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We investigate the transport properties of open Josephson junctions (JJs) through a minimal effective non-Hermitian (NH) approach derived from the equilibrium Green's function (GF) formalism. Specifically, we consider a JJ with a quantum dot barrier coupled to a normal metal reservoir. The coupling introduces an imaginary self-energy term in the JJ Hamiltonian which can be naturally accounted for in the NH formalism. While most approaches to similar problems work with the full junction Hamiltonian we propose a scheme for deriving an effective NH Hamiltonian for the Andreev levels only, that we compute from the singular part of the barrier GF. To establish the range of applicability of this NH model we benchmark our results for both the dot density of states and the supercurrent against exact GF predictions in different transport regimes. We find that, as a rule of thumb, the Andreev NH description is accurate when the spectral overlap between the Andreev bound states (ABS) and the near-gap continuum states is negligible, i.e. when the ABS energies lie sufficiently far from the superconducting gap relative to their line-width. This method not only highlights the effective physics of the JJ but also offers a scalable framework for studying large-size devices., Comment: 23 pages, 17 figures, review

We investigate the topological properties of the Su-Schrieffer-Heeger (SSH) model under dissipative dynamics using the quantum trajectory approach. Our study explores the preservation or breakdown of topological edge states, particularly focusing on the effects of symmetry-preserving and symmetry-breaking dissipations. We employ the Disconnected Entanglement Entropy (DEE) as a marker for detecting topological phases in the system, which is subjected to Lindblad dynamics. The analysis reveals that, while dissipation in the bulk minimally affects the system's topological features, dissipation at the boundary leads to the destabilization of the edge modes, independently of the symmetry properties of the dissipation., Comment: 22 pages, 12 figures

Recently, digitized-counterdiabatic (CD) corrections to the quantum approximate optimization algorithm (QAOA) have been proposed, yielding faster convergence within the desired accuracy than standard QAOA. In this manuscript, we apply this approach to a fully-connected spin model with random couplings. We show that the performances of the algorithm are related to the spectral properties of the instances analyzed. In particular, the larger the gap between the ground state and the first excited states, the better the convergence to the exact solution.

We investigate the robustness of the many-body localized (MBL) phase to the quantum-avalanche instability by studying the dynamics of a localized spin chain coupled to a $T=\infty$ thermal bath through its leftmost site. By analyzing local magnetizations, we estimate the size of the thermalized sector of the chain and find that it increases logarithmically slowly in time. This logarithmically slow propagation of the thermalization front allows us to lower bound the slowest thermalization time, and find a broad parameter range where it scales fast enough with the system size that MBL is robust against thermalization induced by avalanches. The further finding that the imbalance -- a global quantity measuring localization -- thermalizes over a time scale exponential both in disorder strength and system size is in agreement with these results., Comment: 12 pages, 8 figures. More references on logarithmic light cones in MBL. Discussion on the particle-number nonconserving case added

We consider an infinite-range interacting quantum spin-1/2 model, undergoing periodic kicking and dissipatively coupled with an environment. In the thermodynamic limit, it is described by classical mean-field equations that can show regular and chaotic regimes. At finite size, we describe the system dynamics using stochastic quantum trajectories. We find that the asymptotic nonstabilizerness (alias the magic, a measure of quantum complexity), averaged over trajectories, mirrors to some extent the classical chaotic behavior, while the entanglement entropy has no relation with chaos in the thermodynamic limit., Comment: 16 pages, 15 figures

Typical measures of nonstabilizerness of a system of $N$ qubits require computing $4^N$ expectation values, one for each Pauli string in the Pauli group, over a state of dimension $2^N$. For permutationally invariant systems, this exponential overhead can be reduced to just $O(N^3)$ expectation values on a state with a dimension $O(N)$. We exploit this simplification to study the nonstabilizerness phase transitions of systems with hundreds of qubits., Comment: 6 + 4 pages, 4 + 6 figures

We propose a Floquet period-doubling time-crystal model based on a disordered interacting long-range spin chain where the periodic swapping of nearby spin couples is applied. This protocol can be applied to systems with any local spin magnitude $s$ {and in principle also to systems with nonspin (fermionic or bosonic) local Hilbert space}. We explicitly consider the cases $s = 1/2$ and $s = 1$, using analytical and numerical methods to show that the time-crystal behavior appears in a range of parameters. In particular, we study the persistence of period-doubling oscillations in time, the time-crystal properties of the Floquet spectrum (quasienergy $\pi$-spectral pairing and long-range correlations of the Floquet states), and introduce a quantity (the local imbalance) to assess what initial states give rise to a period-doubling dynamics. We also consider the average level spacing ratio and find that the interval of parameters where the system does not thermalize and persistent period-doubling is possible corresponds to the one where the Floquet spectrum shows time-crystal properties., Comment: 19 pages, 18 figures

