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The growing interest in quantum technologies, from fundamental physics experiments to quantum computing, demands for extremely performing electronics only adding the minimum amount of noise admitted by quantum mechanics to the input signal (i.e. quantum-limited electronics). Superconducting microwave amplifiers, due to their dissipationless nature, exhibit outstanding performances in terms of noise (quantum limited), and gain. However, bandwidth and saturation power still show space for substantial improvement. Within the DARTWARS* collaboration, we are developing state-of-the-art microwave superconducting amplifiers based on Josephson junction arrays and on distributed kinetic inductance transmission lines. Here we report the realization of a setup for the characterization of the performances of Josephson Traveling-Wave Parametric Amplifiers (JTWPA) at a temperature of 300 mK. Although in the final experimental setup these amplifiers will operate at a base temperature of about 20 mK, their characterization at 300 mK allows to evidence the main aspects of their performances, but the ultimate noise level. This represents a quick and relatively inexpensive way to test these superconductive devices that can be of help to improve their design and fabrication. IEEE

The recent developments in quantum technologies, as well as advanced detection experiments, have raised the need to detect extremely weak signals in the microwave frequency spectrum. To this aim, the Josephson travelling wave parametric amplifier, a device capable of reaching the quantum noise limit while providing a wide bandwidth, has been proposed as a suitable cryogenic front-end amplifier. This work deals with the numerical study of a Josephson travelling wave parametric amplifier, without approximations regarding the nonlinearity of the key elements. In particular, we focus on the investigation of the system of coupled nonlinear differential equations representing all the cells of the Josephson travelling wave parametric amplifier, with proper input and output signals at the boundaries. The investigation of the output signals generated by the parametric amplification process explores the phase-space and the Fourier spectral analysis of the output voltage, as a function of the parameters describing the pump and signal tones that excite the device. Beside the expected behavior, i.e., the signal amplification, we show that, depending on the system operation, unwanted effects (such as pump tone harmonics, incommensurate frequency generation, and noise rise), which are not accounted for in simple linearized approaches, can be generated in the whole nonlinear system. IEEE

A complete framework for exciting and detecting thermally-induced, stabilized sine-Gordon breathers in ac-driven long Josephson junctions is developed. The formation of long-time stable breathers locked to the ac source occurs for a sufficiently high temperature. The latter emerges as a powerful control parameter, allowing for the remarkably stable localized modes to appear. Nonmonotonic behaviors of both the breather generation probability and the energy spatial correlations versus the thermal noise strength are found. The junction's resistive switching characteristics provides a clear experimental signature of the breather., 5 pages, 4 figures; Supp Mat: 4 pages, 2 figures

The dynamics of sine-Gordon breathers is studied in the presence of dissipative and stochastic perturbations. Taking a stationary breather with a random phase value as the initial state, the performed simulations demonstrate that a spatially-homogeneous noisy source can make the oscillatory excitation more stable, i.e., it enables the latter to last significantly longer than it would in a noise-free scenario. Both the frequency domain and the localization of energy are examined to document the effectiveness of the noise-enhanced stability phenomenon, which emerges as a nonmonotonic behavior of an average characteristic time for the breather as a function of the noise intensity. The influence of the mode's starting frequency on the results and their robustness against an additional thermal background are also addressed., 24 pages, 8 figures

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We discuss the resonant activation phenomenon on a Josephson junction due to the coupling of the Josephson system with axions. We show how such an effect can be exploited for axion detection. A nonmonotonic behavior, with a minimum, of the mean switching time from the superconducting to the resistive state versus the ratio of the axion energy and the Josephson plasma energy is found. We demonstrate how variations in switching times make it possible to detect the presence of the axion field. An experimental protocol for observing axions through their coupling with a Josephson system is proposed.

In superconductors that lack inversion symmetry, the flow of supercurrent can induce a non-vanishing magnetization, a phenomenon which is at the heart of non-dissipative magneto-electric effects, also known as Edelstein effects. For electrons carrying spin and orbital moments a question of fundamental relevance deals with the orbital nature of magneto-electric effects in conventional spin-singlet superconductors with Rashba coupling. Remarkably, we find that the supercurrent-induced orbital magnetization is more than one order of magnitude greater than that due to the spin, giving rise to a colossal magneto-electric effect. The induced orbital magnetization is shown to be sign tunable, with the sign change occurring for the Fermi level lying in proximity of avoiding crossing points in the Brillouin zone and in the presence of superconducting phase inhomogeneities, yielding domains with opposite orbital moment orientation. The orbital-dominated magneto-electric phenomena, hence, have clear-cut marks for detection both in the bulk and at the edge of the system and are expected to be a general feature of multi-orbital superconductors without inversion symmetry breaking., Comment: 7 pages, 5 figures

