... for my family andinmemoryofMichaelTinkham Acknowledgements y physics Ph. D. would not have been possible without several people, the first of whom M is my advisor, Rob Schoelkopf, who convinced me to come to Yale. Rob tolerated mypursuitof(occasionallytangential)directionsinhardwareorsoftwarerelatedtothe experiments. While these explorations sometimes slowed me down, they also gave me a better understanding of the work of RSL. I continue to be amazed at Rob’s experimental intuition, and his skill in presenting and telling
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