We study a superconducting Kitaev ring pierced by a magnetic flux, with and without disorder, in a quantum ring configuration, and in a rf-SQUID one, where a weak link is present. In the rf-SQUID configuration, in the topological phase, the supercurrent shows jumps at specific values of the flux $\Phi^*=\frac{hc}{e}(1/4+n)$, with $n\in\mathbb{N}$. In the thermodynamic limit $\Phi^*$ is constant inside the topological phase, independently of disorder, and we analytically predict this fact using a perturbative approach in the weak-link coupling. The weak link breaks the topological ground-state degeneracy, and opens a spectral gap for $\Phi\neq \Phi^*$, that vanishes at $\Phi^*$ with a cusp providing the current jump. Looking at the quasiparticle excitations, we see that they are Anderson localized, so they cannot carry a resistive contribution to the current, and the localization length shows a peculiar behavior at a flat-band point for the quasiparticles. In the absence of disorder, we analytically and numerically find that the chemical-potential derivative of the supercurrent logarithmically diverges at the topological-to-trivial transition, in agreement with the transition being of the second order., Comment: 16 pages, 17 figures. Substantial rewriting for more clarity and conciseness. More precise analysis of the current-jump closure at the transition in presence of disorder, and of the localization length of quasiparticle. Version published in PRB

We investigate the possibility to employ magnetic Josephson junctions as magnetic-noise detectors. To illustrate our idea, we consider a system consisting of a quantum dot coupled to superconducting leads in the presence of an external magnetic field. Under appropriate assumptions, we relate the noise in the Josephson current to magnetization noise. At the magnetic field driven $0-\pi$ transition the junction sensitivity as magnetic noise detector is strongly enhanced and it diverges in the zero temperature limit. Moreover, we demonstrate that, if also dot energy is affected by fluctuations, only the magnetic noise channel contributes to Josephson current noise response when the quantum dot is tuned in resonance with superconducting leads., Comment: Review. 14 pages. 3 appendices. 14 figures

Recently, Digitized-Counterdiabatic (CD) Quantum Approximate Optimization Algorithm (QAOA) has been proposed to make QAOA converge to the solution of an optimization problem in fewer steps, inspired by Trotterized counterdiabatic driving in continuous-time quantum annealing. In this paper, we critically revisit this approach by focusing on the paradigmatic weighted and unweighted one-dimensional MaxCut problem. We study two variants of QAOA with first and second-order CD corrections. Our results show that, indeed, higher order CD corrections allow for a quicker convergence to the exact solution of the problem at hand by increasing the complexity of the variational cost function. Remarkably, however, the total number of free parameters needed to achieve this result is independent of the particular QAOA variant analyzed.

We study the properties of a monitored ensemble of atoms driven by a laser field and in the presence of collective decay. The properties of the quantum trajectories describing the atomic cloud drastically depend on the monitoring protocol and are distinct from those of the average density matrix. By varying the strength of the external drive, a measurement-induced phase transition occurs separating two phases with entanglement entropy scaling sub-extensively with the system size. Incidentally, the critical point coincides with the superradiance transition of the trajectory-averaged dynamics. Our setup is implementable in current light-matter interaction devices, and most notably, the monitored dynamics is free from the post-selection measurement problem, even in the case of imperfect monitoring., Comment: 7 + 4 pages, 3 + 4 figures

Finding a local Hamiltonian $\hat{\mathcal{H}}$ having a given many-body wavefunction $|\psi\rangle$ as its ground state, i.e. a parent Hamiltonian, is a challenge of fundamental importance in quantum technologies. Here we introduce a numerical method, inspired by quantum annealing, that efficiently performs this task through an artificial inverse dynamics: a slow deformation of the states $|\psi(\lambda(t))\rangle$, starting from a simple state $|\psi_0\rangle$ with a known $\hat{\mathcal{H}}_0$, generates an adiabatic evolution of the corresponding Hamiltonian. We name this approach inverse quantum annealing. The method, implemented through a projection onto a set of local operators, only requires the knowledge of local expectation values, and, for long annealing times, leads to an approximate parent Hamiltonian whose degree of locality depends on the correlations built up by the states $|\psi(\lambda)\rangle$. We illustrate the method on two paradigmatic models: the Kitaev fermionic chain and a quantum Ising chain in longitudinal and transverse fields., Comment: In this second version, inverse annealing is also applied to a quantum Ising chain in longitudinal and transverse fields

