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  • 1. Sjöstrand, Joachim
    et al.
    Hansson, Hans
    KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
    Karlhede, A.
    Walter, Jochen
    KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
    Haviland, David
    KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
    Time domain analysis of dynamical switching in a josephson junction2006In: Quantum Computing in Solid State Systems, Springer, 2006, p. 54-62Chapter in book (Other academic)
    Abstract [en]

    A Josephson junction (JJ) when is connected to an external current source via a twisted pair with impedance Z, presents a probability distribution P of switching of the JJ, as a function of the current pulse from the source. Due to quantum effects and various noise sources, such as resistive leads at finite temperatures, this distribution will have a finite width. In a qubit system, such as the Quantronium, it is necessary that this width is small in order to clearly distinguish between different quantum states, and eventually realise the single shot measurement. © 2006 Springer Science+Business Media, Inc.

  • 2. Sjöstrand, Joachim
    et al.
    Hansson, Hans
    Karlhede, Anders
    Walter, Jochen
    KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
    Tholén, Erik
    KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
    Haviland, David
    KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
    Phase Space Topology of a Switching Current Detector2006In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 73, p. 132511-Article in journal (Refereed)
    Abstract [en]

    We examine in theory and by numerical simulation, the dynamic process of switching from a zero voltage to a finite voltage state in a Josephson junction circuit. The theoretical model describes small capacitance Josephson junctions which are overdamped at high frequencies, and can be applied to detection of the quantum state of a qubit circuit. We show that the speed and fidelity of the readout are strongly influenced by the topology of the phase space attractors. The readout will be close to optimal when choosing the circuit parameters so as to avoid having an unstable limiting cycle which separates the two basins of attraction.

  • 3. Sjöstrand, Joachim
    et al.
    Walter, Jochen
    KTH, Superseded Departments, Physics.
    Haviland, David B.
    KTH, Superseded Departments, Physics.
    Hansson, Hans
    Karlhede, Anders
    Time Domain Analysis of Dynamical Switching in a Josephson Junction2004Manuscript (preprint) (Other academic)
    Abstract [en]

    We have studied the switching behaviour of a small capacitance Josephson junction both in experiment,and by numerical simulation of a model circuit. The switching is a complex process involvingthe transition between two dynamical states of the non-linear circuit, arising from a frequency dependentdamping of the Josephson junction. We show how a specific type of bias pulse-and-hold,can result in a fast detection of switching, even when the measurement bandwidth of the junctionvoltage is severely limited, and/or the level of the switching current is rather low.

  • 4.
    Walter, Jochen
    KTH, School of Engineering Sciences (SCI), Physics.
    Pulse and hold switching current readout of superconducting quantum circuits2006Doctoral thesis, comprehensive summary (Other scientific)
    Abstract [en]

    Josephson junction qubits are promising candidates for a scalable quantum processor. Such qubits are commonly manipulated by means of sequences of rf-pulses and different methods are used to determine their quantum state. The readout should be able to distinguish the two qubit states with high accuracy and be faster than the relaxation time of the qubit. We discuss and experiment with a readout method based on the switching of a Josephson junction from the zero voltage state to a finite voltage state.

    The Josephson junction circuit has a non-linear dynamics and when it is brought to a bifurcation point, it can be made arbitrarily sensitive to small perturbations. This extreme sensitivity at a bifurcation point can be used to distinguish the two quantum states if the topology of the phase space of the circuit leads to a quick separation into the final states where re-crossings of the bifurcation point are negligible. We optimize a switching current detector by analyzing the phase space of a Josephson junction circuit with frequency dependent damping.

    A pulse and hold technique is used where an initial current pulse brings the junction close to its bifurcation point and the subsequent hold level is used to give the circuit enough time to evolve until the two states can be distinguished by the measuring instrument. We generate the pulse and hold waveform by a new technique where a voltage step with following linear voltage rise is applied to a bias capacitor. The frequency dependent damping is realized by an on-chip RC-environment fabricated with optical lithography. Josephson junction circuits are added on by means of e-beam lithography.

    Measurements show that switching currents can be detected with pulses as short as 5 ns and a resolution of 2.5% for a sample directly connected to the measurement leads of the cryostat. Detailed analysis of the switching currents in the RC-environment show that pulses with a duration of 20 us can be explained by a generalization of Kramers' escape theory, whereas switching the same sample with 25 ns pulses occurs out of thermal equilibrium, with sensitivity and speed adequate for qubit readout.

  • 5.
    Walter, Jochen
    KTH, Superseded Departments, Physics.
    Sample and hold measurement for binary detection of a quantum state2004Licentiate thesis, comprehensive summary (Other scientific)
    Abstract [en]

    Measuring the dynamics of a quantum bit (qubit) relies on the accurate detection of the quantum state of the system. A widely used method to measure the state of a solid state Josephson junction qubit is to measure the switching current of a Josephson device.

