Quantum dynamics of a single vortex

Current induced hidden states in Josephson junctions

Josephson junctions enable dissipation-less electrical current through metals and insulators below a critical current. Despite being central to quantum technology based on superconducting quantum bits and fundamental research into self-conjugate quasiparticles, the spatial distribution of super current flow at the junction and its predicted evolution with current bias and external magnetic field remain experimentally elusive. Revealing the hidden current flow, featureless in electrical resistance, helps understanding unconventional phenomena such as the nonreciprocal critical current, i.e., Josephson diode effect. Here we introduce a platform to visualize super current flow at the nanoscale. Utilizing a scanning magnetometer based on nitrogen vacancy centers in diamond, we uncover competing ground states electrically switchable within the zero-resistance regime. The competition results from the superconducting phase re-configuration induced by the Josephson current and kinetic inductance of thin-film superconductors. We further identify a new mechanism for the Josephson diode effect involving the Josephson current-induced phase. The nanoscale super current flow emerges as a new experimental observable for elucidating unconventional superconductivity, and optimizing quantum computation and energy-efficient devices.

Quantum thermodynamics with a single superconducting vortex

We demonstrate complete control over dynamics of a single superconducting vortex in a nanostructure, which we coin the Single Vortex Box. Our device allows us to trap the vortex in a field-cooled aluminum nanosquare and expel it on demand with a nanosecond pulse of electrical current. Using the time-resolving nanothermometry we measure [Formula: see text] joules as the amount of the dissipated heat in the elementary process of the single-vortex expulsion. Our experiment enlightens the thermodynamics of the absorption process in the superconducting nanowire single-photon detectors, in which vortices are perceived to be essential for a formation of a detectable hotspot. The demonstrated opportunity to manipulate a single superconducting vortex reliably in a confined geometry comprises a proof of concept of a nanoscale nonvolatile memory cell with subnanosecond write and read operations, which offers compatibility with quantum processors based either on superconducting qubits or on rapid single-flux quantum circuits.

Revealing Josephson Vortex Dynamics in Proximity Junctions below Critical Current

Made of a thin non-superconducting metal (N) sandwiched by two superconductors (S), SNS Josephson junctions enable novel quantum functionalities by mixing up the intrinsic electronic properties of N with the superconducting correlations induced from S by proximity. Electronic properties of these devices are governed by Andreev quasiparticles (Andreev, A. Sov. Phys. JETP 1965, 20, 1490) which are absent in conventional SIS junctions whose insulating barrier (I) between the two S electrodes owns no electronic states. Here we focus on the Josephson vortex (JV) motion inside Nb-Cu-Nb proximity junctions subject to electric currents and magnetic fields. The results of local (magnetic force microscopy) and global (transport) experiments provided simultaneously are compared with our numerical model, revealing the existence of several distinct dynamic regimes of the JV motion. One of them, identified as a fast hysteretic entry/escape below the critical value of Josephson current, is analyzed and suggested for low-dissipative logic and memory elements.

Lateral Josephson Junctions as Sensors for Magnetic Microscopy at Nanoscale

Lateral Josephson junctions (LJJ) made of two superconducting Nb electrodes coupled by Cu-film are applied to quantify the stray magnetic field of Co-coated cantilevers used in magnetic force microscopy (MFM). The interaction of the magnetic cantilever with LJJ is reflected in the electronic response of LJJ as well as in the phase shift of cantilever oscillations, simultaneously measured. The phenomenon is theorized and used to establish the spatial map of the stray field. Based on our findings, we suggest integrating LJJs directly on the tips of cantilevers and using them as nanosensors of local magnetic fields in scanning probe microscopes. Such probes are less invasive than conventional magnetic MFM cantilevers and simpler to realize than SQUID-on-tip sensors.

Caustic Interpretation of the Abruptly Autofocusing Vortex beams

We propose an effective scheme to interpret the abruptly autofocusing vortex beam. In our scheme, a set of analytical formulae are deduced to well predict not only the global caustic, before and after the focal plane, but also the focusing properties of the abruptly autofocusing vortex beam, including the axial position as well as the diameter of focal ring. Our analytical results are in excellent agreement with both numerical simulation and experimental results. Besides, we apply our analytical technique to the fine manipulation of the focusing properties with a scaling factor. This set of methods would be beneficial to a broad range of applications such as particle trapping and micromachinings.