The generation of travelling sine-Gordon breathers is achieved through the nonlinear supratransmission effect in a magnetically driven long Josephson junction, in the presence of losses, a current bias, and a thermal noise source. We demonstrate how to exclusively induce breather modes by means of controlled magnetic pulses. A nonmonotonic behavior of the breather-only generation probability is observed as a function of the noise intensity. An experimental protocol providing evidence of the Josephson breather's existence is proposed., 5 pages, 4 figures

We review three different approaches to investigate the non-equilibrium stochastic dynamics of a Josephson junction affected by Levy-distributed current fluctuations. First, we study the lifetime in the metastable superconducting state of current-biased short and long junctions, in the presence of Gaussian and Levy noise sources. We highlight the noise-induced nonmonotonic behavior of the mean switching time as a function of noise intensity and driving frequency, that is the noise enhanced stability and the stochastic resonant activation, respectively. Then, we characterize the Levy noise source through the average voltage drop across a current-biased junction. The voltage measurement versus the noise intensity allows to infer the value of the stability index that characterizes Levy-distributed fluctuations. The numerical calculation of the average voltage drop across the junction well agrees with the analytical estimate of the average velocity for Levy-driven escape processes from a metastable state. Finally, we look at the distribution of switching currents out of the zero-voltage state, when a Levy noise signal is added to a linearly ramped bias current. The analysis of the cumulative distribution function of the switching currents gives information on both the Levy stability index and the intensity of fluctuations. We present also a theoretical model to catch the features of the Levy signal from a measured distribution of switching currents. The phenomena discussed in this work can pave the way for an effective and reliable Josephson-based scheme to characterize Levy components eventually embedded in an unknown noisy signal.

This work deals with the numerical analysis of the zero-voltage state lifetimes distribution of an underdamped Josephson junction used for the detection of single microwave photons in the presence of thermal noise. The analysis considers the switching probabilities of a JJ subjected to a train of current pulses, which simulates a weak photon field. To characterize the detection, we take advantage of a statistic tool, the Kumar-Carroll (KC) index, which is a good proxy of the signal-to-noise-ratio. It can be, therefore, exploited to identify the proper device fabrication parameters and the optimal operation point of the junction.

This focus issue is a collection of invited perspective papers on the various subfields of statistical physics for complex systems that covers the topics of the international conference SigmaPhi 2021

We propose a scheme for the detection of microwave induced photons through 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., Comment: 14 pages, 8 figures

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., Comment: 12 pages, 6 figures

We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones.

We discuss the effects of thermal noise on the magnetic response of a lateral ferromagnetic Josephson junction with spin-orbit coupling and out-of-plane magnetization. The direction of the magnetic moment in the ferromagnetic layer can be inverted by using controlled current pulses. This phenomenon is due to the magnetoelectric effect that couples the flowing charge current and the magnetization of the ferromagnet. We investigate the magnetization reversal effect versus intrinsic parameters of the ferromagnet, such as the Gilbert damping and strength of the spin-orbit coupling. We estimate the magnetization reversing time and find the optimal values of the parameters for fast switching. With the aim of increasing the operation temperature we study the effects induced by thermal fluctuations on the averaged stationary magnetization, and find the conditions that make the system more robust against noise., F.S.B. acknowledge funding by the Spanish Ministerio de Ciencia, Innovación y Universidades (MICINN) (Project No. FIS2017-82804-P), partial support by Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT1249-19), and by EU’s Horizon 2020 research and innovation program under Grant Agreement No. 800923 (SUPERTED).