We present Counterdiabatic Reverse Annealing, a novel quantum annealing protocol that extends the range of application of reverse annealing to the previously inaccessible short-time domain. This is achieved by exploiting approximate counterdiabatic driving expanded in low-order nested commutators. In this work, we offer a comparative study of the performance of this new technique to that of unassisted reverse annealing in terms of metrics such as the ground-state fidelity and the time to solution. We provide a quantitative measure of the energetic cost of counterdiabatic reverse annealing and show that significant improvements are possible even using local counterdiabatic potentials, paving the way toward the experimental implementation in near-term quantum devices., Comment: 11 pages, 14 figures

A crucial step in the race towards quantum advantage is optimizing quantum annealing using ad-hoc annealing schedules. Motivated by recent progress in the field, we propose to employ long-short term memory (LSTM) neural networks to automate the search for optimal annealing schedules for random Ising models on regular graphs. By training our network using locally-adiabatic annealing paths, we are able to predict optimal annealing schedules for unseen instances and even larger graphs than those used for training., Comment: 10 pages, 8 figures

Dissipative time crystals can appear in spin systems, when the $Z_2$ symmetry of the Hamiltonian is broken by the environment, and the square of total spin operator $S^2$ is conserved. In this manuscript, we relax the latter condition and show that time-translation-symmetry breaking collective oscillations persist, in the thermodynamic limit, even in the absence of spin symmetry. We engineer an \textit{ad hoc} Lindbladian using power-law decaying spin operators and show that time-translation symmetry breaking appears when the decay exponent obeys $0<\eta\leq 1$. This model shows a surprisingly rich phase diagram, including the time-crystal phase as well as first-order, second-order, and continuous transitions of the fixed points. We study the phase diagram and the magnetization dynamics in the mean-field approximation. We prove that this approximation is quantitatively accurate, when $0<\eta\leq1$ and the thermodynamic limit is taken, because the system does not develop sizable quantum fluctuations, if the Gaussian approximation is considered., Comment: 13 pages, 11 figures

We propose to exploit currently available tunnel ferromagnetic Josephson junctions to realize a hybrid superconducting qubit. We show that the characteristic hysteretic behavior of the ferromagnetic barrier provides an alternative and intrinsically digital tuning of the qubit frequency by means of magnetic field pulses. To illustrate functionalities and limitation of the device, we discuss the coupling to a read-out resonator and the effect of magnetic fluctuations. The possibility to use the qubit as a noise detector and its relevance to investigate the subtle interplay of magnetism and superconductivity is envisaged.

Learning the unknown Hamiltonian governing the dynamics of a quantum many-body system is a challenging task. In this manuscript, we propose a possible strategy based on repeated measurements on a single time-dependent state. We prove that the accuracy of the learning process is maximized for states that are delocalized in the Hamiltonian eigenbasis. This implies that delocalization is a quantum resource for Hamiltonian learning, that can be exploited to select optimal initial states for learning algorithms. We investigate the error scaling of our reconstruction with respect to the number of measurements, and we provide examples of our learning algorithm on simulated quantum systems., Comment: 15 pages, 4 figures

We study adiabatic reverse annealing (ARA) in an open system. In the closed system (unitary) setting, this annealing protocol allows avoidance of first-order quantum phase transitions of selected models, resulting in an exponential speedup compared with standard quantum annealing, provided that the initial state of the algorithm is close in Hamming distance to the target one. Here, we show that decoherence can significantly modify this conclusion: by resorting to the adiabatic master equation approach, we simulate the dynamics of the ferromagnetic $p$-spin model with $p=3$ under independent and collective dephasing. For both models of decoherence, we show that the performance of open system ARA is far less sensitive to the choice of the initial state than its unitary counterpart, and, most significantly, that open system ARA by and large loses its time to solution advantage compared to standard quantum annealing. These results suggest that as a stand-alone strategy, ARA is unlikely to experimentally outperform standard "forward" quantum annealing, and that error mitigation strategies will likely be required in order to realize the benefits of ARA in realistic, noisy settings., Comment: 12 pages, 11 figures

Suppressing unwanted transitions out of the instantaneous ground state is a major challenge in unitary adiabatic quantum computation. A recent approach consists in building counterdiabatic potentials approximated using variational strategies. In this contribution, we extend this variational approach to Lindbladian dynamics, having as a goal the suppression of diabatic transitions between pairs of Jordan blocks in quantum annealing. We show that, surprisingly, unitary counterdiabatic ans\"atze are successful for dissipative dynamics as well, allowing for easier experimental implementations compared to Lindbladian ans\"atze involving dissipation. Our approach not only guarantees improvements of open-system adiabaticity but also enhances the success probability of quantum annealing., Comment: 10 pages, 5 figures

