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arXiv:2307.09452

Experimental evidences of a current-biased Josephson junction device can be worked as a macroscopic "Boson" or "Fermion" and the combination

P. H. Ouyang, He, S. R., Y. Z. Wang, Y. Q. Chai, J. X. He, Chang, H., L. F. Wei

Published Jul 18, 2023• 0 citations
arXivHTMLPDF

Abstract

According to the statistical distribution laws, all the elementary particles in the real 3+1-dimensional world must and only be chosen as either bosons or fermions, without exception and not both. Here, we experimentally verified that a quantized current-biased Josephson junction (CBJJ), as an artificial macroscopic "particle", can be served as either boson or fermion, depending on its biased dc-current. By using the high vacuum two-angle electron beam evaporations, we fabricated the CBJJ devices and calibrated their physical parameters by applying low-frequency signal drivings. The microwave transmission characteristics of the fabricated CBJJ devices are analyzed by using the input-output theory and measured at 50mK temperature environment under low power limit. The experimental results verify the theoretical predictions, i.e., when the bias current is significantly lower than the critical one of the junction, the device works in a well linear regime and thus works as a harmonic oscillator, i.e., a "boson"; while if the biased current is sufficiently large (especially approaches to its critical current), the device works manifestly in the nonlinear regime and thus can be served as a two-level artificial atom, i.e., a "fermion". Therefore, by adjusting the biased dc-current, the CBJJ device can be effectively switched from the boson-type macroscopic particle to the fermion-type one, and thus may open the new approach of the superconducting quantum device application.