We discuss the response of an rf-SQUID formed by anomalous Josephson junctions embedded in a superconducting ring with a non-negligible inductance. We demonstrate that a properly sweeping in-plane magnetic field can cause both the total flux and the current circulating in the device to modulate and to behave hysteretically. The bistable response of the system is analyzed as a function of the anomalous phase shift at different values of the screening parameter, in order to highlight the parameter range within which a hysteretic behavior can be observed. The magnetic flux piercing the SQUID ring is demonstrated to further modulate the hysteretical response of the system. Moreover, we show that the anomalous phase shift can be conveniently determined through the measurement of the out-of-plane magnetic field at which the device switches to the voltage state and the number of trapped flux quanta changes. Finally, we compare the response of two different device configurations, namely, a SQUID including only one or two anomalous junctions. In view of these results, the proposed device can be effectively used to detect and measure the anomalous Josephson effect., F.S.B., C.S.-F., and C.G. acknowledge funding by the Spanish Ministerio de Ciencia, Innovación, y Universidades (MICINN) (Project No. FIS2017-82804-P). F.S.B. acknowledges partial support by Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT1249-19), and by EU’s Horizon 2020 research and innovation program under Grant Agreement No. 800923 (SUPERTED). The work of E.S. was supported by a Marie Curie Individual Fellowship (MSCA-IFEFST No. 660532-SuperMag). E.S., N.L., and F.G. acknowledge partial financial support from the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant No. 615187-COMANCHE. E.S., A.I., N.L., F.S.B., and F.G. were partially supported by EU’s Horizon 2020 research and innovation program under Grant Agreement No. 800923 (SUPERTED). A.B. acknowledges the CNR-CONICET cooperation program Energy Conversion in Quantum Nanoscale Hybrid Devices, the SNS-WIS joint laboratory QUANTRA, funded by the Italian Ministry of Foreign Affairs and International Cooperation, and the Royal Society through the International Exchanges between the UK and Italy (GrantsNo. IES R3 170054 and No. IEC R2 192166).

We investigate an optimal scheme for the detection of single microwave photons by a Josephson junction through the analysis of its switching times distribution. The proposed analysis is of support for the decision about the existence of the photon field, which is important in the case of rare events. We assume that the cavity and the transmission line are ideal (each photon absorbed to the cavity gives a current pulse as the output of the transmission line) and the photon source is periodic. The employed methodology consists in comparing the switching probabilities of a Josephson junction exposed to a train of current pulses, simulating a weak photon field, with that of the same device in absence of pulses. In both cases, thermal noise can induce thermal activated switchings. The investigation of the unbalance in the number of switching events in the two cases, gives an estimate of the efficiency of the detection. Furthermore, in the assumption of escapes described by Kramers model, it is possible to provide a relationship between the properties of the photons field, the quantum efficiency of the detection process, and the Josephson junctions switching features at finite temperatures.

In this perspective we discuss three emerging fields of condensed matter physics which in recent years have attracted considerable attention. In particular, we consider the recent challenging topics on time-dependent phase transitions, topological phenomena, and unconventional superconductivity, with the aim to foster the community towards new applications and technological advancements. As for the time-dependent phase transitions, in recent years the experiments have shown light-induced phase transitions and new fields of application are emerging, including material design. Regarding topological materials, new challenges have arisen to detect the Majorana origin of quantized conductance in superconducting hybrid structures, as well as the effect of interaction on edge channels. Finally, concerning superconductivity, non-conventional pairing and correlation effects dominate the physics of a vast class of two-dimensional materials and novel devices were recently conceived. This work offers a comprehensive overview on these topics for promoting new ideas in these fertile fields of research.

We propose a threshold detector for Lévy-distributed fluctuations based on a Josephson junction. The Lévy-noise current added to a linearly ramped bias current results in clear changes in the distribution of switching currents out of the zero-voltage state of the junction. We observe that the analysis of the cumulative distribution function of the switching currents supplies information on both the characteristics' shape parameter α of the Lévy statistics. Moreover, we discuss a theoretical model, which allows characteristic features of the Lévy fluctuations to be extracted from a measured distribution of switching currents. In view of these results, this system can effectively find an application as a detector for a Lévy signal embedded in a noisy background., This work is supported by the Grant of the Government of the Russian Federation, Contract No. 074-02-2018- 330 (2). We acknowledge also partial support by Ministry of Education, University and Research of the Italian government. C.G. acknowledge the European Research Council under the European Union’s Seventh Framework Program (FP7/2007-2013)/ERC Grant Agreement No. 615187-COMANCHE. V.P. acknowledges INFN, for partial financial support through the project Virgo.