    This work investigates the measurement of the switching current of SQUID samples by means of fast current pulses. The response of a SQUID to a square current pulse has to be measured at the top of a dilution refrigerator through long cables, resulting in bandwidth limitations. A switch in the last instance of a pulse will not be detected, resulting in uncertainties in the detection. We explain how a square bias pulse that is directly followed by a hold level of lower amplitude can be used to circumvent the bandwidth limitations by latching the state of the system it was in after the bias pulse. This corresponds to a sample and hold measurement.

    Every single measurement in a quantum mechanical probability measurement has to be statistically independent. We show correlation measurements for di erent settings of the pulse parameters and at di erent magnitudes of the switching current. A gure of merit for a quantum detector is its resolution. The measurements show that with the sample and hold technique good current resolutions can be obtained, even at very small magnitudes and short pulse durations. In order to make a fast measurement of the switching current, the switching process must occur during the bias pulse. We show in both measurements and computer simulations that a fast switch pulse can induce switching by the hold level,even when the hold level was initially adjusted to a value where it never switched the sample. The computer simulations show that by choosing the hold amplitude low enough, switching occurs rapidly, determined by the bias pulse alone.

  • 6.
    Walter, Jochen
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
    Corlevi, Silvia
    KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
    Haviland, David
    KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
    Fast Switching Current Detection at low Critical Currents2005In: Realizing Controllable Quantum States - MESOSCOPIC SUPERCONDUCTIVITY AND SPINTRONICS, 2005, p. 255-262Conference paper (Refereed)
    Abstract [en]

    A pulse-and-hold technique is used to measure the switching of small critical current Josephson junctions. This technique allows one to achieve a good binary detection and therefore measure switching probabilities. The technique overcomes limitations on simple square pulses and allows for the measurement of junctions with critical currents of the order of 10nA with bias pulses of the order of 100ns. A correlation analysis of the switching events is performed to show how the switching probability depends on the wait time between repeated bias pulses.

  • 7.
    Walter, Jochen
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
    Tholén, Erik
    KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
    Haviland, David
    KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
    Sjöstrand, Joachim
    Pulse and Hold Strategy for Switching Current Measurements2007In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 75, no 9, p. 094515-Article in journal (Refereed)
    Abstract [en]

    We investigate by theory and experiment, the Josephson junction switching current detector in an environment with frequency-dependent damping. Analysis of the circuit's phase space shows that a favorable topology for switching can be obtained with overdamped dynamics at high frequencies. A pulse-and-hold method is described, where a fast switch pulse brings the circuit close to an unstable point in the phase space when biased at the hold level. Experiments are performed on Cooper pair transistors and quantronium circuits, which are overdamped at high frequencies with an on-chip RC shunt. For 20 mu s switch pulses the switching process is well described by thermal equilibrium escape, based on a generalization of the Kramers formula to the case of frequency-dependent damping. A capacitor bias method is used to create very rapid, 25 ns switch pulses, where it is observed that the switching process is not governed by thermal equilibrium noise.

  • 8.
    Ågren, Peter
    et al.
    KTH, Superseded Departments, Physics.
    Walter, Jochen
    KTH, School of Engineering Sciences (SCI), Physics.
    Haviland, David B.
    KTH, Superseded Departments, Physics.
    Switching Current of a Cooper Pair Transistor with Tunable Josephson Junctions2002In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 66, no 1, p. 14510-Article in journal (Refereed)
    Abstract [en]

    We investigate the switching current of a Cooper pair transistor with tunable Josephson energy. The junctions are fabricated in a superconducting quantum interference device (SQUID) geometry which allows for an in situ tunable effective Josephson energy by application of a magnetic field. We find a 2e-periodic switching current versus gate charge. As the magnetic field is increased the switching current stays 2e-periodic but the magnitude is suppressed. At a magnetic field of half a flux quantum through the SQUID's the switching current is minimum. We can theoretically model the experimental data by assuming a switching current which is proportional to the ideal critical current squarred. We show that such a dependence is expected in the limit where the effect of thermal fluctuations on the system is strong.

  • 9.
    Ågren, Peter
    et al.
    KTH, Superseded Departments, Physics.
    Walter, Jochen
    KTH, School of Engineering Sciences (SCI), Physics.
    Schöllmann, Volker
    KTH, School of Engineering Sciences (SCI), Physics.
    Haviland, David B.
    KTH, Superseded Departments, Physics.
    Switching Currents and Quasi-Particle Poisoning in the Superconducting Single Electron Transistor2002In: INTERNATIONAL WORKSHOP ON SUPERCONDUCTING NANO-ELECTRONICS DEVICES, 2002, p. 25-31Conference paper (Refereed)
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