Underdamped Josephson Junctions Research Articles

Resonant switching current detector based on underdamped Josephson junctions

Current-biased Josephson junctions can act as detectors of electromagnetic radiation. At optimal conditions, their sensitivity is limited by fluctuations causing stochastic switching from the superconducting to the resistive state. This work provides a quantitative description of a stochastic switching current detector, based on an underdamped Josephson junction. It is shown that activation of a Josephson plasma resonance can greatly enhance the detector responsivity in proportion to the quality factor of the junction. The ways of tuning the detector for achieving optimal operation are discussed. For realistic parameters of Nb/AlOx/Nb tunnel junctions, the sensitivity and noise-equivalent power (NEP) can reach values of S≃5×1012 (V/W) and NEP≃2×10−23 (WHz−1/2), respectively. These outstanding characteristics facilitate both bolometric and single-photon detection in microwave and terahertz ranges. Published by the American Physical Society 2024

Algorithms for automatic measurement of SIS-type hysteretic underdamped Josephson junction's parameters by current-voltage characteristics

Some electrical parameters of the SIS-type hysteretic underdamped Josephson junction (JJ) can be measured by its current-voltage characteristics (IVCs). Currents and voltages at JJ are commensurate with the intrinsic noise level of measuring instruments. This leads to the need for multiple measurements with subsequent statistical processing. In this paper, the digital algorithms are proposed for the automatic measurement of the JJ parameters by IVC. These algorithms make it possible to implement multiple measurements and check these JJ parameters in an automatic mode with the required accuracy. The complete sufficient statistics are used to minimize the root-mean-square error of parameter measurement. A sequence of current pulses with slow rising and falling edges is used to drive JJ, and synchronous current and voltage readings at JJ are used to realize measurement algorithms. The algorithm performance is estimated through computer simulations. The significant advantage of the proposed algorithms is the independence from current source noise and intrinsic noise of current and voltage meters, as well as the simple implementation in automatic digital measuring systems. The proposed algorithms can be used to control JJ parameters during mass production of superconducting integrated circuits, which will improve the production efficiency and product quality.

Josephson radiation patterns in underdamped topological Josephson junctions

Josephson radiation is a useful signature for detecting Majorana zero modes in topological superconductors. We study the Josephson radiation of the underdamped topological Josephson junction within the quantum resistively and capacitively shunted junction model. We show that the quantum dynamics of the Majorana two-level system induce oscillatory patterns in the Josephson emission spectra. With the Floquet method, we obtain analytical results for these oscillatory patterns and find that they are well described by Bessel functions. We perform numerical simulations to verify the analytical results and demonstrate that these Bessel radiation patterns exist for a wide range of junction parameters.

Towards a microwave single-photon counter for searching axions

The major task of detecting axions or axion-like particles has two challenges. On the one hand, the ultimate sensitivity is required, down to the energy of a single microwave photon of the yoctojoule range. On the other hand, since the detected events are supposed to be rare, the dark count rate of the detector must be extremely low. We show that this trade-off can be approached due to the peculiar switching dynamics of an underdamped Josephson junction in the phase diffusion regime. The detection of a few photons’ energy at 10 GHz with dark count time above 10 s and the efficiency close to unity was demonstrated. Further enhancements require a detailed investigation of the junction switching dynamics.

Insulating regime of an underdamped current-biased Josephson junction supporting Z3 and Z4 parafermions

We study analytically a current-biased topological Josephson junction supporting $\mathbb{Z}_n$ parafermions. First, we show that in an infinite-size system a pair of parafermions on the junction can be in $n$ different states; the $2\pi{n}$ periodicity of the phase potential of the junction results in a significant suppression of the maximal current $I_m$ for an insulating regime of the underdamped junction. Second, we study the behaviour of a realistic finite-size system with avoided level crossings characterized by splitting $\delta$. We consider two limiting cases: when the phase evolution may be considered adiabatic, which results in decreased periodicity of the effective potential, and the opposite case, when Landau-Zener transitions restore the $2\pi{n}$ periodicity of the phase potential. The resulting current $I_m$ is exponentially different in the opposite limits, which allows us to propose a new detection method to establish the appearance of parafermions in the system experimentally, based on measuring $I_m$ at different values of the splitting $\delta$.

Critical current for an insulating regime of an underdamped current-biased topological Josephson junction

We study analytically an underdamped current-biased topological Josephson junction. First, we consider a simplified model at zero temperature, where the parity of the non-local fermionic state formed by Majorana bound states (MBSs) localized on the junction is fixed, and show that a transition from insulating to conducting state in this case is governed by single-quasiparticle tunneling rather than by Cooper pair tunneling in contrast to a non-topological Josephson junction. This results in a significantly lower critical current for the transition from insulating to conducting state. We propose that, if the length of the system is finite, the transition from insulating to conducting state occurs at exponentially higher bias current due to hybridization of the states with different parities as a result of the overlap of MBSs localized on the junction and at the edges of the topological nanowire forming the junction. Finally, we discuss how the appearance of MBSs can be established experimentally by measuring the critical current for an insulating regime at different values of the applied magnetic field.