We study thermal transport induced by soliton dynamics in a long Josephson tunnel junction operating in the flux-flow regime. A thermal bias across the junction is established by imposing the superconducting electrodes to reside at different temperatures, when solitons flow along the junction. Here, we consider the effect of both a bias current and an external magnetic field on the thermal evolution of the device. In the flux-flow regime, a chain of magnetically-excited solitons rapidly moves along the junction driven by the bias current. We explore the range of bias current triggering the flux-flow regime at fixed values of magnetic field, and the stationary temperature distribution in this operation mode. We evidence a steady multi-peaked temperature profile which reflects on the average soliton distribution along the junction. Finally, we analyse also how the friction affecting the soliton dynamics influences the thermal evolution of the system., Comment: 17 pages, 5 figures

Gate-tunable Josephson junctions (JJs) are the backbone of superconducting classical and quantum computation. Typically, these systems exploit low charge concentration materials, and present technological diffculties limiting their scalability. Surprisingly, electric field modulation of supercurrent in metallic wires and JJs has been recently demonstrated. Here, we report the realization of titanium-based monolithic interferometers which allow tuning both JJs independently via voltage bias applied to capacitively-coupled electrodes. Our experiments demonstrate full control of the amplitude of the switching current (IS) and of the superconducting phase across the single JJ in a wide range of temperatures. Astoundingly, by gate-biasing a single junction the maximum achievable total IS suppresses down to values much lower than the critical current of a single JJ. A theoretical model including gate-induced phase fluctuations on a single junction accounts for our experimental findings. This class of quantum interferometers could represent a breakthrough for several applications such as digital electronics, quantum computing, sensitive magnetometry and single-photon detection., Comment: 9 pages, 4 figures

We suggest a single-photon thermal detector based on the abrupt jump of the critical current of a temperature-biased tunnel Josephson junction formed by different superconductors, working in the dissipationless regime. The electrode with the lower critical temperature is used as radiation sensing element, so it is kept thermally floating and is connected to an antenna. The warming up resulting from the absorption of a photon can induce a drastic measurable enhancement of the critical current of the junction. We propose a detection scheme based on a threshold mechanism for single- or multi-photon detection. This Josephson threshold detector has indeed calorimetric capabilities being able to discriminate the energy of the incident photon. So, for the realistic setup that we discuss, our detector can efficiently work as a calorimeter for photons from the mid infrared, through the optical, into the ultraviolet, specifically, for photons with frequencies in the range $[30-9\times10^4]\;\text{THz}$. In the whole range of detectable frequencies a resolving power significantly larger than one results. In order to reveal the signal, we suggest the fast measurement of the Josephson kinetic inductance. Indeed, the photon-induced change in the critical current affects the Josephson kinetic inductance of the junction, which can be non-invasively read through a LC tank circuit, inductively coupled to the junction. Finally, this readout scheme shows remarkable multiplexing capabilities., Comment: 15 pages, 11 figures

We theoretically investigate the critical current of a thermally-biased SIS Josephson junction formed by electrodes made by different BCS superconductors. The response of the device is analyzed as a function of the asymmetry parameter, $r=T_{c_1} /T_{c_2}$. We highlight the appearance of jumps in the critical current of an asymmetric junction, namely, when $r\neq1$. In fact, in such case at temperatures at which the BCS superconducting gaps coincide, the critical current suddenly increases or decreases. In particular, we thoroughly discuss the counterintuitively behaviour of the critical current, which increases by enhancing the temperature of one lead, instead of monotonically reducing. In this case, we found that the largest jump of the critical current is obtained for moderate asymmetries, $r\simeq3$. In view of these results, the discussed behavior can be speculatively proposed as a temperature-based threshold single-photon detector with photon-counting capabilities, which operates non-linearly in the non-dissipative channel., 12 pages, 9 figures

Noise-induced phenomena characterise the nonlinear relaxation of nonequilibrium physical systems towards equilibrium states. Often, this relaxation process proceeds through metastable states and the noise can give rise to resonant phenomena with an enhancement of lifetime of these states or some coherent state of the condensed matter system considered. In this paper three noise induced phenomena, namely the noise enhanced stability, the stochastic resonant activation and the noise-induced coherence of electron spin, are reviewed in the nonlinear relaxation dynamics of three different systems of condensed matter: (i) a long-overlap Josephson junction (JJ) subject to thermal fluctuations and non-Gaussian, Levy distributed, noise sources; (ii) a graphene-based Josephson junction subject to thermal fluctuations; (iii) electrons in a n-type GaAs crystal driven by a fluctuating electric field. In the first system, we focus on the switching events from the superconducting metastable state to the resistive state, by solving the perturbed stochastic sine-Gordon equation. Nonmonotonic behaviours of the mean switching time versus the noise intensity, frequency of the external driving, and length of the junction are obtained. Moreover, the influence of the noise induced solitons on the mean switching time behaviour is shown. In the second system, noise induced phenomena are observed, such as noise enhanced stability (NES) and stochastic resonant activation (SRA). In the third system, the spin polarised transport in GaAs is explored in two different scenarios, i.e. in the presence of Gaussian correlated fluctuations or symmetric dichotomous noise. Numerical results indicate an increase of the electron spin lifetime by rising the strength of the random fluctuating component. Furthermore, our findings for the electron spin depolarization time as a function of the noise correlation time point out (i) a non-monotonic behaviour with a maximum in the case of Gaussian correlated fluctuations, (ii) an increase up to a plateau in the case of dichotomous noise. The noise enhances the coherence of the spin relaxation process.