Josephson devices with ferromagnetic barriers have been widely studied. Much less is known when the ferromagnetic layer is insulating. In this manuscript we investigate the transport properties of superconductor-ferromagnetic insulator-superconductor (SFIS) junctions with particular attention to the temperature behavior of the critical current, that may be used as a fingerprint of the junction. We investigate the specific role of impurities as well as of possible spin mixing mechanisms, due to the spin orbit coupling. Transition between the 0 and the $\pi$ phases can be properly tuned, thus achieving stable $\pi$ junctions over the whole temperature range, that may be possibly employed in superconducting quantum circuits., Comment: Regular article, 13 pages, 9 figures; added references for section I.; fixed the normalization on the y-axis in Figs.2,3,7; fixed small convergence errors occurred in the extrapolation of the Ic(T) curves in Figs.3 and 5; results unchanged

The study of optimal control of quantum annealing by modulating the pace of evolution and by introducing a counterdiabatic potential has gained significant attention in recent times. In this work, we present a numerical approach based on genetic algorithms to improve the performance of quantum annealing, which evades the Landau-Zener transitions to navigate to the ground state of the final Hamiltonian with high probability. We optimize the annealing schedules starting from polynomial ansatz by treating their coefficients as chromosomes of the genetic algorithm. We also explore shortcuts to adiabaticity by computing a practically feasible $k$-local optimal driving operator, showing that even for $k=1$ we achieve substantial improvement of the fidelity over the standard annealing solution. With these genetically optimized annealing schedules and/or optimal driving operators, we are able to perform quantum annealing in relatively short time-scales and with larger fidelity compared to traditional approaches., Comment: 13 pages, 11 figures

The increased capabilities of coupling more and more materials through functional interfaces are paving the way to a series of exciting experiments and extremely advanced devices. Here we focus on the capability of magnetically inhomogeneous superconductor/ferromagnet (S/F) interfaces to generate spin-polarized triplet pairs. We build on previous achievements on spin-filter ferromagnetic Josephson junctions (JJs) and find unique correspondence between neat experimental benchmarks in the temperature behavior of the critical current and theoretical modeling based on microscopic calculations, which allow us to determine a posteriori spin-singlet and triplet correlation functions. This kind of combined analysis provides accurate proof of the coexistence and tunability of singlet and triplet transport. This turns to be a unique opportunity to model disorder and spin-mixing effects in a JJ to enlarge the space of parameters, which regulate the phenomenology of the Josephson effect and could be applied to a variety of novel types of JJs.

Given a generic time-dependent many-body quantum state, we determine the associated parent Hamiltonian. This procedure may require, in general, interactions of any sort. Enforcing the requirement of a fixed set of engineerable Hamiltonians, we find the optimal Hamiltonian once a set of realistic elementary interactions is defined. We provide three examples of this approach. We first apply the optimization protocol to the ground states of the one-dimensional Ising model and a ferromagnetic $p$-spin model but with time-dependent coefficients. We also consider a time-dependent state that interpolates between a product state and the ground state of a $p$-spin model. We determine the time-dependent optimal parent Hamiltonian for these states and analyze the capability of this Hamiltonian of generating the state evolution. Finally, we discuss the connections of our approach to shortcuts to adiabaticity., Comment: 16 pages, 11 figures

The interlayer van der Waals interaction in twisted bilayer graphene (tBLG) induces both in-plane and out-of-plane atomic displacements showing complex patterns that depend on the twist angle. In particular, for small twist angles, within each graphene layer, the relaxations give rise to a vortex-like displacement pattern which is known to affect the dispersion of the flat bands. Here, we focus on yet another structural property, the chirality of the twisted bilayer. We perform first-principles calculations based on density functional theory to investigate the properties induced by twist chirality in both real and momentum space. In real space, we study the interplay between twist chirality and atomic relaxation patterns. In momentum space, we investigate the spin textures around the $K$ points of the Brillouin zone, showing that alternating vortex-like textures are correlated with the chirality of tBLG. Interestingly, the helicity of each vortex is inverted by changing the chirality while the different twist angles also modify the spin textures. We discuss the origin of the spin textures by calculating the layer weights and using plot regression models., Comment: 12 pages and 7 figures in main text, 11 pages and 12 figures in supplemental material; revised according to referees' suggestions; Accepted in Phys. Rev. B