Superconducting properties of in-plane W-C nanowires grown by He+ focused ion beam induced deposition

Focused ion beam induced deposition (FIBID) is a nanopatterning technique that uses a focused beam of charged ions to decompose a gaseous precursor. So far, the flexible patterning capabilities of FIBID have been widely exploited in the fabrication of superconducting nanostructures, using the W(CO)₆ precursor mostly in combination with a focused beam of Ga⁺ ions. Here, the fabrication and characterization of superconducting in-plane tungsten-carbon (W-C) nanostructures by He⁺ FIBID of the W(CO)₆ precursor is reported. A patterning resolution of 10 nm has been achieved, which is virtually unattainable for Ga⁺ FIBID. When the nanowires are patterned with widths of 20 nm and above, the deposited material is superconducting below 3.5-4 K. In addition, nanowires with widths of 60 and 90 nm have been found to sustain long-range controlled nonlocal superconducting vortex transfer along 3 μm. Overall, these findings strengthen the capabilities of He⁺ FIBID of W-C in the growth and patterning of in-plane superconducting nanodevices.

Generating terahertz perfect optical vortex beams by diffractive elements

An effective experiment scheme is proposed to generate the terahertz (THz) perfect optical vortex (POV) beams by diffractive elements at the frequency of 0.1THz. Two diffractive elements are designed and fabricated by 3D-printing to form the generation system. The ring radius of the generated beams is independent of the topological charge and positive linear relationship with the radial wave vector. By controlling the radial wave vector, the ring radius can be freely adjusted. The experiment results are shown to corroborate the numerical simulation ones. Such generated beams hold promise for developing the novel THz fiber communication systems.

Long-range vortex transfer in superconducting nanowires

Under high-enough values of perpendicularly-applied magnetic field and current, a type-II superconductor presents a finite resistance caused by the vortex motion driven by the Lorentz force. To recover the dissipation-free conduction state, strategies for minimizing vortex motion have been intensely studied in the last decades. However, the non-local vortex motion, arising in areas depleted of current, has been scarcely investigated despite its potential application for logic devices. Here, we propose a route to transfer vortices carried by non-local motion through long distances (up to 10 micrometers) in 50 nm-wide superconducting WC nanowires grown by Ga⁺ Focused Ion Beam Induced Deposition. A giant non-local electrical resistance of 36 Ω has been measured at 2 K in 3 μm-long nanowires, which is 40 times higher than signals reported for wider wires of other superconductors. This giant effect is accounted for by the existence of a strong edge confinement potential that hampers transversal vortex displacements, allowing the long-range coherent displacement of a single vortex row along the superconducting channel. Experimental results are in good agreement with numerical simulations of vortex dynamics based on the time-dependent Ginzburg-Landau equations. Our results pave the way for future developments on information technologies built upon single vortex manipulation in nano-superconductors.

Vertical Growth of Superconducting Crystalline Hollow Nanowires by He+ Focused Ion Beam Induced Deposition

Novel physical properties appear when the size of a superconductor is reduced to the nanoscale, in the range of its superconducting coherence length (ξ₀). Such nanosuperconductors are being investigated for potential applications in nanoelectronics and quantum computing. The design of three-dimensional nanosuperconductors allows one to conceive novel schemes for such applications. Here, we report for the first time the use of a He⁺ focused-ion-beam-microscope in combination with the W(CO)₆ precursor to grow three-dimensional superconducting hollow nanowires as small as 32 nm in diameter and with an aspect ratio (length/diameter) of as much as 200. Such extreme resolution is achieved by using a small He⁺ beam spot of 1 nm for the growth of the nanowires. As shown by transmission electron microscopy, they display grains of large size fitting with face-centered cubic WC_1-x phase. The nanowires, which are grown vertically to the substrate, are felled on the substrate by means of a nanomanipulator for their electrical characterization. They become superconducting at 6.4 K and show large critical magnetic field and critical current density resulting from their quasi-one-dimensional superconducting character. These results pave the way for future nanoelectronic devices based on three-dimensional nanosuperconductors.

Phonon engineering in proximity enhanced superconductor heterostructures

In this research, we tailor the phonon density of states (DOS) in thin superconducting films to suppress quasiparticle losses. We examine a model system of a proximity-enhanced three-layered Al/Nb/Al heterostructure and show that the local quantized phonon spectrum of the ultrathin Al cladding layers in the heterostructure has a pronounced effect on the superconducting resonator’s quality factors. Instead of a monotonic increase of quality factors with decreasing temperatures, we observe the quality factor reaches a maximum at 1.2 K in 5/50/5 nm Al/Nb/Al microstrip resonators, because of a quantized phonon ladder. The phonon DOS may be engineered to enhance the performance of quantum devices.

