Current-biased Josephson Junction Research Articles

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

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

Diode Effects in Current-Biased Josephson Junctions.

Current-biased Josephson junctions exhibit hysteretic transitions between dissipative and superconducting states as characterized by switching and retrapping currents. Here, we develop a theory for diodelike effects in the switching and retrapping currents of weakly damped Josephson junctions. We find that while the diodelike behavior of switching currents is rooted in asymmetric current-phase relations, nonreciprocal retrapping currents originate in asymmetric quasiparticle currents. These different origins also imply distinctly different symmetry requirements. We illustrate our results by a microscopic model for junctions involving a single magnetic atom. Our theory provides significant guidance in identifying the microscopic origin of nonreciprocities in Josephson junctions.

Stepping Closer to Pulsed Single Microwave Photon Detectors for Axions Search

Axions detection requires the ultimate sensitivity down to the single photon limit. In the microwave region this corresponds to energies in the yJ range. This extreme sensitivity has to be combined with an extremely low dark count rate, since the probability of axions conversion into microwave photons is supposed to be very low. To face this complicated task, we followed two promising approaches that both rely on the use of superconducting devices based on the Josephson effect. The first one is to use a single Josephson junction (JJ) as a switching detector (i.e. exploiting the superconducting to normal state transition in presence of microwave photons). We designed a device composed of a coplanar waveguide terminated on a current biased Josephson junction. We tested its efficiency to pulsed (pulse duration 10 ns) microwave signals, since this configuration is closer to an actual axions search experiment. We show how our device is able to reach detection capability of the order of 10 photons with frequency 8 GHz. The second approach is based on an intrinsically quantum device formed by two resonators coupled only via a superconducting qubit network (SQN). This approach relies on quantum nondemolition measurements of the resonator photons. We show that injecting RF power into the resonator, the frequency position of the resonant drop in the transmission coefficient (S21) can be modulated up to 4 MHz. We anticipate that, once optimized, both the devices have the potential to reach single photon sensitivity.

Engineering the speedup of quantum tunneling in Josephson systems via dissipation

We theoretically investigate the escape rate occurring via quantum tunneling in a system affected by tailored dissipation. Specifically, we study the environmental assisted quantum tunneling of the superconducting phase in a current-biased Josephson junction. We consider Ohmic resistors inducing dissipation both in the phase and in the charge of the quantum circuit. We find that the charge dissipation leads to an enhancement of the quantum escape rate. This effect appears already in the low Ohmic regime and also occurs in the presence of phase dissipation that favors localization. Inserting realistic circuit parameters, we address the question of its experimental observability and discuss suitable parameter spaces for the observation of the enhanced rate.

Josephson-Based Scheme for the Detection of Microwave Photons

We propose a scheme for the detection of microwave-induced photons through a current-biased Josephson junction, from the point of view of the statistical decision theory. Our analysis is based on the numerical study of the zero-voltage lifetime distribution in response to a periodic train of pulses, that mimics the absorption of photons. The statistical properties of the detection are retrieved comparing the thermally induced transitions with the distribution of the switchings to the finite voltage state due to the joint action of thermal noise and of the incident pulses. The capability to discriminate the photon arrival can be quantified through the Kumar-Caroll index, which is a good indicator of the signal-to-noise ratio. The index can be exploited to identify the system parameters best suited for the detection of weak microwave photons.

Josephson Junctions as Single Microwave Photon Counters: Simulation and Characterization

Detection of light dark matter, such as axion-like particles, puts stringent requirements on the efficiency and dark-count rates of microwave-photon detectors. The possibility of operating a current-biased Josephson junction as a single-microwave photon-detector was investigated through numerical simulations, and through an initial characterization of two Al junctions fabricated by shadow mask evaporation, done in a dilution refrigerator by measuring escape currents at different temperatures, from 40 mK up to the Al transition temperature. The escape dynamics of the junctions were reproduced in the simulation, including the dissipative effects. Inhibition of thermal activation was observed, leaving the macroscopic quantum tunneling as the dominant effect well beyond the crossover temperature.

