We investigate the physics of coherent quantum phase slips in two distinct circuits containing small Josephson junctions: (i) a single junction embedded in an inductive environment and (ii) a long chain of junctions. Starting from the standard Josephson Hamiltonian, the single junction circuit can be analyzed using quasi-classical methods; we formulate the conditions under which the resulting quasi-charge dynamics is exactly dual to the usual phase dynamics associated with Josephson tunneling. For the chain we use the fact that its collective behavior can be characterized by one variable: the number $m$ of quantum phase slips present on it. We conclude that the dynamics of the conjugate quasi-charge is again exactly dual to the standard phase dynamics of a single Josephson junction. In both cases we elucidate the role of the inductance, essential to obtain exact duality. These conclusions have profound consequences for the behavior of single junctions and chains under microwave irradiation. Since both systems are governed by a model exactly dual to the standard resistively and capacitively shunted junction model, we expect the appearance of current-Shapiro steps. We numerically calculate the corresponding current-voltage characteristics in a wide range of parameters. Our results are of interest in view of a metrological current standard.
Irradiating a Josephson junction with microwaves can operate not only on the amplitude but also on the phase of the Josephson current. This requires breaking time inversion symmetry, which is achieved by introducing a phase lapse between the microwave components acting on the two† sides of the junction. General symmetry arguments and the solution of a specific single level quantum dot model show that this induces chirality in the Cooper pair dynamics, due to the topology of the Andreev bound state wavefunction. Another essential condition is to break electron-hole symmetry within the junction.…
Recently, a contact-resistance-measurement method was developed to detect the minigap, hence the Andreev bound states (ABSs), in Josephson junctions constructed on the surface of three-dimensional topological insulators (3D TIs). In this work, we further generalize that method to the circumstance with radio frequency (rf) irradiation. We find that with the increase of rf power, the measured minigap becomes broadened and extends to higher energies, in a way similar to the rf power dependence of the outer border of the Shapiro step region. We show that the corresponding data of contact resistanc…
Josephson transport in YBa${}_{2}$Cu${}_{3}$O${}_{7}$ weak links created by focused-helium-ion-beam irradiation: Analysis based on diffusive-SNS-junction model
National Institute of Advanced Industrial Science and Technology（日本产业技术综合研究所）
The influence of radio frequency microwaves on the Coulomb blockade characteristics in small Josephson junctions was studied using a one-dimensional array of ten small Al tunnel junctions in the frequency range from 1 MHz to 1000 MHz. Coulomb blockade voltage ($V_{\rm th}$) is diminished with increasing microwave power ($V_{\rm ac}$), where the $V_{\rm th}$-$V_{\rm ac}$ plots for varied frequencies fall on a single curve. We observed and theoretically analyzed a magnetic field $dependent$ renormalization of the applied microwave power, in addition to a magnetic-field $independent$ renormalizat…
A superconducting quantum interference device (SQUID) comprising 0- and $π$-Josephson junctions (JJs), called $π$-SQUID, is studied by the resistively shunted junction model. The $π$-SQUID shows half-integer Shapiro-steps (SS) under microwave irradiation at the voltage $V$ = $(\hbar/2e)Ω(n/2)$, with angular frequency $Ω$ and half-integer $n$/2 in addition to integer $n$. We show that the $π$-SQUID can be a $π$-qubit with spontaneous loop currents by which the half-integer SS are induced. Making the 0- and $π$-JJs equivalent is a key for the half-integer SS and realizing the $π$-qubit.