Time-Correlated Vortex Tunneling in Layered Superconductors

The nucleation and dynamics of Josephson and Abrikosov vortices determine the critical currents of layered high-Tc superconducting (HTS) thin films, grain boundaries, and coated conductors, so understanding their mechanisms is of crucial importance. Here, we treat pair creation of Josephson and Abrikosov vortices in layered superconductors as a secondary Josephson effect. Each full vortex is viewed as a composite fluid of micro-vortices, such as pancake vortices, which tunnel coherently via a tunneling matrix element. We introduce a two-terminal magnetic (Weber) blockade effect that blocks tunneling when the applied current is below a threshold value. We simulate vortex tunneling as a dynamic, time-correlated process when the current is above threshold. The model shows nearly precise agreement with voltage-current (V-I) characteristics of HTS cuprate grain boundary junctions, which become more concave rounded as temperature decreases, and also explains the piecewise linear V-I behavior observed in iron-pnictide bicrystal junctions and other HTS devices. When applied to either Abrikosov or Josephson pair creation, the model explains a plateau seen in plots of critical current vs. thickness of HTS-coated conductors. The observed correlation between theory and experiment strongly supports the proposed quantum picture of vortex nucleation and dynamics in layered superconductors.

Engineering double-well potentials with variable-width annular Josephson tunnel junctions

Long Josephson tunnel junctions are non-linear transmission lines that allow propagation of current vortices (fluxons) and electromagnetic waves and are used in various applications within superconductive electronics. Recently, the Josephson vortex has been proposed as a new superconducting qubit. We describe a simple method to create a double-well potential for an individual fluxon trapped in a long elliptic annular Josephson tunnel junction characterized by an intrinsic non-uniform width. The distance between the potential wells and the height of the inter-well potential barrier are controlled by the strength of an in-plane magnetic field. The manipulation of the vortex states can be achieved by applying a proper current ramp across the junction. The read-out of the state is accomplished by measuring the vortex depinning current in a small magnetic field. An accurate one-dimensional sine-Gordon model for this strongly non-linear system is presented, from which we calculate the position-dependent fluxon rest-mass, its Hamiltonian density and the corresponding trajectories in the phase space. We examine the dependence of the potential properties on the annulus eccentricity and its electrical parameters and address the requirements for observing quantum-mechanical effects, as discrete energy levels and tunneling, in this two-state system.

Velocimetry of superconducting vortices based on stroboscopic resonances

An experimental determination of the mean vortex velocity in superconductors mostly relies on the measurement of flux-flow resistance with magnetic field, temperature, or driving current. In the present work we introduce a method combining conventional transport measurements and a frequency-tuned flashing pinning potential to obtain reliable estimates of the vortex velocity. The proposed device is characterized using the time-dependent Ginzburg-Landau formalism, where the velocimetry method exploits the resonances in mean vortex dissipation when temporal commensuration occurs between the vortex crossings and the flashing potential. We discuss the sensitivity of the proposed technique on applied current, temperature and heat diffusion, as well as the vortex core deformations during fast motion.

Fluxon readout of a superconducting qubit

An experiment demonstrating a link between classical single-flux quantum digital logic and a superconducting quantum circuit is reported. We implement coupling between a moving Josephson vortex (fluxon) and a flux qubit by reading out of a state of the flux qubit through a frequency shift of the fluxon oscillations in an annular Josephson junction. The energy spectrum of the flux qubit is measured using this technique. The implemented hybrid scheme opens an opportunity to readout quantum states of superconducting qubits with the classical fluxon logic circuits.

Trapping of topological-structural defects in Coulomb crystals

We study experimentally and theoretically structural defects which are formed during the transition from a laser cooled cloud to a Coulomb crystal, consisting of tens of ions in a linear radio frequency trap. We demonstrate the creation of predicted topological defects ("kinks") in purely two-dimensional crystals and also find kinks which show novel dynamical features in a regime of parameters not considered before. The kinks are always observed at the center of the trap, showing a large nonlinear localized excitation, and the probability of their occurrence saturates at ∼0.5. Simulations reveal a strong anharmonicity of the kink's internal mode of vibration, due to the kink's extension into three dimensions. As a consequence, the periodic Peierls-Nabarro potential experienced by a discrete kink becomes a globally confining potential, capable of trapping one cooled defect at the center of the crystal.