Single-Photon Detection with a Josephson Junction Coupled to a Resonator

We use semiclassical formalism to optimize a microwave single photon detector based on switching events of a current biased Josephson junction coupled to a resonator. In order to detect very rare events, the average time between dark counts $\tau_{\rm dark}$ should be maximized taking into account that the switching time $\tau_{\rm sw}$ should be sufficiently small. We demonstrate that these times can be tuned in the wide range by changing the junction parameters, and the ratios $\tau_{\rm dark}/\tau_{\rm sw} \sim 10^9$ can be achieved. Therefore, a junction-resonator arrangement can be used for detecting extremely low photon fluxes, for instance for searching galactic axions.

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 $\delta$.

Voltage staircase in a current-biased quantum-dot Josephson junction

We calculate the current-voltage ($I\ensuremath{-}V$) characteristic of a Josephson junction containing a resonant level in the weakly coupled regime (resonance width small compared to the superconducting gap). The phase $\ensuremath{\phi}$ across the junction becomes time dependent in response to a DC current bias. Rabi oscillations in the Andreev levels produce a staircase $I\ensuremath{-}V$ characteristic. The number of voltage steps counts the number of Rabi oscillations per $2\ensuremath{\pi}$ increment of $\ensuremath{\phi}$, providing a way to probe the coherence of the qubit in the absence of any external AC driving. The phenomenology is the same as the Majorana-induced DC Shapiro steps in topological Josephson junctions of Choi et al. [Phys. Rev. B 102, 140501(R) (2020)]---but now for a nontopological Andreev qubit.

Voltage drop across Josephson junctions for Lévy noise detection

We propose to characterize L\'evy-distributed stochastic fluctuations through the measurement of the average voltage drop across a current-biased Josephson junction. We show that the noise induced switching process in the Josephson washboard potential can be exploited to reveal and characterize L\'evy fluctuations, also if embedded in a thermal noisy background. The measurement of the average voltage drop as a function of the noise intensity allows to infer the value of the stability index that characterizes L\'evy-distributed fluctuations. An analytical estimate of the average velocity in the case of a L\'evy-driven escape process from a metastable state well agrees with the numerical calculation of the average voltage drop across the junction. The best performances are reached at small bias currents and low temperatures, \emph{i.e.}, when both thermally activated and quantum tunneling switching processes can be neglected. The effects discussed in this work pave the way toward an effective and reliable method to characterize L\'evy components eventually present in an unknown noisy signal.

Thermal preparation of an entangled steady state of distant nitrogen-vacancy-center ensembles

Steady state entanglement is studied in the continuous-variable system of two distant nitrogen-vacancy-center ensembles (NVEs) driven by squeezed microwave field. Transmission line resonators and a current-biased Josephson junction are used for transfer of excitations between two NVEs. The circuit is enhanced by Josephson parametric amplifiers (JPAs), which produce squeezed microwave field. Squeezed fields of JPAs are driving force, which provides generation of an entangled steady state of two bosonic modes of NVEs for a wide range of system parameters.

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.

Status of the SIMP Project: Toward the Single Microwave Photon Detection

The Italian institute for nuclear physics (INFN) has financed the SIMP project (2019-2021) in order to strengthen its skills and technologies in the field of meV detectors with the ultimate aim of developing a single microwave photon detector. This goal will be pursued by improving the sensitivity and the dark count rate of two types of photodetectors: current biased Josephson Junction (JJ) for the frequency range 10-50 GHz and Transition Edge Sensor (TES) for the frequency range 30-100 GHz. Preliminary results on materials and devices characterization are presented.

Multipurpose Quantum Simulator Based on a Hybrid Solid-State Quantum Device

This paper proposes a scheme to enhance the fidelity of symmetric and asymmetric quantum cloning using a hybrid system based on nitrogen-vacancy (N-V) centers. By setting different initial states, the present scheme can implement optimal symmetric (asymmetric) universal (phase-covariant) quantum cloning, so that the copies with the assistance of a Current-biased Josephson junction (CBJJ) qubit and four transmission-line resonators (TLRs) can be obtained. The scheme consists of two stages: cjhothe first stage is the implementation of the conventional controlled-phase gate, and the second is the realization of different quantum cloning machines (QCM) by choosing a suitable evolution time. The results show that the probability of success for QCM of a copy of the equatorial state can reach 1. Furthermore, the | W 4 ± ⟩ entangled state can be generated in the process of the phase-covariant quantum anti-cloning. Finally, the decoherence effects caused by the N-V center qubits and CBJJ qubit are discussed.