The structural and electronic properties of twisted bilayer graphene are investigated from first principles and tight binding approach as a function of the twist angle (ranging from the first "magic" angle $\theta=1.08^\circ$ to $\theta=3.89^\circ$, with the former corresponding to the largest unit cell, comprising 11164 carbon atoms). By properly taking into account the long-range van der Waals interaction, we provide the patterns for the atomic displacements (with respect to the ideal twisted bilayer). The out-of-plane relaxation shows an oscillating ("buckling") behavior, very evident for the smallest angles, with the atoms around the AA stacking regions interested by the largest displacements. The out-of-plane displacements are accompanied by a significant in-plane relaxation, showing a vortex-like pattern, where the vorticity (intended as curl of the displacement field) is reverted when moving from the top to the bottom plane and viceversa. Overall, the atomic relaxation results in the shrinking of the AA stacking regions in favor of the more energetically favorable AB/BA stacking domains. The measured flat bands emerging at the first magic angle can be accurately described only if the atomic relaxations are taken into account. Quite importantly, the experimental gaps separating the flat band manifold from the higher and lower energy bands cannot be reproduced if only in-plane or only out-of-plane relaxations are considered. The stability of the relaxed bilayer at the first magic angle is estimated to be of the order of 0.5-0.9 meV per atom (or 7-10 K). Our calculations shed light on the importance of an accurate description of the vdW interaction and of the resulting atomic relaxation to envisage the electronic structure of this really peculiar kind of vdW bilayers., Comment: 10 pages, 5 figures

Finding the exact counterdiabatic potential is, in principle, particularly demanding. Following recent progresses about variational strategies to approximate the counterdiabatic operator, in this paper we apply this technique to the quantum annealing of the $p$-spin model. In particular, for $ p = 3 $ we find a new form of the counterdiabatic potential originating from a cyclic ansatz, that allows us to have optimal fidelity even for extremely short dynamics, independently of the size of the system. We compare our results with a nested commutator ansatz, recently proposed in P. W. Claeys, M. Pandey, D. Sels, and A. Polkovnikov, Phys. Rev. Lett. 123, 090602 (2019), for $ p = 1 $ and $ p = 3 $. We also analyze generalized $ p $-spin models to get a further insight into our ansatz., Comment: 11 pages, 8 figures

In reverse quantum annealing, the initial state is an eigenstate of the final problem Hamiltonian and the transverse field is cycled rather than strictly decreased as in standard (forward) quantum annealing. We present a numerical study of the reverse quantum annealing protocol applied to the $p$-spin model ($p=3$), including pausing, in an open system setting accounting for dephasing in the energy eigenbasis, which results in thermal relaxation. We consider both independent and collective dephasing and demonstrate that in both cases the open system dynamics substantially enhances the performance of reverse annealing. Namely, including dephasing overcomes the failure of purely closed system reverse annealing to converge to the ground state of the $p$-spin model. We demonstrate that pausing further improves the success probability. The collective dephasing model leads to somewhat better performance than independent dephasing. The protocol we consider corresponds closely to the one implemented in the current generation of commercial quantum annealers, and our results help to explain why recent experiments demonstrated enhanced success probabilities under reverse annealing and pausing., Comment: 11 pages, 7 figures

Embedding $p$-body interacting models onto the $2$-body networks implemented on commercial quantum annealers is a relevant issue. For highly interacting models, requiring a number of ancilla qubits, that can be sizable and make unfeasible (if not impossible) to simulate such systems. In this manuscript, we propose an alternative to minor embedding, developing a new approximate procedure based on genetic algorithms, allowing to decouple the $p$-body in terms of $2$-body interactions. A set of preliminary numerical experiments demonstrates the feasibility of our approach for the ferromagnetic $p$-spin model, and pave the way towards the application of evolutionary strategies to more complex quantum models., Comment: 15 pages, 6 figures

Graphene grown epitaxially on SiC, close to the charge neutrality point (CNP), in an orthogonal magnetic field shows an ambipolar behavior of the transverse resistance accompanied by a puzzling longitudinal magnetoresistance. When injecting a transverse current at one end of the Hall bar, a sizeable non local transverse magnetoresistance is measured at low temperature. While Zeeman spin effect seems not to be able to justify these phenomena, some dissipation involving edge states at the boundaries could explain the order of magnitude of the non local transverse magnetoresistance, but not the asymmetry when the orientation of the orthogonal magnetic field is reversed. As a possible contribution to the explanation of the measured non local magnetoresistance which is odd in the magnetic field, we derive a hydrodynamic approach to transport in this system, which involves particle and hole Dirac carriers, in the form of charge and energy currents. We find that thermal diffusion can take place on a large distance scale, thanks to long recombination times, provided a non insulating bulk of the Hall bar is assumed, as recent models seem to suggest in order to explain the appearance of the longitudinal resistance. In presence of the local source, some leakage of carriers from the edges generates an imbalance of carriers of opposite sign, which are separated in space by the magnetic field and diffuse along the Hall bar generating a non local transverse voltage., Comment: 25 pages, 12 figures