Drastic suppression of noise-induced errors in underdamped long Josephson junctions

The fluctuational propagation of solitons (magnetic fluxons) in long Josephson junctions is studied both numerically and analytically. It is demonstrated that operation in conditions where solitons are subjected to Lorentz contraction for a significant part of the junctions length leads to drastic suppression of thermal jitter at the output junction end. Specifically, for large-to-critical damping and small values of bias current, the physically obvious dependence of the jitter versus length σ~√L is confirmed, while for small damping starting from the experimentally relevant α=0.1 and below, strong deviation from σ~√L is observed, up to nearly complete independence of the jitter versus length, which is supported by the obtained theory.

Quantum tunneling of a vortex between two pinning potentials

A vortex can tunnel between two pinning potentials in an atomic Bose-Einstein condensate on a time scale of the order of 1s under typical experimental conditions. This makes it possible to detect the tunneling experimentally. We calculate the tunneling rate by phenomenologically treating vortices as charged particles moving in an inhomogeneous magnetic field. The obtained results are in close agreement with numerical simulations based on the stochastic c-field theory.

A single Abrikosov vortex trapped in a mesoscopic superconducting cylindrical surface

We investigate the behaviour of a single Abrikosov vortex trapped in a mesoscopic superconducting cylindrical surface with a magnetic field applied transverse to its axis. In the framework of the time-dependent Ginzburg-Landau formalism we show that, provided the transport current and the magnetic field are not large, the vortex behaves as an overdamped quasi-particle in a tilted washboard potential. The cylindrical thin strip with the trapped vortex exhibits E(J) curves and time-dependent electric fields very similar to the ones exhibited by a resistively shunted Josephson weak link.

Observing Majorana bound states of Josephson vortices in topological superconductors

In recent years there has been an intensive search for Majorana fermion states in condensed matter systems. Predicted to be localized on cores of vortices in certain nonconventional superconductors, their presence is known to render the exchange statistics of bulk vortices non-abelian. Here we study the equations governing the dynamics of phase solitons (fluxons) in a Josephson junction in a topological superconductor. We show that the fluxon will bind a localized zero energy Majorana mode and will consequently behave as a non-abelian anyon. The low mass of the fluxon, as well as its experimentally observed quantum mechanical wave-like nature, will make it a suitable candidate for vortex interferometry experiments demonstrating non-abelian statistics. We suggest two experiments that may reveal the presence of the zero mode carried by the fluxon. Specific experimental realizations will be discussed as well.

Topological quantum buses: coherent quantum information transfer between topological and conventional qubits

We propose computing bus devices that enable quantum information to be coherently transferred between topological and conventional qubits. We describe a concrete realization of such a topological quantum bus acting between a topological qubit in a Majorana wire network and a conventional semiconductor double quantum dot qubit. Specifically, this device measures the joint (fermion) parity of these two different qubits by using the Aharonov-Casher effect in conjunction with an ancilliary superconducting flux qubit that facilitates the measurement. Such a parity measurement, together with the ability to apply Hadamard gates to the two qubits, allows one to produce states in which the topological and conventional qubits are maximally entangled and to teleport quantum states between the topological and conventional quantum systems.

Superconducting nanowires fabricated using molecular templates

The application of single molecules as templates for nanodevices is a promising direction for nanotechnology. We use suspended deoxyribonucleic acid molecules or single-walled carbon nanotubes as templates for fabricating superconducting devices and then study these devices at cryogenic temperatures. Because the resulting nanowires are extremely thin, comparable in diameter to the templating molecule itself, their electronic state is highly susceptible to thermal fluctuations. The most important family of these fluctuations are the collective ones, which take the form of Little's phase slips or ruptures of the many-electron organization. These phase slips break the quantum coherence of the superconducting condensate and render the wire slightly resistive (i.e., not fully superconducting), even at temperatures substantially lower than the critical temperature of the superconducting transition. At low temperatures, for which the thermal fluctuations are weak, we observe the effects of quantum fluctuations, which lead to the phenomenon of macroscopic quantum tunneling. The modern fabrication method of molecular templating, reviewed here, can be readily implemented to synthesize nanowires from other materials, such as normal metals, ferromagnetic alloys, and semiconductors.

Quantum coherence of discrete kink solitons in ion traps

We propose to realize quantized discrete kinks with cold trapped ions. We show that long-lived solitonlike configurations are manifested as deformations of the zigzag structure in the linear Paul trap, and are topologically protected in a circular trap with an odd number of ions. We study the quantum-mechanical time evolution of a high-frequency, gap separated internal mode of a static kink and find long coherence times when the system is cooled to the Doppler limit. The spectral properties of the internal modes make them ideally suited for manipulation using current technology. This suggests that ion traps can be used to test quantum-mechanical effects with solitons and explore ideas for the utilization of the solitonic internal modes as carriers of quantum information.

