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DOE OSTI2024

Collective neural network behavior in a dynamically driven disordered system of superconducting loops

Collective properties of complex systems composed of many interacting components such as neurons in our brain can be modeled by artificial networks based on disordered systems. We show that a disordered neural network of superconducting loops with Josephson junctions can exhibit computational properties like categorization and associative memory in the time evolution of its state in response to information from external excitations. Superconducting loops can trap multiples of fluxons in many discrete memory configurations defined by the local free energy minima in the configuration space of all possible states. A memory state can be updated by exciting the Josephson junctions to fire or allow the movement of fluxons through the network as the current through them surpasses their critical current thresholds. Simulations performed with a lumped element circuit model of a 4-loop network show that information written through excitations is translated into stable states of trapped flux and their time evolution. Experimental implementation on a high-Tc superconductor YBCO-based 4-loop network shows dynamically stable flux flow in each pathway characterized by the correlations between junction firing statistics. Neural network behavior is observed as energy barriers separating state categories in simulations in response to multiple excitations, and experimentally as junction responses characterizing different flux flow patterns in the network. The state categories that produce these patterns have different temporal stabilities relative to each other and the excitations. This provides strong evidence for time-dependent (short-to-long-term) memories, that are dependent on the geometrical and junction parameters of the loops, as described with a network model.

Josephson junctions↗

DOE OSTI2021

Multiterminal Inverse AC Josephson Effect

When a Josephson junction is exposed to microwave radiation, it undergoes the inverse AC Josephson effect–the phase of the junction locks to the drive frequency. As a result, the I–V curves of the junction acquire “Shapiro steps” of quantized voltage. If the junction has three or more superconducting contacts, coupling between different pairs of terminals must be taken into account and the state of the junction evolves in a phase space of higher dimensionality. Here, we study the multiterminal inverse AC Josephson effect in a graphene sample with three superconducting terminals. We observe robust fractional Shapiro steps and correlated switching events, which can only be explained by considering the device as a completely connected Josephson network. We successfully simulate the observed behaviors using a modified two-dimensional RCSJ model. Our results suggest that multiterminal Josephson junctions are a playground to study highly connected nonlinear networks with novel topologies.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

Evaluation of fluxon synapse device based on superconducting loops for energy efficient neuromorphic computing

With Moore’s law nearing its end due to the physical scaling limitations of CMOS technology, alternative computing approaches have gained considerable attention as ways to improve computing performance. Here, we evaluate performance prospects of a new approach based on disordered superconducting loops with Josephson-junctions for energy efficient neuromorphic computing. Synaptic weights can be stored as internal trapped fluxon states of three superconducting loops connected with multiple Josephson-junctions (JJ) and modulated by input signals applied in the form of discrete fluxons (quantized flux) in a controlled manner. The stable trapped fluxon state directs the incoming flux through different pathways with the flow statistics representing different synaptic weights. We explore implementation of matrix–vector-multiplication (MVM) operations using arrays of these fluxon synapse devices. We investigate the energy efficiency of online-learning of MNIST dataset. Our results suggest that the fluxon synapse array can provide ~100× reduction in energy consumption compared to other state-of-the-art synaptic devices. This work presents a proof-of-concept that will pave the way for development of high-speed and highly energy efficient neuromorphic computing systems based on superconducting materials.

42 ENGINEERING↗

DOE OSTI2023

Flux-based three-dimensional electrodynamic modeling approach to superconducting circuits and materials

Modeling the behavior of superconducting electronic circuits containing Josephson junctions is crucial for the design of superconducting information processors and devices. In this paper, we introduce DEC-QED, a computational approach for modeling the electrodynamics of superconducting electronic circuits containing Josephson junctions in arbitrary three-dimensional electromagnetic environments. DEC-QED captures the nonlinear response and induced currents in BCS superconductors and accurately captures phenomena such as the Meissner effect, flux quantization, and Josephson effects. Using a spatial coarse-graining formulation based on discrete exterior calculus (DEC), DEC-QED can accurately simulate transient and long-time dynamics in superconductors. Finally, the expression of the entire electrodynamic problem in terms of the gauge-invariant flux field and charges makes the resulting classical field theory suitable for second quantization.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Suppression of quasiparticle poisoning in transmon qubits by gap engineering