Adiabatic quantum computation (AQC) is a promising counterpart of universal quantum computation, based on the key concept of quantum annealing (QA). QA is claimed to be at the basis of commercial quantum computers and benefits from the fact that the detrimental role of decoherence and dephasing seems to have poor impact on the annealing towards the ground state. While many papers show interesting optimization results with a sizable number of qubits, a clear evidence of a full quantum coherent behavior during the whole annealing procedure is still lacking. In this paper we show that quantum non-demolition (weak) measurements of Leggett Garg inequalities can be used to efficiently assess the quantumness of the QA procedure. Numerical simulations based on a weak coupling Lindblad approach are compared with classical Langevin simulations to support our statements., Comment: 7 pages, 3 figures. Includes supplementary material file

The probability of success of quantum annealing can be improved significantly by pausing the annealer during its dynamics, exploiting thermal relaxation in a controlled fashion. In this paper, we investigate the effect of pausing the quantum annealing of the fully-connected ferromagnetic $ p $-spin model. We numerically show that (i) the optimal pausing point is 60% longer than the avoided crossing time for the analyzed instance, and (ii) at the optimal pausing point, we register a 45% improvement in the probability of success with respect to a quantum annealing with no pauses of the same duration. These results are in line with those observed experimentally for less connected models with the available quantum annealers. The observed improvement for the $ p $-spin model can be up to two orders of magnitude with respect to an isolated quantum dynamics of the same duration., Comment: 12 pages, 10 figures

We combine state-of-the-art large-scale first principles calculations with a low-energy continuum model to describe the nearly flat bands of twisted bilayer graphene at the first magic angle $\theta =1.08^\circ$. We show that the energy width of the flat band manifold, as well as the energy gap separating it from the valence and conduction bands, can be obtained only if the out-of-plane relaxations are fully taken into account. The results agree both qualitatively and quantitatively with recent experimental outcomes., Comment: Published in Phys. Rev. B 99, 195419 (2019)

The study of superconductor-ferromagnet interfaces has generated great interest in the last decades, leading to the observation of spin-aligned triplet supercurrents and 0-pi transitions in Josephson junctions where two superconductors are separated by an itinerant ferromagnet. Recently, spin-filter Josephson junctions with ferromagnetic barriers have shown unique transport properties, when compared to standard metallic ferromagnetic junctions, due to the intrinsically nondissipative nature of the tunneling process. Here we present the first extensive characterization of spin polarized Josephson junctions down to 0.3 K, and the first evidence of an incomplete 0-pi transition in highly spin polarized tunnel ferromagnetic junctions. Experimental data are consistent with a progressive enhancement of the magnetic activity with the increase of the barrier thickness, as neatly captured by the simplest theoretical approach including a nonuniform exchange field. For very long junctions, unconventional magnetic activity of the barrier points to the presence of spin-triplet correlations.

We discuss the quantum annealing of the fully-connected ferromagnetic $ p $-spin model in a dissipative environment at low temperature. This model, in the large $ p $ limit, encodes in its ground state the solution to the Grover's problem of searching in unsorted databases. In the framework of the quantum circuit model, a quantum algorithm is known for this task, providing a quadratic speed-up with respect to its best classical counterpart. This improvement is not recovered in adiabatic quantum computation for an isolated quantum processor. We analyze the same problem in the presence of a low-temperature reservoir, using a Markovian quantum master equation in Lindblad form, and we show that a thermal enhancement is achieved in the presence of a zero temperature environment moderately coupled to the quantum annealer., Comment: 4 pages, 1 figure, proceeding of IQIS 2018

We study the anomalous Josephson effect, as well as the dependence on the direction of the critical Josephson current, in an S/N/S junction, where the normal part is realized by alternating spin-orbit coupled and ferromagnetic layers. We show that to observe these effects it is sufficient to break spin rotation and time reversal symmetry in spatially separated regions of the junction. Moreover, we discuss how to further improve these effects by engineering multilayers structures with more that one couple of alternating layers., Comment: 10 pages, 8 figures