Macroscopic quantum tunneling in "small" Josephson junctions in a magnetic field

We study the phenomenon of macroscopic quantum tunneling (MQT) in small Josephson junctions (JJ) with an externally applied magnetic field. The latter results in the appearance of the Fraunhofer type modulation of the current density along the barrier. The problem of MQT for a pointlike JJ is reduced to the motion of the quantum particle in the washboard potential. In the case of a finite size JJ under consideration, this problem corresponds to a MQT in a potential which itself, besides the phase, depends on space variables. The general expression for the crossover temperature T0 between thermally activated and macroscopic quantum tunneling regimes and the escaping time tau(esc) have been calculated.

Flux cloning in Josephson transmission lines

We describe a novel effect related to the controlled birth of a single Josephson vortex. In this phenomenon, the vortex is created in a Josephson transmission line at a T-shaped junction. The "baby" vortex arises at the moment when a "mother" vortex propagating in the adjacent transmission line passes the T-shaped junction. In order to give birth to a new vortex, the mother vortex must have enough kinetic energy. Its motion can also be supported by an externally applied driving current. We determine the critical velocity and the critical driving current for the creation of the baby vortices and briefly discuss the potential applications of the found effect.

Noise-induced escape of periodically modulated systems: from weak to strong modulation

Noise-induced escape from a metastable state is studied for an overdamped periodically modulated system. We develop an asymptotic technique that gives both the instantaneous and period-average escape rates, including the prefactor, for an arbitrary modulation amplitude A . We find the parameter range where escape is strongly synchronized and the instantaneous escape rate displays sharp peaks. The peaks vary with increasing modulation frequency or amplitude from Gaussian to strongly asymmetric. The prefactor nu in the period-average escape rate depends on A nonmonotonically. Near the bifurcation amplitude A(c) it scales as nu approximately (A(c) - A)(zeta). We identify three scaling regimes, with zeta = 1/4, -1, and 1/2.

Activated escape of periodically modulated systems

The rate of noise-induced escape from a metastable state of a periodically modulated overdamped system is found for an arbitrary modulation amplitude A. The instantaneous escape rate displays peaks that vary with the modulation from Gaussian to strongly asymmetric. The prefactor nu in the period-averaged escape rate depends on A nonmonotonically. Near the bifurcation amplitude A(c) it scales as nu proportional, variant(A(c) - A)(zeta). We identify three scaling regimes, with zeta = 1/4, -1, and 1/2.

New fluxon resonant mechanism in annular Josephson tunnel structures

A novel dynamical state has been observed in the dynamics of a perturbed sine-Gordon system. This resonant state has been experimentally observed as a singularity in the dc current-voltage characteristic of an annular Josephson tunnel junction, excited in the presence of a magnetic field. In this respect it can be assimilated to self-resonances known as Fiske steps. Differently from these, however, we demonstrate, on the basis of numerical simulations, that its detailed dynamics involves rotating fluxon pairs, a mechanism associated, so far, to self-resonances known as zero-field steps. This occurs because the size of nonlinear excitations is comparable with that of the system.

Criteria for the experimental observation of multidimensional optical solitons in saturable media

Criteria for experimental observation of multidimensional optical solitons in media with saturable refractive nonlinearities are developed. The criteria are applied to actual material parameters (characterizing the cubic self-focusing and quintic self-defocusing nonlinearities, two-photon loss, and optical-damage threshold) for various glasses. This way, we identify operation windows for soliton formation in these glasses. It is found that two-photon absorption sets stringent limits on the windows. We conclude that, while a well-defined window of parameters exists for two-dimensional solitons (spatial or spatiotemporal), for their three-dimensional spatiotemporal counterparts such a window does not exist, due to the nonlinear loss in glasses.

Quantum dissociation of a vortex-antivortex pair in a long josephson junction

The thermal and the quantum dissociation of a single vortex-antivortex (VAV) pair in an annular Josephson junction is experimentally observed and theoretically analyzed. In our experiments, the VAV pair is confined in a pinning potential controlled by external magnetic field and bias current. The dissociation of the pinned VAV pair manifests itself in a switching of the Josephson junction from the superconducting to the resistive state. The observed temperature and field dependence of the switching current distribution is in agreement with the analysis. The crossover from the thermal to the macroscopic quantum tunneling mechanism of dissociation occurs at a temperature of about 100 mK. We also predict the specific magnetic field dependence of the oscillatory energy levels of the pinned VAV state.