The performance of various superconducting devices operating at ultra-low temperatures is impaired by the presence of non-equilibrium quasiparticles. Inelastic quasiparticle (QP) tunneling across Josephson junctions in superconducting qubits results in decoherence and spurious excitations and, notably, can trigger correlated errors that severely impede quantum error correction. In this work, we use "gap engineering" to suppress the tunneling of low-energy quasiparticles in Al-based transmon qubits, a leading building block for superconducting quantum processors. By implementing potential barriers for QP, we strongly suppress QP tunneling across the junction and preserve charge parity for over $10^3$ seconds. The suppression of QP tunneling also results in a reduction in the qubit energy relaxation rates. The demonstrated approach to gap engineering can be easily implemented in all Al-based circuits with Josephson junctions.

Kamenov, Plamen↗

DOE OSTI2022

Superconducting disordered neural networks for neuromorphic processing with fluxons

In superconductors, magnetic fields are quantized into discrete fluxons (flux quanta Φ 0 ), made of microscopic circulating supercurrents. We introduce a multiterminal synapse network comprising a disordered array of superconducting loops with Josephson junctions. The loops can trap fluxons defining memory, while the junctions allow their movement between loops. Dynamics of fluxons through such a disordered system through a complex reconfigurable energy landscape represents brain-like spiking information flow. In this work, we experimentally demonstrate a three-loop network using YBa 2 Cu 3 O 7 –δ -based superconducting loops and Josephson junctions, which exhibit stable memory configurations of trapped flux in loops that determine the rate of flow of fluxons through synaptic connections. The memory states are, in turn, affected by the applied input signals but can also be externally configured electrically through control current/feedback terminals. These results establish a previously unexplored, biologically similar architectural approach to neuromorphic computing that is scalable while dissipating energy of atto Joules/spike.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2005

SCB Quantum Computers Using iSWAP and 1-Qubit Rotations

Units of superconducting circuitry that exploit the concept of the single- Cooper-pair box (SCB) have been built and are undergoing testing as prototypes of logic gates that could, in principle, constitute building blocks of clocked quantum computers. These units utilize quantized charge states as the quantum information-bearing degrees of freedom. An SCB is an artificial two-level quantum system that comprises a nanoscale superconducting electrode connected to a reservoir of Cooper-pair charges via a Josephson junction. The logical quantum states of the device, .0. and .1., are implemented physically as a pair of charge-number states that differ by 2e (where e is the charge of an electron). Typically, some 109 Cooper pairs are involved. Transitions between the logical states are accomplished by tunneling of Cooper pairs through the Josephson junction. Although the two-level system contains a macroscopic number of charges, in the superconducting regime, they behave collectively, as a Bose-Einstein condensate, making possible a coherent superposition of the two logical states. This possibility makes the SCB a candidate for the physical implementation of a qubit. A set of quantum logic operations and the gates that implement them is characterized as universal if, in principle, one can form combinations of the operations in the set to implement any desired quantum computation. To be able to design a practical quantum computer, one must first specify how to decompose any valid quantum computation into a sequence of elementary 1- and 2-qubit quantum gates that are universal and that can be realized in hardware that is feasible to fabricate. Traditionally, the set of universal gates has been taken to be the set of all 1-qubit quantum gates in conjunction with the controlled-NOT (CNOT) gate, which is a 2-qubit gate. Also, it has been known for some time that the SWAP gate, which implements square root of the simple 2-qubit exchange interaction, is as computationally universal as is the CNOT operation.