We propose a numerical technique based on a combination of short-iterative Lanczos and exact diagonalization methods, suitable for simulating the time evolution of the reduced density matrix of a single qubit interacting with an environment. By choosing a mode discretization method and a flexible bath states truncation scheme, we are able to include in the physical description multiple-excitation processes, beyond weak coupling and Markov approximations. We apply our technique to the simulation of three different model Hamiltonians, which are relevant in the field of adiabatic quantum computation. We compare our results with those obtained on the basis of the widely used Lindblad master equation, as well as with well-known exact and approximated approaches. We show that our method is able to recover the thermodynamic behavior of the qubit-bath system, beyond the Born-Markov approximation. Finally, we show that even in the case of the adiabatic quantum annealing of a single qubit the bath can be beneficial in reaching the reduced system ground state., Comment: 14 pages, 20 figures

In this work, we investigate the thermoelectric properties of a hybrid junction realised coupling surface states of a three-dimensional topological insulator with a conventional $s$-wave superconductor. We focus on the ballistic devices and study the quasiparticle flow, carrying both electric and thermal currents, adopting a scattering matrix approach based on conventional Blonder-Tinkham-Klapwijk formalism. We calculate the cooling efficiency of the junction as a function of the microscopic parameters of the normal region (i.e. the chemical potential etc.). The cooling power increases when moving from a regime of Andreev specular-reflection to a regime where Andreev retro-reflection dominates. Differently from the case of a conventional N/S interface, we can achieve efficient cooling of the normal region, without including any explicit impurity scattering at the interface, to increase normal reflection., Comment: 9 pages, 5 figures

We investigate the quantum annealing of the ferromagnetic $ p $-spin model in a dissipative environment ($ p = 5 $ and $ p = 7 $). This model, in the large $ p $ limit, codifies the Grover's algorithm for searching in an unsorted database. The dissipative environment is described by a phonon bath in thermal equilibrium at finite temperature. The dynamics is studied in the framework of a Lindblad master equation for the reduced density matrix describing only the spins. Exploiting the symmetries of our model Hamiltonian, we can describe many spins and extrapolate expected trends for large $ N $, and $ p $. While at weak system bath coupling the dissipative environment has detrimental effects on the annealing results, we show that in the intermediate coupling regime, the phonon bath seems to speed up the annealing at low temperatures. This improvement in the performance is likely not due to thermal fluctuation but rather arises from a correlated spin-bath state and persists even at zero temperature. This result may pave the way to a new scenario in which, by appropriately engineering the system-bath coupling, one may optimize quantum annealing performances below either the purely quantum or classical limit., Comment: 9 Pag, 5 Fig, Submitted

We study possible applications of high critical temperature nodal superconductors for the search for Majorana bound states in the DIII class. We propose a microscopic analysis of the proximity effect induced by d-wave superconductors on a semiconductor wire with strong spin-orbit coupling. We characterize the induced superconductivity on the wire employing a numerical self-consistent tight-binding Bogoliubov-de Gennes approach, and analytical considerations on the Green's function. The order parameter induced on the wire, the pair correlation function, and the renormalization of the Fermi points are analyzed in detail, as well as the topological phase diagram in the case of weak coupling. We highlight optimal Hamiltonian parameters to access the nontrivial topological phase which could display time-reversal invariant Majorana doublets at the boundaries of the wire.

Superconducting hybrid junctions are revealing a variety of novel effects. Some of them are due to the special layout of these devices, which often use a coplanar configuration with relatively large barrier channels and the possibility of hosting Pearl vortices. A Josephson junction with a quasi ideal two-dimensional barrier has been realized by growing graphene on SiC with Al electrodes. Chemical Vapor Deposition offers centimeter size monolayer areas where it is possible to realize a comparative analysis of different devices with nominally the same barrier. In samples with a graphene gap below 400 nm, we have found evidence of Josephson coherence in presence of an incipient Berezinskii-Kosterlitz-Thouless transition. When the magnetic field is cycled, a remarkable hysteretic collapse and revival of the Josephson supercurrent occurs. Similar hysteresis are found in granular systems and are usually justified within the Bean Critical State model (CSM). We show that the CSM, with appropriate account for the low dimensional geometry, can partly explain the odd features measured in these junctions., Comment: 13 pages, 9 figures

Graphene on silicon carbide (SiC) has proved to be highly successful in Hall conductance quantization for its homogeneity at the centimetre scale. Robust Josephson coupling has been measured in co-planar diffusive Al/monololayer graphene/Al junctions. Graphene on SiC substrates is a concrete candidate to provide scalability of hybrid Josephson graphene/superconductor devices, giving also promise of ballistic propagation.

