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arXiv:cond-mat/0610704 · Physical Review B

Pulse and hold strategy for switching current measurements

Jochen Walter, Erik A. Tholén, David B. Haviland, Joachim Sjöstrand

Published Mar 30, 2007• 6 citations
arXivHTMLPDF

Abstract

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 $20\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ 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, $25\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$ switch pulses, where it is observed that the switching process is not governed by thermal equilibrium noise.

DOI
10.1103/physrevb.75.094515

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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\ensuremathμs20\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}20\ensuremathμs 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, 25ns25\phantom{\rule{0.3em}{0ex}}\mathrm{ns}25ns switch pulses, where it is observed that the switching process is not governed by thermal equilibrium noise.
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.
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.
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.
A new phase diffusive regime in a current biased Josephson junction is theoretically explored which originates from embedding the junction in a circuit environment with anomalous dissipation. This is realized by placing parallel to the junction a resistor in series with a capacitor such that electromagnetic fluctuations effectively couple also to the charge of the junction. This leads to rich Josephson dynamics, in particular for the switching of the junction out of a zero voltage state. Modelled as the escape process of a fictitious phase-particle out of a metastable well, a detailed study reveals that anomalous dissipation has a strong impact at low temperatures when quantum tunneling dominates against thermal activation. As a manifestation, a regime is found, where for realistic circuit parameters the quantum escape process is substantially enhanced, followed by a short voltage pulse and re-trapping with high probability. This class of circuits may be leveraged for detecting microwave photons or dissipative quantum annealing processes. In addition, the analysis provides a general framework for engineering dissipative dynamics in nonlinear systems using anomalous environments.
The use of high-T/sub c/ Josephson junctions for digital applications requires a careful study of the influence of thermal noise on circuit performance. We investigated a balanced current comparator, which contains a basic component of all RSFQ circuits: two overdamped Josephson junctions connected in series. The dependence of the dc-voltage across the Josephson junctions on signal current was measured to determine the threshold uncertainty of switching of the comparator. The experimental data obtained at different sampling pulse frequencies, in a temperature range from 10 to 50 K, were compared with a theoretical model, taking into account the influence of thermal noise as well as of sampling pulse frequency.
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.