We investigate the superconducting lifetime of a long overdamped current-biased Josephson junction, in the presence of telegraph noise sources. The analysis is performed by randomly choosing the initial condition for the noise source. However, in order to investigate how the initial value of the dichotomous noise affects the phase dynamics, we extend our analysis using two different fixed initial values for the source of random fluctuations. In our study, the phase dynamics of the Josephson junction is analyzed as a function of the noise signal intensity, for different values of the parameters of the system and external driving currents. We find that the mean lifetime of the superconductive metastable state as a function of the noise intensity is characterized by nonmonotonic behavior, strongly related to the soliton dynamics during the switching towards the resistive state. The role of the correlation time of the noise source is also taken into account. Noise-enhanced stability is observed in the investigated system.

Since its recent foundation, phase-coherent caloritronics has sparkled continuous interest giving rise to numerous concrete applications. This research field deals with the coherent manipulation of heat currents in mesoscopic superconducting devices by mastering the Josephson phase difference. Here, we introduce a new generation of devices for fast caloritronics able to control local heat power and temperature through manipulation of Josephson vortices, i.e., solitons. Although most salient features concerning Josephson vortices in long Josephson junctions were comprehensively hitherto explored, little is known about soliton-sustained coherent thermal transport. We demonstrate that the soliton configuration determines the temperature profile in the junction, so that, in correspondence of each magnetically induced soliton, both the flowing thermal power and the temperature significantly enhance. Finally, we thoroughly discuss a fast solitonic Josephson heat oscillator, whose frequency is in tune with the oscillation frequency of the magnetic drive. Notably, the proposed heat oscillator can effectively find application as a tunable thermal source for nanoscale heat engines and coherent thermal machines., Comment: 14 pages, 8 figures

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., Comment: 9 pages, 5 figures

We explore the coherent thermal transport sustained by solitons through a long Josephson junction, as a thermal gradient across the system is established. We observe that a soliton causes the heat current through the system to increase. Correspondingly, the junction warms up in correspondence of the soliton, with temperature peaks up to, e.g., approximately 56 mK for a realistic Nb-based proposed setup at a bath temperature Tbath = 4.2 K. The thermal effects on the dynamics of the soliton are also discussed. Markedly, this system inherits the topological robustness of the solitons. In view of these results, the proposed device can effectively find an application as a superconducting thermal router in which the thermal transport can be locally mastered through solitonic excitations, which positions can be externally controlled through a magnetic field and a bias current., 9 pages, 6 figures

We propose a superconducting thermal memory device that exploits the thermal hysteresis in a flux-controlled, temperature-biased superconducting quantum-interference device (SQUID). This system reveals a flux-controllable temperature bistability, which can be used to define two well-distinguishable thermal logic states. We discuss a suitable writing-reading procedure for these memory states. The time of the memory writing operation is expected to be on the order of ~0.2 ns, for a Nb-based SQUID in thermal contact with a phonon bath at 4:2 K. We suggest a non-invasive readout scheme for the memory states based on the measurement of the effective resonance frequency of a tank circuit inductively coupled to the SQUID. The proposed device paves the way for a practical implementation of thermal logic and computation. The advantage of this proposal is that it represents also an example of harvesting thermal energy in superconducting circuits., 10 pages, 7 figures

We explore the effect of noise on the ballistic graphene-based small Josephson junctions in the framework of the resistively and capacitively shunted model. We use the non-sinusoidal current-phase relation specific for graphene layers partially covered by superconducting electrodes. The noise induced escapes from the metastable states, when the external bias current is ramped, give the switching current distribution, i.e. the probability distribution of the passages to finite voltage from the superconducting state as a function of the bias current, that is the information more promptly available in the experiments. We consider a noise source that is a mixture of two different types of processes: a Gaussian contribution to simulate an uncorrelated ordinary thermal bath, and non-Gaussian, $\alpha$-stable (or L\'evy) term, generally associated to non-equilibrium transport phenomena. We find that the analysis of the switching current distribution makes it possible to efficiently detect a non-Gaussian noise component in a Gaussian background.