We study current-current correlation in an electronic analog of a beam splitter realized with edge channels of a fractional quantum Hall liquid at Laughlin filling fractions. In analogy with the known result for chiral electrons, if the currents are measured at points located after the beam splitter, we find that the zero frequency equilibrium correlation vanishes due to the chiral propagation along the edge channels. Furthermore, we show that the current-current correlation, normalized to the tunneling current, exhibits clear signatures of the Laughlin quasi-particles' fractional statistics., Comment: 9 pages, 3 figures, extended bibliography

We have identified anomalous behavior of the escape rate out of the zero-voltage state in Josephson junctions with a high critical current density Jc. For this study we have employed YBa2Cu3O7-x grain boundary junctions, which span a wide range of Jc and have appropriate electrodynamical parameters. Such high Jc junctions, when hysteretic, do not switch from the superconducting to the normal state following the expected stochastic Josephson distribution, despite having standard Josephson properties such as a Fraunhofer magnetic field pattern. The switching current distributions (SCDs) are consistent with nonequilibrium dynamics taking place on a local rather than a global scale. This means that macroscopic quantum phenomena seem to be practically unattainable for high Jc junctions. We argue that SCDs are an accurate means to measure nonequilibrium effects. This transition from global to local dynamics is of relevance for all kinds of weak links, including the emergent family of nanohybrid Josephson junctions. Therefore caution should be applied in the use of such junctions in, for instance, the search for Majorana fermions., Comment: 8 pages, 4 figures

In this review article we describe spin-dependent transport in materials with spin-orbit interaction of Rashba type. We mainly focus on semiconductor heterostructures, topological insulators, graphene and hybrid structures involving superconductors as well. We start from basic properties of Rashba Hamiltonian in a two dimensional electron gas and then describe transport properties in two- and quasi-one-dimensional systems. The problem of spin current generation and interference effects in mesoscopic devices is described in detail. We address also the role of Rashba interaction on localisation effects in lattices with nontrivial topology, as well as on the Ahronov-Casher effect in ring structures. A brief section, in the end, describes also some related topics including the spin-Hall effect, the transition from weak localisation to weak anti localisation and the physics of Majorana Fermions in hybrid heterostructures involving Rashba materials in the presence of superconductivity., Comment: 28 pages and 21 figures, Revised in the text and bibliography compared to first version

A superconductor-semiconducting nanowire-superconductor heterostructure in the presence of spin orbit coupling and magnetic field can support a supercurrent even in the absence of phase difference between the superconducting electrodes. We investigate this phenomenon, the anomalous Josephson effect, employing a model capable of describing many bands in the normal region. We discuss geometrical and symmetry conditions required to have finite anomalous supercurrent and in particular we show that this phenomenon is enhanced when the Fermi level is located close to a band opening in the normal region., Comment: 7+epsilon pages, 6 figures, Revised version

In superconductor-topological insulator-superconductor hybrid junctions, the barrier edge states are expected to be protected against backscattering, to generate unconventional proximity effects, and, possibly, to signal the presence of Majorana fermions. The standards of proximity modes for these types of structures have to be settled for a neat identification of possible new entities. Through a systematic and complete set of measurements of the Josephson properties we find evidence of ballistic transport in coplanar Al-Bi2Se3-Al junctions that we attribute to a coherent transport through the topological edge state. The shunting effect of the bulk only influences the normal transport. This behavior, which can be considered to some extent universal, is fairly independent of the specific features of superconducting electrodes. A comparative study of Shubnikov - de Haas oscillations and Scanning Tunneling Spectroscopy gave an experimental signature compatible with a two dimensional electron transport channel with a Dirac dispersion relation. A reduction of the size of the Bi2Se3 flakes to the nanoscale is an unavoidable step to drive Josephson junctions in the proper regime to detect possible distinctive features of Majorana fermions., Comment: 11 pages, 14 figures

Majorana Bound States are predicted to appear as boundary states of the Kitaev model. Here we show that a pi-Josephson Junction, inserted in a topologically non trivial model ring, sustains a Majorana Bound State, which is robust with respect to local and non local perturbations. The realistic structure could be based on a High Tc Superconductor tricrystal structure, similar to the one used to spot the d-wave order parameter. The presence of the Majorana Bound State changes the ground state of the topologically non trivial ring in a measurable way, with respect to that of a conventional one., Comment: 6 pages, 5 figures, to appear in Phys. Rev. B

We propose an alternative platform to observe Majorana bound states in solid state systems. High critical temperature cuprate superconductors can induce superconductivity, by proximity effect, in quasi one dimensional nanowires with strong spin orbit coupling. They favor a wider and more robust range of conditions to stabilize Majorana fermions due to the large gap values, and offer novel functionalities in the design of the experiments determined by different dispersion for Andreev bound states as a function of the phase difference., Comment: 4 Pages, 3 figures, submission date 30-Apr-2012