Williams, Colin↗

NASA NTRS1985

Quasiperiodically forced damped pendula and Schroedinger equations with quasiperiodic potentials - Implications of their equivalence

Certain first-order nonlinear ordinary differential equations exemplified by strongly damped, quasiperiodically driven pendula and Josephson junctions are isomorphic to Schroedinger equations with quasiperiodic potentials. The implications of this equivalence are discussed. In particular, it is shown that the transition to Anderson localization in the Schroedinger problem corresponds to the occurrence of a novel type of strange attractor in the pendulum problem. This transition should be experimentally observable in the frequency spectrum of the pendulum of Josephson junction.

Bondeson, A.↗

DOE OSTI2021

Crystalline materials for quantum computing: Semiconductor heterostructures and topological insulators exemplars

Abstract High-purity crystalline solid-state materials play an essential role in various technologies for quantum information processing, from qubits based on spins to topological states. New and improved crystalline materials emerge each year and continue to drive new results in experimental quantum science. This article summarizes the opportunities for a selected class of crystalline materials for qubit technologies based on spins and topological states and the challenges associated with their fabrication. We start by describing semiconductor heterostructures for spin qubits in gate-defined quantum dots and benchmark GaAs, Si, and Ge, the three platforms that demonstrated two-qubit logic. We then examine novel topologically nontrivial materials and structures that might be incorporated into superconducting devices to create topological qubits. We review topological insulator thin films and move onto topological crystalline materials, such as PbSnTe, and its integration with Josephson junctions. We discuss advances in novel and specialized fabrication and characterization techniques to enable these. We conclude by identifying the most promising directions where advances in these material systems will enable progress in qubit technology.

Scappucci, G. (ORCID:0000000325120079)↗

DOE OSTI2023

Powerful Terahertz Emission from a Bi 2 Sr 2 Ca Cu 2 O 8+ δ Mesa Operating Above 77 K

Mesa-shaped structures of the high critical temperature (high-T c ) superconductor Bi 2 Sr 2 CaCu 2 O 8+δ ; contain stacked intrinsic Josephson junctions. As such, they are a promising source of coherent radiation in the "terahertz gap" range, spanning from approximately 0.3 to 2.0 THz. Technological applications of these devices become far more practical if they can be operated at a cryogenic bath temperature of 77 K or higher. Previous works have reported emission from this type of device at high terahertz power levels at lower operating temperatures, 40-60 K, while at T bath >= 77 K observed power levels have generally been low. Here we report generation of 130 mu W of coherent power at 0.456 THz from a mesa of Bi 2 Sr 2 CaCu 2 O 8+δ ; doped with 0.16 holes per Cu atom, at a bath temperature of 77.4 K. Here, we find that the device radiates terahertz power when clearly identifiable cavity modes are excited, and that the frequency and bias voltage corresponding to each of these modes is almost independent of temperature. This is consistent with these modes having terahertz-frequency electric fields with very little dependence on vertical position within the mesa. We also find that the terahertz power radiated from any given mode decreases monotonically as the mesa temperature is increased. On the other hand, the low-frequency modes become inaccessible at low temperatures due to retrapping of the intrinsic Josephson junctions, and the maximum radiation power for the emitting mode is typically achieved at the temperature at which the retrapping voltage reaches the resonance voltage for this mode.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

A Method to Probe the Interfaces in La2−xSrxCuO4-LaSrAlO4-La2−xSrxCuO4 Trilayer Junctions

C-axis trilayer cuprate Josephson junctions are essential for basic science and digital circuit applications of high-temperature superconductors. We present a method for probing the interface perfection in La2−xSrxCuO4 (LSCO)-LaSrAlO4 (LSAO)-La2−xSrxCuO4 trilayer junctions. A series of LSCO-LSAO superlattices with atomically smooth surfaces and sharp interfaces were grown by the atomic-layer-by-layer molecular beam epitaxy (ALL-MBE) technique. We have systematically varied the thickness of LSCO and LSAO layers with monolayer precision. By studying the mutual inductance and electrical transport in these superlattices, we detect the non-superconducting (“dead”) layers at the interfaces and quantify their thicknesses. Our results indicate that two optimally doped LSCO monolayers just above and below the one monolayer LSAO barrier are no longer superconducting, rendering the actual barrier thickness of five monolayers. Next, we have shown that introducing a protective highly-overdoped LSCO layer reduces the thickness of dead layers by one or two monolayers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Atomic-scale frustrated Josephson coupling and multicondensate visualization in FeSe