Resonance phenomena in an annular array of underdamped Josephson junctions

Appearance and origin of resonance phenomena have been studied in the annular system of underdamped Josephson junctions. If no fluxon is trapped in the system, dynamics is governed by the motion of fluxon-antifluxon pairs, while if trapped fluxons are present, they can move solely but also simultaneously with the pairs. Locking between the rotating excitations (fluxons and antifluxons) and the Josephson frequency leads to the appearance of zero field steps in the current-voltage characteristics, which can further exhibit branching due to resonance between the rotating excitations and plasma oscillations in their tale. The number of zero field steps and their branching are strongly determined by the total number of excitations present in the system. High resolution analysis further reveals not only some interesting properties of zero field steps, but also shows that the current-voltage characteristics is determined not only by the number, but also by the type of excitations, i.e., whether the dynamics is governed only by the motion of fluxon-antifluxon pairs or the trapped fluxons, or they move simultaneously in the system.

Ac-driven annular Josephson junctions: The missing Shapiro steps

Examination of an annular system of underdamped Josephson junctions in the presence of external radiation showed that the ability of the system to lock with some external radiation was determined not only by the number but also by the type of rotating excitations (fluxons or antifluxons). Shapiro steps can be observed in the current-voltage characteristics only in the system with trapped fluxons or in the system with fluxon-antifluxon pairs. If the trapped fluxons circulate simultaneously with fluxon-antifluxon pairs, there are no Shapiro steps regardless of the amplitude or frequency of the applied external radiation.

Influence of Correlated Coloured Noises on an Underdamped Josephson Junction

Influence of Correlated Coloured Noises on an Underdamped Josephson Junction

Superconducting nano Josephson junctions patterned with a focused helium ion beam

We report the fabrication of nanoscale wires and Josephson junctions in 25 nm thick YBa2Cu3O7–δ thin films with wire widths as narrow as 50 nm. Our approach utilizes a finely focused gas field ion source from a helium ion microscope to directly modify the material on the nanometer scale to convert irradiated regions of the film into insulators. In this manner, the film remains intact and no material is milled or removed. Transport data show that the electrical properties, critical current and conductance, scale linearly with the lithographically defined width ensuring that the actual and lithographically defined dimensions are commensurate with each other. Unlike in typical ion damage proximity effect Josephson junctions, we observe a low temperature saturation of the critical current and near temperature interdependent resistance which we attribute to a narrower and more resistive barrier. Furthermore, we also demonstrate the ability to fabricate devices exhibiting high resistance and capacitance with hysteretic underdamped Josephson junction properties. This patterning technique allows for a broad range of electrical properties for Josephson devices that will expand potential applications.

Single Photon Counter Based on a Josephson Junction at 14 GHz for Searching Galactic Axions

Axions and axion-like particles appear in well-motivated extensions of the standard model of particle physics and may be the solution to the long-standing puzzle of the dark matter in our Universe. Several new experiments are foreseen in the next decade searching them in a wide range of the parameter space. In the mass region from few to several tens of microelectronvolt, detector sensitivity will be limited by the standard quantum limit of linear amplifiers and a new class of single microwave-photon detector will be needed. We have developed a single photon counter based on the voltage switching of an underdamped Josephson junction that is coupled to a coplanar waveguide. By measuring the switching voltage, we can register single photons at 14 GHz with the rate less than 1 photon per 3000 s.

A double-flux-quantum amplifier with a single flux-biasing line

A Double-Flux-Quantum (DFQ) amplifier can multiply its input voltage with quantum accuracy using DFQ generation at under-damped Josephson junctions. We conducted research on digital-to-analogue converters that were implemented using DFQ amplifiers for metrological applications. Conventional DFQ amplifiers were usually operated using two flux-biasing lines. In this study, we redesigned the circuit layout to realize operation using a single flux-biasing line. We designed a new layout of a 20-fold DFQ amplifier and fabricated it using a 2.5-kA/cm2 Nb/AlOx/Nb process. The measurement was performed in liquid He. The Single-Flux-Quantum (SFQ) pulse train was fed using an over-biasing method, and the input-output characteristics are acquired using an oscilloscope. When the magnetic flux bias current Ifb1 was not supplied, the maximum input voltage Vinmax was 68 μV, which was 4.2 times larger than the value of 17 μV that was observed in our previous study. Vinmax was enhanced to 120 μV when we supplied an Ifb1 of 1.00 mA.

Switching Dynamics of an Underdamped Josephson Junction Coupled to a Microwave Cavity

Current-biased Josephson junctions are promising candidates for the detection of single photons in the microwave frequency domain. With modern fabrication technologies, the switching properties of the junction can be adjusted to achieve quantum limited sensitivity. Namely, the width of the switching current distribution can be reduced well below the current amplitude produced by a single photon trapped inside a superconducting cavity. However, for an effective detection a strong junction cavity coupling is required, providing nonlinear system dynamics. We compare experimental findings for our prototype device with a theoretical analysis aimed to describe the switching dynamics of junctions under microwave irradiation. Measurements are found in qualitative agreement with our simulations.

