Phase-slip Processes Research Articles

Dephasing in Fluxonium Qubits from Coherent Quantum Phase Slips

Phase slips occur across all Josephson junctions (JJs) at a rate that increases with the impedance of the junction. In superconducting qubits composed of JJ-array superinductors—such as fluxonium—phase slips in the array can lead to decoherence. In particular, phase-slip processes at the individual array junctions can coherently interfere, each with an Aharonov-Casher phase that depends on the offset charges of the array islands. These coherent quantum phase slips (CQPS) perturbatively modify the qubit frequency, and therefore charge noise on the array islands will lead to dephasing. By varying the impedance of the array junctions, we design a set of fluxonium qubits in which the expected phase-slip rate within the JJ array changes by several orders of magnitude. We characterize the coherence times of these qubits and demonstrate that the scaling of CQPS-induced dephasing rates agrees with our theoretical model. Furthermore, we perform noise spectroscopy of two qubits in regimes dominated by either CQPS or flux noise. We find that the noise power spectrum associated with CQPS dephasing appears to be featureless at low frequencies and not 1/f. Numerical simulations indicate that this behavior is consistent with charge noise generated by charge-parity fluctuations within the array. Our findings broadly inform JJ-array-design trade-offs, relevant for the numerous superconducting-qubit designs employing JJ-array superinductors. Published by the American Physical Society 2024

Direct observation of positron capture process at the positron source of the superKEKB B-factory

A direct simultaneous detection of electron (e^-) and positron (e^+) bunches was successfully performed using wideband beam monitors and a detection system at the e^+ capture section of the SuperKEKB B-factory. The time intervals between the secondary-generated e^- and e^+ bunches were measured to investigate their dynamical capture process. The results show that the time intervals were measured in the range of 20–280 ps on average, and the line-order switch of the e^- and e^+ bunches and their dynamical phase-slip process in the axial direction were clearly observed as a function of the capture phase of accelerating structures. In this report, the dynamical capture and phase-slip process for the e^- and e^+ bunches under the two-bunch acceleration scheme is described in detail. This study opens up a new window for direct observation of the e^- and e^+ capture process at any present and future e^+ sources.

The essential role of surface pinning in the dynamics of charge density waves submitted to external dc fields

A Charge Density Wave (CDW) submitted to an electric field displays a strong shear deformation because of pinning at the lateral surfaces of the sample. This CDW transverse pinning was recently observed but has received little attention from a theoretical point of view until now despite important consequences on electrical conductivity properties. Here, we provide a description of this phenomenon by considering a CDW submitted to an external dc electric field and constrained by boundary conditions including both longitudinal pinning due to electrical contacts and transverse surface pinning. A simple formula for the CDW phase is obtained in 3D by using the Green function and image charges method. In addition, an analytical expression of the threshold field dependence on both length and sample cross section is obtained by considering the phase slip process. We show that the experimental data are well reproduced with this model and that bulk pinning can be neglected. This study shows that the dynamical properties of CDW systems could be mainly driven by boundary effects, despite the comparatively huge sample volumes.

Electronic Transport on W-Rich Films Deposited by Focused Ion Beam

The electrical transport properties of W films obtained through focused ion beam deposition reveal a transition from weakly insulating to metallic behavior for increasing film thickness. At low temperatures, all the films make a transition to the superconducting state. The observed stochastic distribution of the critical superconducting current is related to the occurrence of phase slip processes as documented by the statistical distribution of the depairing current and its temperature dependence according to the thermally activated model of the superconducting phase in a tilted washboard potential.

Phase slip process and charge density wave dynamics in a one dimensional conductor

In this paper, we study the phase slip effect on the charge density wave (CDW) dynamics in a one-dimensional conductor in the weak pinning limit. A considerable enhancement of JCDW is observed in the presence of phase slips. In addition, a spatial dependence of the CDW current density JCDW is also studied showing that a decrease of JCDW with distance from the current contact occurs. The results are discussed in terms the relationship between additional phase slips and the mobility of phase dislocations nucleated at electrical contacts.