In a Josephson junction involving multiband superconductors, competition between interband and interjunction Josephson couplings gives rise to frustration and spatial disjunction of superfluid densities among superconducting condensates. Such frustrated coupling manifests as the quantum interference of Josephson currents from different tunnelling channels and becomes tunable if channel transparency can be varied. To explore these unconventional effects in the prototypical s ± -wave superconductor FeSe, we use atomic-resolution scanned Josephson tunnelling microscopy for condensate-resolved imaging and junction tuning—capabilities unattainable in macroscopic Josephson devices with fixed characteristics. We quantitatively demonstrate frustrated Josephson tunnelling by examining two tunnelling inequalities. The relative transparency of two parallel tunnelling pathways is found tunable, revealing a tendency towards a 0–π transition with decreasing scanned Josephson tunnelling microscopy junction resistance. Here, the simultaneous visualization of both superconducting condensates reveals anticorrelated superfluid modulations, highlighting the role of interband scattering. Our study establishes scanned Josephson tunnelling microscopy as a powerful tool enabling new research frontiers of multicondensate superconductivity.

Scanning probe microscopy↗

NASA NTRS2008

Thermally Driven Josephson Effect

A concept is proposed of the thermally driven Josephson effect in superfluid helium. Heretofore, the Josephson effect in a superfluid has been recognized as an oscillatory flow that arises in response to a steady pressure difference between two superfluid reservoirs separated by an array of submicron-sized orifices, which act in unison as a single Josephson junction. Analogously, the thermally driven Josephson effect is an oscillatory flow that arises in response to a steady temperature difference. The thermally driven Josephson effect is partly a consequence of a quantum- mechanical effect known as the fountain effect, in which a temperature difference in a superfluid is accompanied by a pressure difference. The thermally driven Josephson effect may have significance for the development of a high-resolution gyroscope based on the Josephson effect in a superfluid: If the pressure-driven Josephson effect were used, then the fluid on the high-pressure side would become depleted, necessitating periodic interruption of operation to reverse the pressure difference. If the thermally driven Josephson effect were used, there would be no net flow and so the oscillatory flow could be maintained indefinitely by maintaining the required slightly different temperatures on both sides of the junction.

Penanen, Konstantin↗

DOE OSTI2023

Nonreciprocal Supercurrents in a Field-Free Graphene Josephson Triode

Superconducting diodes are proposed non-reciprocal circuit elements that should exhibit nondissipative transport in one direction while being resistive in the opposite direction. Multiple examples of such devices have emerged in the past couple of years, however their efficiency is typically limited, and most of them require magnetic field to function. Here we present a device achieving efficiencies upwards of 90% while operating at zero field. Our samples consist of a network of three graphene Josephson junctions linked by a common superconducting island, to which we refer as a Josephson triode. The triode is tuned by applying a control current to one of the contacts, thereby breaking the time-reversal symmetry of the current flow. The triode’s utility is demonstrated by rectifying a small (tens of nA amplitude) applied square wave. Finally, we speculate that devices of this type could be realistically employed in the modern quantum circuits.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Junctions and Superconducting Symmetry in Twisted Bilayer Graphene

Junctions provide a wealth of information on the symmetry of the order parameter of superconductors. Here, we analyze junctions between a scanning tunneling microscope (STM) tip and superconducting twisted bilayer graphene (TBG) and TBG Josephson junctions (JJs). We compare superconducting phases that are even or odd under valley exchange (s- or ƒ-wave). The critical current in mixed (s and ƒ) JJs strongly depends on the angle between the junction and the lattice. In STM-TBG junctions, due to Andreev reflection, the ƒ-wave leads to a prominent peak in subgap conductance, as seen in experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Nonequilibrium steady state and heat transport in nonlinear open quantum systems: Stochastic influence action and functional perturbative analysis