Topological Josephson junctions (JJs), which contain Majorana bound states, are expected to exhibit 4$π$-periodic current-phase relation, thereby resulting in doubled Shapiro steps under microwave irradiation. We performed numerical calculations of dynamical properties of topological JJs using a modified resistively and capacitively shunted junction model and extensively investigated the progressive evolution of Shapiro steps as a function of the junction parameters and microwave power and frequency. Our calculation results indicate that the suppression of odd-integer Shapiro steps, i.e., evid…
Diode effect in microwave irradiated Josephson junctions with Yu-Shiba-Rusinov states
Institute for Theoretical Physics and Astrophysics, University of Würzburg（维尔茨堡大学理论物理与天体物理研究所）；Würzburg-Dresden Cluster of Excellence ct.qmat（维尔茨堡-德累斯顿卓越集群 ct.qmat）
By measuring the Josephson emission of a diffusive Superconductor-Normal metal-Superconductor (SNS) junction at a finite temperature we reveal a non-trivial sensitivity of the supercurrent to microwave irradiation. We demonstrate that the harmonic content of the current-phase relation is modified due to the energy redistribution of quasiparticles in the normal wire induced by the electromagnetic field. The distortion originates from the phase-dependent out-of-equilibrium distribution function which is strongly affected by the ac-response of the spectral supercurrent. For phases close to $π$, t…
We experimentally study electron transport between two superconducting indium leads, coupled to a single WTe$_2$ crystal, which is a three-dimensional Weyl semimetal. We demonstrate Josephson current in long 5~$μ$m In-WTe$_2$-In junctions, as confirmed by the observation of integer (1,2,3) and fractional (1/3, 1/2, 2/3) Shapiro steps under microwave irradiation. Demonstration of fractional a.c. Josephson effect indicates multivalued character of the current-phase relationship, which we connect with Weyl topological surface states contribution to Josephson current. In contrast to topological in…
Topological Josephson junctions designed on the surface of a 3D-topological insulator (TI) harbor Majorana bound states (MBS's) among a continuum of conventional Andreev bound states. The distinct feature of these MBS's lies in the $4π$-periodicity of their energy-phase relation that yields a fractional ac Josephson effect and a suppression of odd Shapiro steps under $r\!f$ irradiation. Yet, recent experiments showed that a few, or only the first, odd Shapiro steps are missing, casting doubts on the interpretation. Here, we show that Josephson junctions tailored on the large bandgap 3D TI Bi$_…
A junction with two superconductors coupled by a normal metal hosts Andreev bound states whose energy spectrum is phase-dependent and exhibits a minigap, resulting in a periodic supercurrent. Phase-dependent dissipation also appears at finite frequency due to relaxation of Andreev bound states. While dissipation and supercurrent versus phase have previously been measured near thermal equilibrium, their behavior in nonequilibrium is still elusive. By measuring the ac susceptibility of a graphene-superconductor junction under microwave irradiation, we find supercurrent response deviates from adi…
Quantum Phase-Slip Junction Under Microwave Irradiation
我们考虑量子相位滑移结（QPSJ）-一个双约瑟夫森结-连接到频率为$ω_\textrm{mw}$的微波源的动力学。相对于普通的约瑟夫森结，QPSJ可以维持双夏皮罗台阶，其由在电流-电压（I-V）特性中的多个整数$ e ω_\textrm{mw} / π$处的明确定义的电流平台组成。到目前为止，对这些高原的实验观察还很困难。我们认为，热以及量子涨落可以涂抹的I-V特性相当大。为了理解这些影响，我们研究了微波辐射下的电流偏置QPSJ，并连接到电感和电阻的环境。我们发现，这些波动的影响是由环境的电阻和由相位滑移能和感应能的比例。我们的结果是有趣的实验，旨在观察双夏皮罗步骤在QPSJ设备的定义一个新的量子电流标准。
Semiconductor/superconductor hybrids exhibit a range of phenomena that can be exploited for the study of novel physics and the development of new technologies. Understanding the origin the energy spectrum of such hybrids is therefore a crucial goal. Here, we study Josephson junctions defined by shadow epitaxy on InAsSb/Al nanowires. The devices exhibit gate-tunable supercurrents at low temperatures and multiple Andreev reflections (MARs) at finite voltage bias. Under microwave irradiation, photon assisted tunneling (PAT) of MARs produces characteristic oscillating sidebands at quantized energi…
We have theoretically demonstrated the emission of circularly-polarized terahertz (THz) waves from intrinsic Josephson junctions (IJJs) which is locally heated by an external heat source such as the laser irradiation. We focus on a mesa-structured IJJ whose geometry is slightly deviate from a square and find that the local heating make it possible to emit circularly-polarized THz waves. In this mesa, the inhomogeneity of critical current density induced by the local heating excites the electromagnetic cavity modes TM (1,0) and TM (0,1), whose polarizations are orthogonal to each other. The mix…