Quantum Phase Slips in 6 mm Long Niobium Nanowire.

Transport measurements were made to study the superconducting transition of four 6 mm long niobium nanowires with different cross-sectional dimensions. A low-temperature residual resistance tail measured with an excitation current of 5 nA is found in the thinnest wire down to 50 mK or 7.7% of Tc of Nb. The functional form of the residual resistance is consistent with quantum phase slip (QPS) processes. Resistance measured at high bias excitation current switches among many discrete values that are well below the normal state resistance. These discrete resistance values as a function of temperature fall into several parallel curves all showing QPS-like decay in the low temperature limit similar to that found at low current. The coexistence of QPS-like resistance tails and resistance jumps found in the same wire unifies results from previous experiments where these two distinct sets of evidence for QPS are exclusive of each other.

Tailoring phase slip events through magnetic doping in superconductor-ferromagnet composite films.

The interplay between superconductivity (SC) and ferromagnetism (FM) when embedded together has attracted unprecedented research interest due to very rare coexistence of these two phenomena. The focus has been mainly put into the proximity induced effects like, coexistence of magnetism and superconductivity, higher critical current, triplet superconductivity etc. However, very little attention has been paid experimentally to the role of magnetic constituent on triggering phase slip processes in the composite films (CFs). We demonstrate that less than 1 at.% of magnetic contribution in the CFs can initiate phase slip events efficiently. Due to advanced state-of-the-art fabrication techniques, phase slip based studies have been concentrated mainly on superconducting nanostructures. Here, we employ wide mesoscopic NbGd based CFs to study the phase slip processes. Low temperature current-voltage characteristics (IVCs) of CFs show stair-like features originated through phase slip events and are absent in pure SC films. Depending on the bias current and temperature, distinct regions, dominated by Abrikosov type vortex-antivortex (v-av) pairs and phase slip events, are observed. The results presented here open a new way to study the phase slip mechanism, its interaction with v-av pairs in two dimensions and hence can be useful for future photonic and metrological applications.

Superconductor–insulator transition in nanowires and nanowire arrays

Superconducting nanowires are the dual elements to Josephson junctions, with quantum phase-slip (QPS) processes replacing the tunneling of Cooper pairs. When the QPS amplitude ES is much smaller than the inductive energy EL, the nanowire responds as a superconducting inductor. When the inductive energy is small, the response is capacitive. The crossover at low temperatures as a function of ES/EL is discussed and compared with earlier experimental results. For one-dimensional and two-dimensional arrays of nanowires quantum phase transitions are expected as a function of ES/EL. They can be tuned by a homogeneous magnetic frustration.

Resistive states in wide superconducting films induced by dc and ac currents (Review Article)

This review is devoted to the studies of the resistive state in wide superconducting films induced by dc and ac currents in the absence of an external magnetic field. It is found experimentally that the current-voltage characteristics and their parameters are well described by the Aslamazov–Lempitskii theory of the resistive vortex state, which has long been lacking an adequate evidence to support it. There is experimental evidence that the vortex mechanism of resistivity is absent for currents exceeding the maximum current at which the resistive vortex state exists in wide films. The non-vortex nature of phase slip lines (PSL) in wide films is proved experimentally. It is shown that the phase-slip lines arise in a wide superconducting film subjected to an external microwave irradiation with the power exceeding some critical value. The resistance of these phase-slip lines depends on irradiation frequency. Results obtained in studies of PSL in wide films are similar to those obtained for the phase-slip centers in narrow channels. This suggests the identical nature of the phase-slip processes in these two phenomena. It is established that the current-carrying resistive state of a wide film arises due to two different mechanisms that occur one after the other: the penetration into the film and transverse motion of the Pearl vortices induced by the magnetic field of the transport current and the emergence of the phase-slip lines of the superconducting order parameter.