A method of determining microwave dissipation of Josephson junctions with non-linear frequency response

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.

Nonequilibrium charge dynamics in Majorana-Josephson devices

We investigate the impact of introducing Majorana bound states, formed by a proximitized semiconducting nanowire in the topological regime, into a current biased capacitive Josephson junction, thereby adding delocalized states below the superconducting gap. We find that this qualitatively changes the charge dynamics of the system, diminishing the role of Bloch oscillations and causing single-particle tunnelling effects to dominate. We fully characterize the resulting charge dynamics and the associated voltage and current signals. Our work reveals a rich landscape of behaviours in both the static and time-varying driving modes. This can be directly attributed to the presence of Majorana bound states, which serve as a pathway for charge transport and enable non-equilibrium excitations of the Majorana-Josephson device.

Solitonic thermal transport in a current-biased long Josephson junction

We investigate the coherent energy and thermal transport in a temperature-biased long Josephson tunnel junction, when a Josephson vortex, i.e., a soliton, steadily drifts driven by an electric bias current. We demonstrate that thermal transport through the junction can be controlled by the bias current, since it determines the steady-state velocity of the drifting soliton. We study the effects on thermal transport of the damping affecting the soliton dynamics. In fact, a soliton locally influences the power flowing through the junction and can cause the variation of the temperature of the device. When the soliton speed increases approaching its limiting value, i.e., the Swihart velocity, we demonstrate that the soliton-induces thermal effects significantly modify. Finally, we discuss how the appropriate material selection of the superconductors forming the junction is essential, since short quasiparticle relaxation times are required to observe fast thermal effects.

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.

Enhancement of macroscopic quantum tunneling in the higher-order phase switches of Bi2212 intrinsic Josephson junctions

The macroscopic quantum tunneling (MQT) in the current-biased intrinsic Josephson junctions (IJJs) of high-Tc cuprates has attracted much attention for decades. Although the MQT for the phase switches from the zero to the first voltage state (1st SW) in the multiple-branched I-V curves is well explained by the conventional theory, the occurrence of MQT for the higher order switches such as the switch from the 1st to 2nd voltage state (2nd SW) has been still debated. Here, we present an experimental study on the phase switches of small IJJs fabricated from underdoped Bi2Sr2(Ca,Y)Cu2Oy. We observed the single photon transition between quantized energy levels in the 3rd phase switches at 59.15 GHz and 2 K. The comparison with the previous studies on the nearly optimal-doped Bi2Sr2CaCu2Oy clearly suggests a possibility that the MQT rate for the higher-order phase switches is commonly enhanced by the effective suppression of the energy barrier for the higher-order phase escape due to the phase-running state after the 1st SW, in spite of the large difference in a critical current density and Tc.

Strong mechanically induced effects in DC current-biased suspended Josephson junctions

Superconductivity is a result of quantum coherence at macroscopic scales. Two superconductors separated by a metallic or insulating weak link exhibit the AC Josephson effect - the conversion of a DC voltage bias into an AC supercurrent. This current may be used to activate mechanical oscillations in a suspended weak link. As the DC voltage bias condition is remarkably difficult to achieve in experiments, here we analyse theoretically how the Josephson effect can be exploited to activate and detect mechanical oscillations in the experimentally relevant condition with purely DC current bias. We unveil for the first time how changing the strength of the electromechanical coupling results in two qualitatively different regimes showing dramatic effects of the oscillations on the DC current-voltage characteristic of the device. These include the apperance of Shapiro-like plateaux for weak coupling and a sudden mechanically-induced retrapping for strong coupling. Our predictions, measurable in state of the art experimental setups, allow the determination of the frequency and quality factor of the resonator using DC only techniques.