### Session W1: Quantum Coherence in Superconducting Devices

 Thursday, March 8, 2007 2:30PM - 3:06PM W1.00001: Flux Qubits: Coupling and Decoherence Invited Speaker: John Clarke The principles of the three-junction flux qubit are briefly reviewed. We investigated two such qubits coupled together via their mutual inductance and via the dc SQUID (Superconducting Quantum Interference Device) that reads out their magnetic flux states. On-chip flux lines enabled us to bias the two qubits individually. Microwave spectroscopy revealed that the energy splittings of the symmetric and antisymmetric states of the two qubits at their respective degeneracy points were remarkably close, 8.872 GHz and 8.990 GHz. At the double degeneracy point, the energy difference between the first and second excited states of the coupled qubits was enhanced by level repulsion as predicted. We performed time domain measurements on the individual qubits and on excited states of the coupled qubits, including Rabi oscillations, flux echoes, Ramsey fringes and measurements of the relaxation time, and also determined the linewidths of the individual peaks. These measurements enable us to compare the relaxation and decoherence times of the individual and coupled qubits. For example, at the double degeneracy point of the coupled qubits, the decoherence rate determined by flux echoes is equal to the sum of the rates in the separate qubits. Sources of decoherence are discussed, and estimates given of the various known contributions including those of the biasing and measurement circuitry. This work was performed in collaboration with T. Hime, B.L.T. Plourde, P.A. Reichardt, T.L. Robertson, A.V. Ustinov and C.-E. Wu. Thursday, March 8, 2007 3:06PM - 3:42PM W1.00002: Mach-Zehnder Interferometry and Microwave-Induced Cooling in Persistent-Current Qubits Invited Speaker: William Oliver Superconducting persistent-current qubits are quantum-coherent artificial atoms with multiple energy levels. In the presence of large-amplitude harmonic excitation, the qubit state can be driven through one or more of the energy-level avoided crossings. The resulting Landau-Zener transitions mediate a rich array of quantum-coherent phenomena as a function of the driving amplitude and frequency. In this talk, we present three such demonstrations of quantum coherence in a strongly-driven niobium persistent-current qubit. The first is Mach-Zehnder-type interferometry [1], for which we observe quantum interference fringes for 1-50 photon transitions. The second is a new operating regime exhibiting coherent quasi-classical dynamics [2], for which the MZ quantum interference persists even for driving frequencies smaller than the resonance linewidth. The third is microwave-induced cooling [3], for which we achieve effective qubit temperatures < 3 mK, a factor 10x-100x lower than the dilution refrigerator ambient temperature. These experiments exhibit a remarkable agreement with theory, and are extensible to other solid-state qubit modalities. In addition to our interest in these techniques for fundamental studies of quantum coherence in strongly-driven solid-state systems, we anticipate they will find application to nonadiabatic qubit control and state-preparation methods for quantum information science and technology. [1] W.D. Oliver, Y. Yu, J.C. Lee, et al., Science 310, 1653 (2005). [2] D.M. Berns, W.D. Oliver, S.O. Valenzuela et al., PRL 97, 150502 (2006). [3] S.O. Valenzuela, W.D. Oliver, D.M. Berns, et al., Science (2006). Thursday, March 8, 2007 3:42PM - 4:18PM W1.00003: Vacuum Rabi oscillations observed in a flux qubit LC-oscillator system Invited Speaker: Kouichi Semba Superconducting circuit containing Josephson junctions is one of the promising candidates as a quantum bit (qubit) which is an essential ingredient for quantum computation [1]. A three-junction flux qubit [2] is one of such candidates. On the basis of fundamental qubit operations [3,4], the cavity QED like experiments are possible on a superconductor chip by replacing an atom with a flux qubit, and a high-Q cavity with a superconducting LC-circuit. By measuring qubit state just after the resonant interaction with the LC harmonic oscillator, we have succeeded in time domain experiment of vacuum Rabi oscillations, exchange of a single energy quantum, in a superconducting flux qubit