Growth and characterization of superconducting β-FeSe type iron chalcogenide nanowires

We have grown highly crystalline β-FeSe type iron chalcogenide nanowires (NWs) by annealing thin film that is prepared by a pulsed laser deposition method. Three kinds of NWs with compositions of Fe0.8Se, Fe0.88Se0.32Te0.68 and Fe0.88Te0.91S0.09 have been prepared and carefully characterized by a high-resolution transmission electron microscope (HRTEM). The NWs reveal ideal tetragonal structure with crystal growth along the [100] direction. Energy dispersive spectroscopy (EDS) studies and HRTEM images show the NWs to have good compositional uniformity, except for the existence of a thin layer of oxide on the surface. No superconducting transition was observed in the FeSex NWs, which is possibly caused by Fe deficiency. The other two types of NWs show relatively higher and sharper superconducting transitions than their bulk counterparts. Interestingly, a resistive transition tail is observed in the NWs with diameter smaller than 100 nm, which might originate from a phase slip process in the quasi-one-dimensional system. The success in producing these high quality NWs provides a new avenue for better understanding the origin of superconductivity in β-FeSe type iron chalcogenides.

Quantum phase slips in Josephson junction rings

We study quantum phase-slip (QPS) processes in a superconducting ring containing $N$ Josephson junctions and threaded by an external static magnetic flux ${\ensuremath{\Phi}}_{B}$. In such a system, a QPS consists of a quantum tunneling event connecting two distinct classical states of the phases with different persistent currents [Matveev et al., Phys. Rev. Lett. 89, 096802 (2002)]. When the Josephson coupling energy ${E}_{J}$ of the junctions is larger than the charging energy ${E}_{C}={e}^{2}/2C$, where $C$ is the junction capacitance, the quantum amplitude for the QPS process is exponentially small in the ratio ${E}_{J}/{E}_{C}$. At given magnetic flux, each QPS can be described as the tunneling of the phase difference of a single junction of almost $2\ensuremath{\pi}$, accompanied by a small harmonic displacement of the phase difference of the other $N\ensuremath{-}1$ junctions. As a consequence, the total QPS amplitude ${\ensuremath{\nu}}_{\mathrm{ring}}$ is a global property of the ring. Here, we study the dependence of ${\ensuremath{\nu}}_{\mathrm{ring}}$ on the ring size $N$, taking into account the effect of a finite capacitance ${C}_{0}$ to ground, which leads to the appearance of low-frequency dispersive modes. Josephson and charging effects compete and lead to a nonmonotonic dependence of the ring's critical current on $N$. For $N\ensuremath{\rightarrow}\ensuremath{\infty}$, the system converges either towards a superconducting or an insulating state, depending on the ratio between the charging energy ${E}_{0}={e}^{2}/2{C}_{0}$ and the Josephson coupling energy ${E}_{J}$.

High critical current density and scaling of phase-slip processes in YBaCuO nanowires

YBaCuO nanowires were reproducibly fabricated down to widths of 50 nm. A Au/Ti cap layer on YBCO yielded high electrical performance up to temperatures above 80 K in single nanowires. Critical current density of tens of MA cm−2 at T = 4.2 K and of 10 MA cm−2 at 77 K were achieved that survive in high magnetic fields. Phase-slip processes were tuned by choosing the size of the nanochannels and the intensity of the applied external magnetic field. Data indicate that YBCO nanowires are a rather attractive system for the fabrication of efficient sensors, supporting the notion of futuristic THz devices.