DOI
10.48550/arxiv.2307.09452

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Acta Physica Sinica•Jan 1, 2019•1 citation
According to the statistical distribution laws, all the elementary particles in the real 3+1-dimensional world must and only be chosen as either bosons or fermions, without exception and not both. Here, we experimentally verified that a quantized current-biased Josephson junction (CBJJ), as an artificial macroscopic "particle", can be served as either boson or fermion, depending on its biased dc-current. By using the high vacuum two-angle electron beam evaporations, we fabricated the CBJJ devices and calibrated their physical parameters by applying low-frequency signal drivings. The microwave transmission characteristics of the fabricated CBJJ devices are analyzed by using the input-output theory and measured at 50mK temperature environment under low power limit. The experimental results verify the theoretical predictions, i.e., when the bias current is significantly lower than the critical one of the junction, the device works in a well linear regime and thus works as a harmonic oscillator, i.e., a "boson"; while if the biased current is sufficiently large (especially approaches to its critical current), the device works manifestly in the nonlinear regime and thus can be served as a two-level artificial atom, i.e., a "fermion". Therefore, by adjusting the biased dc-current, the CBJJ device can be effectively switched from the boson-type macroscopic particle to the fermion-type one, and thus may open the new approach of the superconducting quantum device application.
It is well known that elementary particles in the real 3+1 -dimensional world are either bosons or fermions, without exception, and not both. Here, we show that a quantized current-biased Josephson junction (CBJJ), as an artificial macroscopic “particle,” can serve as either a boson or a fermion or the combination, depending on the amplitude of the biased dc current. By using high vacuum two-angle electron beam evaporations, we fabricated CBJJ devices and calibrated their physical parameters by applying low-frequency signal drivings. At 50mK temperature environment, the microwave transmission characteristics of the fabricated CBJJ devices were measured at the low power limit. The experimental results verify the relevant theoretical predictions, i.e., when the bias current is significantly lower than the critical ones of the junctions, the device works in a very linear regime and thus behaves as a harmonic oscillator “boson”; while if the biased current is sufficiently large (especially approaching the junctions' critical currents), the device works manifestly in the nonlinear regime and thus behaves as a two-level artificial atom “fermion.” Therefore, by adjusting the biased dc current, the CBJJ device can be effectively switched from a Bose-type macroscopic particle to a Fermi-type one and thus might open an approach for quantum technology applications at a macroscopic scale. Published by the American Physical Society 2024
Experiments are described that demonstrate the quantum behavior of a macroscopic degree of freedom, namely the phase difference \ensuremath{\delta} across a current-biased Josephson tunnel junction. The behavior of \ensuremath{\delta} was deduced from measurements of the escape rate \ensuremath{\Gamma} of the junction from its zero-voltage state. The relevant parameters of the junction, that is, its critical current and shunting admittance, were determined in situ in the thermal regime from the dependence of \ensuremath{\Gamma} on bias current and from resonant activation in the presence of microwaves. It was found that the shunting capacitance was dominated by the self-capacitance of the junction while the shunting conductance was dominated by the bias circuitry. For an underdamped junction in the quantum regime, \ensuremath{\Gamma} became independent of temperature at low temperatures with a value that, with no adjustable parameters, was in excellent agreement with predictions for macroscopic quantum tunneling at T=0. When the critical current was reduced with a magnetic field so that the junction remained in the thermal regime at low temperatures, \ensuremath{\Gamma} followed the predictions of the thermal model, thereby showing the influence of extraneous noise to be negligible. In a further series of experiments, the existence of quantized energy levels in the potential well of the junction was demonstrated spectroscopically. The positions of the energy levels agreed quantitatively with quantum-mechanical predictions involving junction parameters measured in the thermal regime. The relative heights and widths of the resonances are in reasonable agreement with the predictions of a simple model.
A quantum-mechanical analysis of the Josephson phase escape in the presence of both dc and ac bias currents is presented. We find that the potential barrier for the escape of the phase is effectively suppressed as the resonant condition occurs, i.e., when the frequency $\ensuremath{\omega}$ of the ac bias matches the Josephson-junction energy-level separation. This effect manifests itself by a pronounced drop in the dependence of the switching current Is{I}_{s}Is​ on the power W of the applied microwave radiation and by a peculiar double-peak structure in the switching current distribution P(Is).{P(I}_{s}).P(Is​). The developed theory is in a good accord with an experiment which we also report in this paper. The obtained features can be used to characterize certain aspects of the quantum-mechanical behavior of the Josephson phase, such as the energy level quantization, the Rabi frequency of coherent oscillations, and the effect of damping.
We investigate the distribution of the switching current of a current-biased Josephson junction (CBJJ) and its dependence on the microwave frequency using two theoretical methods, one of which is the quantum trajectory method and the other is the master equation method. Both the methods show that the distribution of the switching current of CBJJ will exhibit double peaks in a certain range of microwave frequency if proper microwave power is given, and the gap between the two peaks will increase with the microwave frequency. The obtained results can be used to identify the energy difference of the ground and first excited states in a Josephson junction for any bias current.
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..
Based on Josephson junction (JJ), superconducting quantum bit (qubit) is operated at frequencies of several GHz. Dissipation of JJs in this frequency range can cause energy relaxation in qubits, and limit coherence time, therefore it is highly concerned and needs to be determined quantitatively. The dissipation of JJs can be quantified by microwave quality factor. It is usually done at very low temperature (~mK) to determine whether a JJ is suitable for qubit devices by measuring the quality factor. In this paper, a method based on nonlinear frequency response of JJs is proposed to determine the quality factor. This method can be used in thermal activation regime, which may bring great conveniences to experiments. To analyze high frequency properties of JJs, the dynamic equation of a current-biased JJ, which describes high frequency oscillation of the JJ, is introduced. A fourth-order potential approximation is used to obtain the analytical equation of non-linear response. The dependence on quality factor, as well as on amplitude, of difference between JJ’s plasma frequency and resonant frequency, is derived from the equation. The approximate treatment is quantitatively validated by our numerical simulations with practical JJ parameters including different environment influences. Thus, based on nonlinear frequency response of JJs, a reliable and simple method to determine quality factor of JJ is proposed, which is desirable for exploring JJ based microwave devices such as parametric amplifier, superconducting qubit. Being driven well into the nonlinear microwave response regime, due to frequency-amplitude interaction, the resonant frequency of a current bias JJ deviates from the JJ’s plasma frequency. The deviation is directly related to the microwave quality factor. Hence, the quality factor can be deducted from the experimental measurement of the resonant frequency deviation, with different microwave power values applied. In comparison with linear resonance experiment, the nonlinear resonance used by the proposed method produces stronger signal. Therefore it is more robust against external noise. When being conducted at high temperature, the proposed method is more reliable. The accuracy of the measured quality factor primarily depends on those of the JJ’s parameters such as critical current and capacitance, while those parameters can be experimentally determined with high precision.