Memristors, memcapacitors, and meminductors, collectively called memelements, represent an innovative generation of circuit elements whose properties depend on the state and history of the system. The hysteretic behavior of one of their constituent variables, under the effect of an external time-dependent perturbation, is their distinctive fingerprint. In turn, this feature endows them with the ability to both store and process information on the same physical location, a property that is expected to benefit many applications ranging from unconventional computing to adaptive electronics to robotics, to name just a few. For all these types of applications, it is important to find appropriate memelements that combine a wide range of memory states (multi-state memory), long memory retention times, and protection against unavoidable noise. Although several physical systems belong to the general class of memelements, few of them combine all of these important physical features in a single component. Her we demonstrate theoretically a superconducting memory structure based on solitonic long Josephson junctions (LJJs). We show that the Josephson critical current of the junction behaves hysteretically as an external magnetic field is properly swept. According to the hysteretic path displayed by the critical current, a LJJ can be used as a multi-state memory, with a controllable number of available states. In addition, since solitons are at the core of its operation, this system provides an intrinsic topological protection against external perturbations. Solitonic Josephson-based memelements may find applications as memories, and in other emerging areas such as memcomputing, i.e., computing directly in/by the memory., Comment: 14 pages, 9 figures

We discuss heat transport in a thermally-biased SQUID in the presence of an external magnetic flux, when a non-negligible inductance of the SQUID ring is taken into account. A properly sweeping driving flux causes the thermal current to modulate and behave hysteretically. The response of this device is analysed as a function of both the hysteresis parameter and degree of asymmetry of the SQUID, highlighting the parameter range over which hysteretic behavior is observable. Markedly, also the temperature of the SQUID shows hysteretic evolution, with sharp transitions characterized by temperature jumps up to, e.g., ~ 38mK for a realistic Al-based setup. In view of these results, the proposed device can effectively find application as a temperature-based superconducting memory element, working even at GHz frequencies by suitably choosing the superconductor on which the device is based., Comment: 9 pages, 10 figures

We numerically investigate the generation of solitons in current-biased long Josephson junctions in relation to the superconducting lifetime and the voltage drop across the device. The dynamics of the junction is modelled with a sine-Gordon equation driven by an oscillating field and subject to an external non-Gaussian noise. A wide range of $\alpha$-stable L\'evy distributions is considered as noise source, with varying stability index $\alpha$ and asymmetry parameter $\beta$. In junctions longer than a critical length, the mean switching time (MST) from superconductive to the resistive state assumes a values independent of the device length. Here, we demonstrate that such a value is directly related to the mean density of solitons which move into or from the washboard potential minimum corresponding to the initial superconductive state. Moreover, we observe: (i) a connection between the total mean soliton density and the mean potential difference across the junction; (ii) an inverse behavior of the mean voltage in comparison with the MST, with varying the junction length; (iii) evidences of non-monotonic behaviors, such as stochastic resonant activation and noise enhanced stability, of MST versus the driving frequency and noise intensity for different values of $\alpha$ and $\beta$; (iv) finally, these non-monotonic behaviors are found to be related to the mean density of solitons formed along the junction., Comment: 24 pages, 8 figures, submitted to J. Stat. Mech.: Theory Exp. arXiv admin note: text overlap with arXiv:1406.4813

We discuss heat transport in thermally-biased long Josephson tunnel junctions in the presence of an in-plane magnetic field. In full analogy with the Josephson critical current, the phase-dependent component of the heat current through the junction displays coherent diffraction. Thermal transport is analyzed as a function of both the length and the damping of the junction, highlighting deviations from the standard Fraunhofer pattern characteristic of short junctions. The heat current diffraction patterns show features strongly related to the formation and penetration of Josephson vortices, i.e. solitons. We show that a dynamical treatment of the system is crucial for the realistic description of the Josephson junction and it leads to peculiar results. In fact, hysteretic behaviors in the diffraction patterns when the field is swept up and down are observed, corresponding to the trapping of vortices in the junction., 9 pages, 7 figures