Coulomb blockade due to quantum phase slips illustrated with devices

To illustrate the emergence of Coulomb blockade from coherent quantum phase-slip processes in thin superconducting wires, we propose and theoretically investigate two elementary setups, or devices. The setups are derived from the Cooper-pair box and Cooper-pair transistor, so we refer to them as the QPS box and QPS transistor, respectively. We demonstrate that the devices exhibit sensitivity to a charge induced by a gate electrode, this being the main signature of Coulomb blockade. Experimental realization of these devices will unambiguously prove the Coulomb blockade as an effect of coherence of phase-slip processes. We analyze the emergence of discrete charging in the limit of strong phase slips. We have found and investigated six distinct regimes that are realized depending on the relation between three characteristic energy scales: inductive energy, charging energy, and phase-slip amplitude. For completeness, we include a brief discussion of dual Josephson-junction devices.

Materials for superconducting nanowires for quantum phase-slip devices

Quantum phase-slip processes in superconducting nanowires of suitably small cross-section have been proposed as the basis for a new current standard, based on physics dual to that for the Josephson voltage standard. The practical realisation of such devices presents several challenges. We consider the requirements which need to be met in constructing a nanowire quantum-phase-slip device and in particular the need to maximise Rξ, the normal-state resistance of a length of nanowire equal to the superconducting coherence length. Titanium and niobium-silicon are promising materials for the nanowires.

Superconductivity of ultra-fine tungsten nanowires grown by focused-ion-beam direct-writing

The electrical properties of lateral ultra-fine tungsten nanowires, which were grown by focused-ion-beam-induced deposition with 1pA ion-beam current, were investigated. Temperature-dependent electrical measurements show that the wires are conducting and have a superconducting transition with a transition temperature (Tc) about 5.1K. Resistance vs. temperature measurements reveal that, with decreasing cross-sectional area, the wires display an increasingly broad superconducting transition. A residual resistive tail extending down to the low-temperature region is found only for the thinnest tungsten nanowire, which is 10nm thick and 19nm wide. The logarithm of the residual resistance of this wire appears as two linear sections as a function of temperature, one within 300mK below Tc and the other extending down to the lowest measuring temperature of 4.26K. Such features have previously been identified with phase slip processes. Our results are suggestive that the focused-ion-beam technique might be a potential approach to fabricate ultra-thin and ultra-narrow nanowires for the study of superconducting suppression in nanoscale materials and for maskless superconducting device fabrication.

Insights into phase-slip events via dynamics of current-induced transitions from a superconductive to a resistive state

Phase-slip fluctuations play a central role in a variety of systems and are responsible for dissipation via a loss of coherence. By virtue of these fluctuations, quasi-one-dimensional superconductors acquire a non-zero resistance unlike the bulk superconductors in which the resistance drops to zero upon entering the superconducting phase. The present generation of experiments on superconducting nanowires are capable of characterizing non only the thermally activated phase slips in detail, but also the quantum phase slip processes as well as the crossover from thermal to quantal. The proceeding will report on the recent progress made towards achieving this goal by studying the dynamics of current-induced transitions from superconductive to resistive state and analyzing the switching statistics.

Strong influence of nonlocal nonequilibrium effects on the dynamics of the order parameter in a phase-slip center: Ring studies

We study the influence of the inelastic relaxation time ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{E}$ of the quasiparticle distribution function $f(E)$ on the phase slip process in quasi-one-dimensional superconducting rings at a temperature close to the critical temperature ${T}_{c}$. We find that the initial time of growth of the order parameter $|\ensuremath{\Delta}|$ in the phase slip core after the phase slip is a nonmonotonic function of ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{E}$ which has a maximum at ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{E}\ensuremath{\simeq}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{GL}=\ensuremath{\pi}\ensuremath{\hbar}/8{k}_{B}({T}_{c}\ensuremath{-}T)$ and has a tendency to saturate for large ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{E}⪢{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{GL}$. The effective ``heating'' of the electron subsystem due to the increase in $|\ensuremath{\Delta}|$ in the phase slip center together with the above effect result in a nonmonotonic dependence of the number of subsequent phase slips on ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{E}$ in rings of relatively large radius (in which each phase slip reduces the current density to a small fraction of its initial value). During the phase slip process the order parameter distribution has two peaks near the phase slip core due to the diffusion of the nonequilibrium quasiparticles from that region.