This work reports a novel time-domain expression for the current-response kernels of a Josephson tunnel junction between BCS superconductors with in general different energy gaps, and its use to simulate the classical dynamics of such junctions. The simulations show a dynamic regime characterized by the resonance between the Josephson oscillations and the gap oscillations in the asymptotics of the current kernels that has not been studied previously. The resonance manifests itself as a hysteresis in the dc current-voltage characteristics of the current-biased junctions in the voltage range abo…
Electromotive interference in a mechanically oscillating superconductor: generalized Josephson relations and self-sustained oscillations of a torsional SQUID
The Majorana zero-energy modes (MZMs) residing at the boundary of topological superconductors have attracted a great deal of interest recently, as they provide a platform to explore fundamental physics such as non-Abelian statistics, as well as fault-tolerant quantum computation. Period doubling of Shapiro steps in a Josephson junction under microwave irradiation has been regarded as strong evidence for the emergence of the MZMs at the junction edges. However, questions remain as to how the Shapiro steps respond to the presence of a 4π-periodic Josephson current. In this study, we investigated…
Superconducting circuits are a versatile platform to implement a multitude of Hamiltonians which perform quantum computation, simulation and sensing tasks. A key ingredient for realizing a desired Hamiltonian is the irradiation of the circuit by a strong drive. These strong drives provide an in-situ control of couplings, which cannot be obtained by near-equilibrium Hamiltonians. However, as shown in this paper, out-of-equilibrium systems are easily plagued by complex dynamics leading to instabilities. Predicting and preventing these instabilities is crucial, both from a fundamental and applica…
The Josephson junction (JJ) is the corner stone of superconducting electronics and quantum information processing. While the technology for fabricating low $T_{c}$ JJ is mature and delivers quantum circuits able to reach the "quantum supremacy", the fabrication of reproducible and low-noise high-$T_{c}$ JJ is still a challenge to be taken up. Here we report on noise properties at RF frequencies of recently introduced high-$T_{c}$ Josephson nano-junctions fabricated by mean of a Helium ion beam focused at sub-nanometer scale on a $\mathrm{YBa}_2\mathrm{Cu}_3\mathrm{O}_7$ thin film. We show that…
Electrons in a Dirac semimetals possess linear dispersion in all three spatial dimensions, and form part of a developing platform of novel quantum materials. Bi$_{1-x}$Sb$_x$ supports a three-dimensional Dirac cone at the Sb-induced band inversion point. Nanoscale phase-sensitive junction technology is used to induce superconductivity in this Dirac semimetal. Radio frequency irradiation experiments reveal a significant contribution of 4$π$-periodic Andreev bound states to the supercurrent in Nb-Bi$_{0.97}$Sb$_{0.03}$-Nb Josephson junctions. The conditions for a substantial $4π$ contribution to…
Inspired by recent experiments, we study a short superconducting junction of length $L\ll ξ$ (coherence length) inserted in a dc-SQUID containing an ancillary Josephson tunnel junction. We evaluate the nonequilibrium occupation of the Andreev bound states (ABS) for the case of a conventional junction and a topological junction, with the latter case of ABS corresponding to a Majorana mode. We take into account small phase fluctuations of the Josephson tunnel junction, acting as a damped LC resonator, and analyze the role of the distribution of the quasiparticles of the continuum assuming that t…
Emission of Microwave Photon Pairs by a Tunnel Junction
非经典电磁场的产生和控制是量子信息物理中的一个重要问题。虽然用于产生这种场的通常方法依赖于（晶体、约瑟夫森结等的）非线性，最近在正常导体（微波辐射下的隧道结）上进行的实验揭示了一种替代方案：在量子导体\cite{PAN_squeezing}中使用电子散粒噪声。在这里，我们表明，这样的设备可以发射不同频率的\emph{pairs of microwave photons}的速率一样高的超导约瑟夫森结\cite{Flurin}。这导致在光子散粒噪声之下相关的两个不同频率处的光子场的强度波动，即双模振幅压缩。我们的实验是从量子光学的角度理解电子噪声的基本步骤，并表明即使是正常的导体也可以用作量子信息处理的资源。
Microwave Response of the Superconducting Diode Effect in Proximitized Bilayer Graphene Interferometers
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC)（马德里材料科学研究所，西班牙国家科学研究委员会）；Quantum Advanced Research Center (QuARC), Consejo Superior de Investigaciones Científicas (CSIC)（量子先进研究中心，西班牙国家科学研究委员会）；Department of Physics, Norwegian University of Science and Technology（挪威科技大学物理系）；Beijing Key Laboratory of Quantum Devices, Peking University（北京大学量子器件北京市重点实验室）
