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Physical Review Research

Experimental evidence for a current-biased Josephson junction acting as either a macroscopic boson or fermion

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

Published Mar 4, 2024• 9 citations
Publisher

Abstract

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

DOI
10.1103/physrevresearch.6.013236

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

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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.

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Experimental tests for the quantum behavior of a macroscopic degree of freedom: The phase difference across a Josephson junction

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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.

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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..

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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 ${I}_{s}$ on the power W of the applied microwave radiation and by a peculiar double-peak structure in the switching current distribution ${P(I}_{s}).$ 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.

arXiv:cond-mat/0307668•Physical review. B, Condensed matter•Aug 19, 2003•29 citations
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
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.
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 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..
The possibility of maser action using a current-biased mesoscopic Josephson junction in a high-Q microcavity is discussed. A mesoscopic Josephson junction behaves like an artificial atom as far as the interaction with the photon field is concerned. Under a certain bias current, the Josephson ``atom'' is resonantly excited or pumped by quantum-mechanical fluctuations of the Josephson phase, i.e., macroscopic resonant tunneling. When the pumping overcomes the loss of photons from the cavity, maser action is possible. Quantum statistical properties of photons are also investigated numerically, taking into acount the microcavity effect on the basis of a Jaynes-Cummings model with pumping and cavity damping. We found that a mesoscopic Josephson junction within the high-Q microcavity acts as a thresholdless maser with sub-Poissonian photon statstics. \textcopyright{} 1996 The American Physical Society.
This thesis examines Josephson tunnel junctions as candidate qubits for quantum computation. A large area current-biased junction, known as a phase qubit, uses the two lowest energy levels in a tilted washboard potential as the qubit states |0> and |1>. I performed experiments with 10 x 10 um^2 Nb/AlOx/Nb qubit junctions, with critical currents of roughly 30 uA. The state of a device was initialized by cooling below 50 mK in a dilution refrigerator. In order for quantum mechanical superpositions to be long-lived, it is necessary to isolate the junction from noisy bias leads that originate at room temperature. I studied two types of isolation: an LC filter, and a broadband scheme that used an auxiliary junction, resulting in a dc SQUID. One of the main goals of this work was to determine how well a simple Hamiltonian, derived assuming just a few lumped elements, describes the observed behavior of a macroscopic Josephson device, including coherent dynamics such as Rabi oscillations. I did this by comparing results to the expected behavior of ideal two-level systems and with more detailed master equation and density matrix simulations. I performed state manipulation by applying dc bias currents and resonant microwave currents, and through temperature control. The tunneling escape rate of the junction from the states |0> and |1> (zero voltage) to the running state (finite voltage) depends on the occupation probability of the energy levels and served as state readout. Experiments to measure the relaxation time T1 between |1> and |0> were performed by examining the dependence of the escape rate with temperature, yielding a maximum T1 = 15 ns. Measuring the decay to the ground state after applying a microwave pulse revealed at least two time constants, one of about 10 ns and another as long as 50 ns. The spectroscopic coherence time T2* was estimated to be roughly 5 ns by measuring resonance widths and the decay envelope of coherent Rabi oscillations was found to have a time constant T' = 10 ns over a wide range of conditions.
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.