We investigate the superconducting lifetime of long current-biased Josephson junctions, in the presence of Gaussian and non-Gaussian noise sources. In particular, we analyze the dynamics of a Josephson junction as a function of the noise signal intensity, for different values of the parameters of the system and external driving currents. We find that the mean lifetime of the superconductive state is characterized by nonmonotonic behavior as a function of noise intensity, driving frequency and junction length. We observe that these nonmonotonic behaviours are connected with the dynamics of the junction phase string during the switching towards the resistive state. An important role is played by the formation and propagation of solitons, with two different dynamical regimes characterizing the dynamics of the phase string. Our analysis allows to evidence the effects of different bias current densities, that is a simple spatially homogeneous distribution and a more realistic inhomogeneous distribution with high current values at the junction edges. Stochastic resonant activation, noise enhanced stability and temporary trapping phenomena are observed in the system investigated., Comment: 16 pages, 9 figures, Physical Review B, in press

In this work we study by numerical methods the phase dynamics in ballistic graphene-based short Josephson junctions. The supercurrent through a graphene junction shows a non-sinusoidal phase-dependence, unlike a conventional junction ruled by the well-known d.c. Josephson relation. A superconductor-graphene-superconductor system exhibits superconductive quantum metastable states similar to those present in normal current-biased JJs. We explore the effects of thermal and correlated fluctuations on the escape time from these metastable states, when the system is stimulated by an oscillating bias current. As a first step, the analysis is carried out in the presence of an external Gaussian white noise source, which mimics the random fluctuations of the bias current. Varying the noise intensity, it is possible to analyze the behavior of the escape time from a superconductive metastable state in different temperature regimes. Noise induced phenomena, such as resonant activation and noise induced stability, are observed. The study is extended to the case of a coloured Gaussian noise source, analyzing how the escape time from the metastable state is affected by correlated random fluctuations for different values of the noise correlation time., Comment: 12 pages, 8 figures

We analyze the effects of different non-Gaussian noise sources on the transient dynamics of an overdamped long Josephson junction. We find nonmonotonic behavior of the mean escape time as a function of the noise intensity and frequency of the external driving signal for all the noise sources investigated.

arXiv:2001.03393v2, A classical battery converts chemical energy into a persistent voltage bias that can power electronic circuits. Similarly, a phase battery is a quantum device that provides a persistent phase bias to the wave function of a quantum circuit. It represents a key element for quantum technologies based on phase coherence. Here we demonstrate a phase battery in a hybrid superconducting circuit. It consists of an n-doped InAs nanowire with unpaired-spin surface states, that is proximitized by Al superconducting leads. We find that the ferromagnetic polarization of the unpaired-spin states is efficiently converted into a persistent phase bias φ0 across the wire, leading to the anomalous Josephson effect1,2. We apply an external in-plane magnetic field and, thereby, achieve continuous tuning of φ0. Hence, we can charge and discharge the quantum phase battery. The observed symmetries of the anomalous Josephson effect in the vectorial magnetic field are in agreement with our theoretical model. Our results demonstrate how the combined action of spin–orbit coupling and exchange interaction induces a strong coupling between charge, spin and superconducting phase, able to break the phase rigidity of the system., The work of E.S. was supported by a Marie Curie Individual Fellowship (MSCA-IFEF-ST no. 660532-SuperMag). E.S., N.L. and F.G. acknowledge partial financial support from the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant no. 615187-COMANCHE. E.S., A.I., O.D., N.L., F.S.B. and F.G. were partially supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 800923 (SUPERTED). L.S. and V.Z. acknowledge partial support by the SuperTop QuantERA network and the FET Open And QC. I.V.T., C.S.F. and F.S.B. acknowledge financial support by the Spanish Ministerio de Ciencia, Innovacion y Universidades through projects no. FIS2014-55987-P, no. FIS2016-79464-P and no. FIS2017-82804-P and by the grant ‘Grupos Consolidados UPV/EHU del Gobierno Vasco (grant no. IT1249-19). A.B. thanks the CNR-CONICET cooperation programme ‘Energy conversion in quantum nanoscale hybrid devices’; the SNS-WIS joint laboratory QUANTRA, funded by the Italian Ministry of Foreign Affairs and International Cooperation; and the Royal Society through the international exchanges between the United Kingdom and Italy (grant no. IEC R2192166).