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IEEE Transactions on Applied Superconductivity

Observation of Quantized Energy Levels in a Josephson Junction Using SFQ Circuits

Yuki Yamanashi, M. Ito, A. Tagami, Nobuyuki Yoshikawa

Published Jun 1, 2005• 5 citations
Publisher

Abstract

A single flux quantum (SFQ) circuit to measure quantized energy levels in a Josephson junction has been proposed and implemented, which allows us to perform high-speed and low-noise measurements of the escape rate in Josephson junctions. By using this technique, the measurement of escape rate has been carried out at 4.2 K, the temperature three times higher than the crossover temperature. The test results show periodic dependence of the escape rate on the junction bias current, which is caused by the energy quantization effect in the Josephson junction.

DOI
10.1109/tasc.2005.850088

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A single flux quantum (SFQ) circuit to measure quantized energy levels in a Josephson junction has been proposed and implemented, which allows us to perform high-speed and low-noise measurements of the escape rate in Josephson junctions. By using this technique, the measurement of escape rate has been carried out at 4.2 K, the temperature three times higher than the crossover temperature. The test results show periodic dependence of the escape rate on the junction bias current, which is caused by the energy quantization effect in the Josephson junction.
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We present a clear observation of the presence of energy levels quantization in high quality $\mathrm{Nb}\ensuremath{-}{\mathrm{AlO}}_{x}\ensuremath{-}\mathrm{Nb}$ underdamped Josephson junctions at temperatures above the quantum crossover temperature. This has been possible by extending the measurements of the escape rate out of the zero-voltage state at higher sweeping frequency ( dI/dtdI/dtdI/dt up to 25 A/sec) in order to induce nonstationary conditions in the energy potential describing the junction dynamics.
A macroscopic variable, the phase difference across a Josephson junction, is shown to obey quantum mechanics by observing the phenomena of energy-level quantization and quantum tunneling.The relevant parameters of the junction were determined .!.!! .ill!:!, in the thermal regime from the dependence of the escape rate on bias current and from resonant activation in the presence of microwaves.The first observation of quantized energy levels for this system is reported.The positions of these energy levels are in quantitative agreement with the quantum mechanical predictions based on the measured junction parameters.A model is presented that predicts correctly the observed resonance shapes.The measured value of the escape rate out of the zero-voltage state for an underdamped (Q -30) junction was found to be independent of temperature at low temperatures.This low temperature escape rate was in excellent agreement with the prediction for macroscopic quantum tunneling, with no adjustable parameters.Jolw rJt..
We report experiments on energy level quantization in Nb/AlOx/Nb Josephson junctions while measurements on SQUIDs are in progress. Data on the presence of energy level quantization are shown at temperatures above the classical-quantum regime crossover temperature. This has been possible by extending the measurements of the rate of the escape from the zero-voltage state at higher sweep bias rate in order to induce non-stationary conditions in the energy potential describing the junction dynamics. Data are compatible with extremely low "effective" dissipation in our system. Theoretical predictions on quantum effects related to the presence of non-stationary conditions in the potential associated to a rf SQUID are reported in view of new possible experiments.
As quantum computing processors increase in size, there is growing interest in developing cryogenic electronics to overcome significant challenges to system scaling. Single flux-quantum (SFQ) circuits offer a promising alternative to remote, bulky, and power-hungry room temperature electronics. To meet the need for digital qubit control, readout, and co-processing, SFQ circuits must be adapted to operate at millikelvin temperatures near quantum processors. SEEQC's SFQuClass digital quantum management approach proximally places energy-efficient SFQ (ERSFQ) circuits and qubits in a multi-chip module. This enables extremely low power dissipation, compatible with a typical dilution cryostat's limited cooling power, while maintaining high processing speed and low error rates. We report on systematic testing from 4 K to 10 mK of a comprehensive set of ERSFQ cells, as well as more complex circuits such as programmable counters and demultiplexers used in digital qubit control. We compare the operating margins and error rates of these circuits and find that, at millikelvin, bias margins decrease and the center of the margins (i.e., the optimal bias current value) increases by ~15%, compared to 4.2 K. The margins can be restored by thermal annealing by reducing Josephson junction (JJ) critical current Ic. To provide guidance for how circuit parameters vary from 4.2 K to millikelvin, relevant analog process control monitors (PCMs) were tested in the temperature range of interest. The measured JJ critical current (of the PCM JJ arrays) increases by ~15% when decreasing temperature from 4.2 K to millikelvin, in good agreement with both theory and the empirically measured change in the center of bias margins for the tested digital circuits.
When a Josephson junction in the zero-voltage state is current-biased below its critical current, the rate that it escapes to the finite-voltage state depends on the quantum state of the junction. By employing a slow current sweep, it is possible to observe experimentally the emptying of the thermally populated first excited level as a well-defined feature in the escape rate. This feature provides a simple method of determining the junction's energy relaxation time T1{T}_{1}T1​, a key parameter for evaluating its utility for quantum computation. We discuss the temperature regime where this effect is readily observable and describe how the emptying depends directly on the relaxation time. Our model of the junction dynamics agrees well with the measured escape rate of a $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}\ifmmode\times\else\texttimes\fi{}10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ $\mathrm{Nb}\text{\ensuremath{-}}\mathrm{AlOx}\text{\ensuremath{-}}\mathrm{Nb}$ device in the 25 to 300mK300\phantom{\rule{0.3em}{0ex}}\mathrm{mK}300mK temperature range, yielding ${T}_{1}\ensuremath{\approx}4\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$.