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arXiv:cond-mat/0403467 · International Symposium on Mesoscopic Superconductivity and Spintronics (MS+S)

FAST SWITCHING CURRENT DETECTION AT LOW CRITICAL CURRENTS

J. WALTER, S. Corlevi, David B. Haviland

Published Aug 1, 2005• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1142/9789812701619_0039

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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.
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.
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, 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.
Josepshon junction has its switching current distribution, from which one could get not only the escape rate but also other quantum information like the energy level quantization, Rabi oscillation with proper microwave. The measurements on the switching current distribution of a Josephson junction is very helpful to the development of supercondutor qubit including phase qubit, chage qubit, flux qubit and their combinations. We present three measurement techniques and perform a measurement (10+4 times) on the switching current distribution of a homemade NbN/AlN-x/NbN Josephson junction at certain temperature. According to the disadvantages of the presently used technique and the result we get, more advices are given to the next measurements on the switching current distribution at the ultra low temperature (mK).
Josephson junctions can be employed to reveal a sinusoidal signal in presence of Gaussian noise. To mimic realistic setups, the detection is performed linearly ramping the bias current until a switch to the finite voltage occurs; the analysis of the resulting switching currents can be exploited to decide about the presence of the harmonic drive. The signal is applied in two conditions: with an unknown initial phase (incoherent strategy) and with a known initial phase (coherent strategy). In both conditions, the analysis of the efficiency of the detection, performed through the signal-to-noise ratio, as estimated by the Kumar-Carrol index, shows that the dependence upon the Josephson junction ramp rate is beneficial, especially for relatively fast speed. One can conclude that the collection of the switching currents is a robust technique, and thus it is possible to exploit the advantages of a predetermined finite time to collect the data.
The quantum character of Josephson junctions is ordinarily revealed through the analysis of the switching currents, i.e., the current at which a finite voltage appears: A sharp rise of the voltage signals the passage (tunnel) from a trapped state (the zero voltage solution) to a running state (the finite voltage solution). In this context, we investigate the probability distribution of the Josephson-junction switching current taking into account the effect of the bias sweeping rate and introducing a simple nonideal quantum measurement scheme. The measurements are modeled as repeated voltage samplings at discrete time intervals, that is, with repeated projections of the time-dependent quantum solutions on the static or the running states, to retrieve the probability distribution of the switching currents. The distribution appears to be immune to the quantum Zeno effect, and it is close to, but distinguishable from, the Wentzel-Kramers-Brillouin approximation. For energy barriers comparable to the quantum fundamental energy state and in the fast bias current ramp rate the difference is neat, and remains sizable in the asymptotic slow rate limit. This behavior is a consequence of the quantum character of the system that confirms the presence of a backreaction of quantum measurements on the outcome of mesoscopic Josephson junctions.