LC harmonic oscillator system [5]. The observed vacuum Rabi frequency 140 MHz is roughly 2800 times larger than that of Rydberg atom coupled to a single photon in a high-Q cavity [6]. This is a direct evidence that strong coupling condition can be rather easily established in the case of macroscopic superconducting quantum circuit. We are also considering this quantum LC oscillator as a quantum information bus by sharing it with many flux qubits, then spatially separated qubits can be controlled coherently by a set of microwave pulses. [1] F. Wilhelm and K. Semba, in Physical Realizations of Quantum Computing: Are the DiVincenzo Criteria Fulfilled in 2004?, (World Scientific; April, 2006) [2] J. E. Mooij \textit{et al.}, Science \textbf{285}, 1036 (1999). [3] T. Kutsuzawa\textit{ et al.}, Appl. Phys. Lett. \textbf{87}, 073501 (2005). [4] S. Saito\textit{ et al.}, Phys. Rev. Lett. \textbf{96}, 107001 (2006). [5] J. Johansson\textit{ et al.}, Phys. Rev. Lett. \textbf{93}, 127006 (2006). [6] J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys.\textbf{ 73}, 565 (2001). Thursday, March 8, 2007 4:18PM - 4:54PM W1.00004: Controllable coupling of superconducting flux qubits Invited Speaker: Evgeni Il'ichev As a first step, by making use of conventional niobium technology, we have implemented controllable flux coupling between two qubit prototypes (in our case single junction interferometers) by using a third one as the coupler. The fabricated qubit prototypes operate in the hysteretic mode, where the screening parameter $>$1, which provides double degenerate state for an external flux equal to half a flux quantum. The coupler parameters were chosen so that it operates in the non-hysteretic mode with a screening parameter of 0.9. The coupling amplitude is proportional to the derivative of the coupler's current-flux relation. By changing the coupler's magnetic flux, we have shown ferromagnetic as well as anti-ferromagnetic coupling between the interferometers. In particular, we have demonstrated that the coupling could also be switched off. As the next step of our investigation we implemented similar ideas in to our Al shadow-evaporation technology. Recently, we have also demonstrated a tuneable coupling between three junctions persistent current qubits in the quantum regime. A possible combination of Al and Nb technologies is discussed. Thursday, March 8, 2007 4:54PM - 5:30PM W1.00005: Quantum Dynamics of a d-wave Josephson Junction Invited Speaker: Thilo Bauch Thilo Bauch $^{1}$, Floriana Lombardi $^{1}$, Tobias Lindstr\"{o}m $^{2}$, Francesco Tafuri $^{3}$, Giacomo Rotoli $^{4}$, Per Delsing $^{1}$, Tord Claeson $^{1}$ 1 Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, MC2, Chalmers University of Technology, S-412 96 G\"{o}teborg, Sweden. 2 National Physical Laboratory, Queens Road, Teddington, Middlesex TW11 0LW, UK. 3 Istituto Nazionale per la Fisica della Materia-Dipartimento Ingegneria dell'Informazione, Seconda Universita di Napoli, Aversa (CE), Italy. 4 Dipartimento di Ingegneria Meccanica, Energetica e Gestionale, Universita of L'Aquila, Localita Monteluco, L'Aquila, Italy. We present direct observation of macroscopic quantum properties in an all high critical temperature superconductor d-wave Josephson junction. Although dissipation caused by low energy excitations is expected to strongly suppress quantum effects we demonstrate macroscopic quantum tunneling [1] and energy level quantization [2] in our d-wave Josephson junction. The results clearly indicate that the role of dissipation mechanisms in high temperature superconductors has to be revised, and may also have consequences for a new class of solid state quiet'' quantum bit with superior coherence time. We show that the dynamics of the YBCO grain boundary Josephson junctions fabricated on a STO substrate are strongly affected by their environment. As a first approximation we model the environment by the stray capacitance and stray inductance of the junction electrodes. The total system consisting of the junction and stray elements has two degrees of freedom resulting in two characteristic resonance frequencies. Both frequencies have to be considered to describe the quantum mechanical behavior of the Josephson circuit. [1] T. Bauch et al, Phys. Rev. Lett. 94, 087003 (2005). [2] T. Bauch et al, Science 311, 57 (2006).