Magnon Bose–Einstein condensation and spin superfluidity

Bose–Einstein condensation (BEC) is a quantum phenomenon of formation of a collectivequantum state in which a macroscopic number of particles occupy the lowest energy stateand thus is governed by a single wavefunction. Here we highlight the BEC in a magneticsubsystem—the BEC of magnons, elementary magnetic excitations. The magnon BEC ismanifested as the spontaneously emerging state of the precessing spins, in whichall spins precess with the same frequency and phase even in an inhomogeneousmagnetic field. The coherent spin precession was observed first in superfluid 3He-B and this domain was called the homogeneously precessing domain (HPD).The main feature of the HPD is the induction decay signal, which ranges overmany orders of magnitude longer than is prescribed by the inhomogeneity ofmagnetic field. This means that spins precess not with a local Larmor frequency, butcoherently with a common frequency and phase. This BEC can also be created andstabilized by continuous NMR pumping. In this case the NMR frequency playsthe role of a magnon chemical potential, which determines the density of themagnon condensate. The interference between two condensates has also beendemonstrated. It was shown that HPD exhibits all the properties of spin superfluidity. Themain property is the existence of a spin supercurrent. This spin supercurrentflows separately from the mass current. Transfer of magnetization by the spinsupercurrent by a distance of more than 1 cm has been observed. Also related phenomenahave been observed: the spin current Josephson effect; the phase-slip processes atthe critical current; and the spin current vortex—a topological defect which isthe analog of a quantized vortex in superfluids and of an Abrikosov vortex insuperconductors; and so on. It is important to mention that the spin supercurrent is amagnetic phenomenon, which is not directly related to the mass superfluidity of 3He: it is the consequence of a specific antiferromagnetic ordering in superfluid 3He. Several different states of coherent precession have been observed in 3He-B: the homogeneously precessing domain (HPD); a persistent signal formed byQ-balls at very low temperatures; coherent precession with fractionalmagnetization; and two new modes of coherent precession in compressedaerogel. In compressed aerogel the coherent precession has been also found in 3He-A. We demonstrate that the coherent precession of magnetization is a true BEC ofmagnons, with the magnon interaction term in the Gross–Pitaevskii equation beingprovided by spin–orbit coupling which is different for different states of the magnonBEC.

Influence of microwave irradiation on the dc resistive state of a wide superconducting film

The influence of a microwave field on the resistive state brought on in a wide film by the passage of a dc current is investigated experimentally. In this situation the resistivity arises as a consequence of two processes: the motion of Pearl–Abrikosov vortices of the self-magnetic field of the current, and phase slip of the superconducting order parameter. It is shown that under microwave irradiation the resistivity of the film due to the vortex mechanism decreases, and at high power levels (P>0.4Pc) it vanishes, and then the resistivity of the film is due solely to phase slip processes, as in narrow vortex-free channels. It is found experimentally that, starting at some power level P*<Pc, the electromagnetic field plays a governing role in the processes giving rise to phase-slip lines. A similar conclusion is reached from a study of the influence of a microwave field on the differential resistance of a phase-slip center in narrow vortex-free channels; this suggests that phase-slip processes in wide and narrow films share a common nature.

Phase-Slip Processes in Superconducting Films: AC Josephson Effect and New Phase Transition

The resistive direct current state in wide thin superconducting films as the phase transition from superconducting to normal state is investigated in the absence of external magnetic field. We showed that the states of a wide film with increasing transport current appear in the following order: the superconducting state; the resistive vortex state; the critical state; the new vortex-free resistive state with phase-slip lines; the normal state. We detected the Shapiro current steps on the current–voltage characteristic of the wide film, which arise due to interaction of intrinsic Josephson radiation of phase-slip lines with external microwave irradiation.