Study of microwave-induced phase switches from the finite voltage state in Bi2Sr2CaCu2Oy intrinsic Josephson junctions

We study the microwave-induced phase switches from the finite voltage state for the underdamped intrinsic Josephson junctions (IJJs) made of Bi2Sr2CaCu2Oy (Bi2212). We observe the resonant double-peak structure in the switching current distribution at low temperatures. This feature is successfully explained by a quantum mechanical model where the strong microwave field effectively suppresses the potential barrier for the phase escape from a potential well and the macroscopic quantum tunneling (MQT) is resonantly enhanced. The detailed analyses considering the effects of multiple phase retrapping processes after the phase escape strongly suggest that the intense microwave field suppresses the energy-level spacing in the potential well, by effectively decreasing the fluctuation-free critical current and the Josephson plasma frequency. This effect also reduces the number of photons required for the multiphoton transition between the ground and the first excited states, making it possible to observe the energy level quantization in the MQT state. The temperature dependence of the resonance peak emerging in the switching rate clearly demonstrates that the quantized energy state can be survived up to ~10 K, which is much higher than a crossover temperature predicted by the conventional Caldeira-Leggett theory.

Detection of Weak Microwave Fields with an Underdamped Josephson Junction

We have constructed a microwave detector based on the voltage switching of an underdamped Josephson junction, that is positioned at a current antinode of a {\lambda}/4 coplanar waveguide resonator. By measuring the switching current and the transmission through a waveguide capacitively coupled to the resonator at different drive frequencies and temperatures we are able to fully characterize the system and assess its detection efficiency and sensitivity. Testing the detector by applying a classical microwave field with the strength of a single photon yielded a sensitivity parameter of 0.5 in qualitative agreement with theoretical calculations.

A Farey staircase from the two-extremum return map of a Josephson junction

We report the presence of a Farey staircase in the simulated current–voltage characteristics between the second and third harmonic steps of an underdamped Josephson junction under external electromagnetic radiation. The steps constituting the staircase are interrupted by chaotic intervals. The dynamics is due to a two-extremum return map and is not associated with phase locking on an invariant torus. On decreasing the current, the third harmonic step ends in the bifurcation known as blue-sky catastrophe.

Experimental Study of Spectral Properties of a Frenkel-Kontorova System.

We report on microwave emission from linear parallel arrays of underdamped Josephson junctions, which are described by the Frenkel-Kontorova (FK) model. Electromagnetic radiation is detected from the arrays when biased on current singularities (steps) appearing at voltages V(n)=Φ(0)(nc̅/L), where Φ(0)=2.07×10(-15) Wb is the magnetic flux quantum, and c̅, L, and n are, respectively, the speed of light in the transmission line embedding the array, L its physical length, and n an integer. The radiation, detected at fundamental frequency c̅/2L when biased on different singularities, indicates shuttling of bunched 2π kinks (magnetic flux quanta). Resonance of flux-quanta motion with the small-amplitude oscillations induced in the arrays gives rise to fine structures in the radiation spectrum, which are interpreted on the basis of the FK model describing the resonance. The impact of our results on design and performances of new digital circuit families is discussed.

Structured Chaos in 1-D Stacks of Intrinsic Josephson Junctions Irradiated by Electromagnetic Waves

We investigate the effect of the capacitive and diffusive coupling on a novel type of structured chaos that was recently reported in numerical simulations of the IV characteristics of a single underdamped irradiated Josephson junction. A detailed characterization of the synchronization patterns in 1-D stacks of junctions is made through high-resolution (with respect to steps in the dc bias current) numerical simulations within the CCJJ+DC model. We show that the inclusion of coupling can result in complete synchronization of all the chaotic signals from the different junctions in the stack, a phenomenon that occurs when all the phases remain range-bound relative to that of the applied external radiation.

Note: Cryogenic coaxial microwave filters

The careful filtering of microwave electromagnetic radiation is critical for controlling the electromagnetic environment for experiments in solid-state quantum information processing and quantum metrology at millikelvin temperatures. We describe the design and fabrication of a coaxial filter assembly and demonstrate that its performance is in excellent agreement with theoretical modelling. We further perform an indicative test of the operation of the filters by making current-voltage measurements of small, underdamped Josephson junctions at 15 mK.

Underdamped Josephson junction as a switching current detector

We demonstrate the narrow switching distribution of an underdamped Josephson junction from the zero to the finite voltage state at millikelvin temperatures. We argue that such junctions can be used as ultrasensitive detectors of the single photons in the GHz range, operating close to the quantum limit: a given initial (zero voltage) state can be driven by an incoming signal to the finite voltage state. The width of the switching distribution at a nominal temperature of about T = 10 mK was 4.5 nA, which corresponds to an effective noise temperature of the device below 60 mK.