In this paper, we show that a nonequilibrium steady state (NESS) exists at late times in open quantum systems with weak nonlinearity by following its nonequilibrium dynamics with a perturbative analysis. We consider an oscillator chain containing three-types of anharmonicity: cubic α- and quartic β-type Fermi–Pasta–Ulam–Tsingou (FPUT) nearest-oscillator interactions and the on-site (pinned) Klein–Gordon (KG) quartic self-interaction. Assuming weak nonlinearity, we introduce a stochastic influence action approach to the problem and obtain the energy flows in different junctures across the chain. The formal results obtained here can be used for quantum transport problems in weakly nonlinear quantum systems. For α-type anharmonicity, we observe that the first-order corrections do not play any role in the thermal transport in the NESS of the configuration we considered. For KG and β-types anharmonicity, we work out explicitly the case of two weakly nonlinearly coupled oscillators, with results scalable to any number of oscillators. We examine the late-time energy flows from one thermal bath to the other via the coupled oscillators, and show that both the zeroth- and the first-order contributions of the energy flows become constant in time at late times, signaling the existence of a late-time NESS to first order in nonlinearity. Our perturbative calculations provide a measure of the strength of nonlinearity for nonlinear open quantum systems, which may help control the mesoscopic heat transport distinct from or close to linear transport. Furthermore, our results also give a benchmark for the numerical challenge of simulating heat transport. Our setup and predictions can be implemented and verified by investigating heat flow in an array of Josephson junctions in the limit of large Josephson energy with the platform of circuit QED.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Coupling of Klein-Andreev resonant states in B⁢i 2 ⁢S⁢r 2 ⁢CaC⁢u 2 ⁢O 8+𝑥 -graphene-B⁢i 2⁢ S⁢r 2 ⁢CaC⁢u 2 ⁢O 8+𝑥 devices

Quantum devices require coherent coupling over macroscopic distances. Recently, resonances due to Klein tunneling and Andreev reflection states (KARS) have been observed in a naturally occurring p-n junction at the interface between B⁢i 2 ⁢S⁢r 2 ⁢CaC⁢u 2 ⁢O 8+𝑥 (BSCCO), a high−⁢𝑇 c superconductor (HTS), and graphene. The resonances appear as conductance oscillations with gating. Here, in this study, we show coupling between the KARS in BSCCO-graphene-BSCCO devices of varying separation (L). The coupling is evidenced by a power-law decay of resonance period as L increases from tens of nanometers to microns. These results demonstrate the long-distance coupling of KARS cavities in graphene-HTS junctions. The length dependence seen in experiments is supported by single-particle spectral functions which show KARS are coupled by transport modes in graphene. The strong coupling between KARS in BSCCO-graphene-BSCCO devices showcases the possibility of HTS-graphene junctions for quantum circuits and unconventional Josephson junctions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Higher-order topological superconductivity in twisted bilayer graphene

In this work, we show that introducing spin-singlet or spin-triplet superconductivity into twisted bilayer graphene induces higher-order topological superconductivity. Multiple copies of C 2z ⁢T-protected Majorana Kramers pairs appear at corners on pairing domain walls. The topology originates from the anomaly analyzed in Song et al.—the absence of a lattice support—of the single-valley band structure of twisted bilayer graphene, which is protected by C 2z ⁢T and approximate particle-hole symmetry $\mathcal{P}$. We prove that any pairing (spin-singlet or spin-triplet) term preserving valley-U(1), spin-SU(2), time-reversal, C 2z ⁢T, and $\mathcal{P}$ must drive the system into a higher-order topological superconductor. Here spin-SU(2) is the global spin-SU(2) for the singlet pairing and is broken to U(1) for the triplet pairing. Using a Dirac Hamiltonian, we derive the corner modes and confirm with numerics. These corner states are stable even if $\mathcal{P}$ is weakly broken, which is true in experimental setups. Finally, we suggest experimental detection via the fractional Josephson effect in a TBG-TSC Josephson junction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