Phase slips are topological fluctuation events that carry the superconducting order-parameter field between distinct current carrying states 1 . Owing to these phase slips low-dimensional superconductors acquire electrical resistance 2 . In quasi-one-dimensional nanowires it is well known that at higher temperatures phase slips occur via the process of thermal barrier-crossing by the orderparameter field. At low temperatures, the general expectation is that phase slips should proceed via quantum tunnelling events, which are known as quantum phase slips (QPS). However, resistive measurements have produced evidence both pro 3-6 and con [7][8][9] and hence the precise requirements for the observation of QPS are yet to be established firmly. Here we report strong evidence for individual quantum tunnelling events undergone by the superconducting order-parameter field in homogeneous nanowires. We accomplish this via measurements of the distribution of switching currents-the high-bias currents at which superconductivity gives way to resistive behaviour-whose width exhibits a rather counter-intuitive, monotonic increase with decreasing temperature. We outline a Quantum phenomena involving systems far larger than individual atoms are one of the most exciting fields of modern physics. Initiated by Leggett more than twentyfive years ago 14,15 , the field has seen widespread development, important realizations being furnished, e. g., by macroscopic quantum tunnelling (MQT) of the phase in Josephson junctions, and of the magnetization in magnetic nanoparticles [16][17][18][19] . More recently, the breakthrough recognition of the potential advantages of quantum-based computational methods has initiated the search for viable implementations of qubits 20 , several of which are rooted in MQT in superconducting systems. In particular, it has been recently proposed that superconducting nanowires (SCNWs) could provide a valuable setting for realizing qubits 12 . In this case, the essential behaviour needed of SCNWs that they undergo QPS, i.e., topological quantum fluctuations of the superconducting order-parameter field via which tunnelling occurs between currentcarrying states. It has also been proposed that QPS in nanowires could allow one to build a current standard, and thus could play a useful role in aspects of metrology 13 .Additionally, QPS are believed to provide the pivotal processes underpinning the 3 superconductor-insulator transition observed in nanowires 21-25, Observations of QPS have been reported previously on wires having high normal resistance (i.e., R N > R Q , where R Q = h/4e 2 ≈ 6,450 Ω) via low-bias resistance (R) vs. temperature (T) measurements 3,4 . Yet, low-bias measurements on short wires with normal resistance R N < R Q have been unable to reveal QPS 7,8 . Also, it has been suggested that some results ascribed to QPS could in fact have originated in inhomogeneity of the nanowires.Thus, no consensus exists about the conditions under which QPS occur, and qualitatively new evidence for QPS remains highl...

Superconducting nanowires fabricated via carbon-nanotube-templating can be used to realize and study quasi-one-dimensional superconductors. However, measurement of the linear resistance of these nanowires have been inconclusive in determining the low-temperature behavior of phase-slip fluctuations, both quantal and thermal. Thus, we are motivated to study the nonlinear currentvoltage characteristics in current-biased nanowires and the stochastic dynamics of superconductiveresistive switching, as a way of probing phase-slip events. In particular, we address the question: Can a single phase-slip event occurring somewhere along the wire-during which the order-parameter fluctuates to zero-induce switching, via the local heating it causes? We explore this and related issues by constructing a stochastic model for the time-evolution of the temperature in a nanowire whose ends are maintained at a fixed temperature. We derive the corresponding master equation as tool for evaluating and analyzing the mean switching time at a given value of current (smaller than the de-pairing critical current). The model indicates that although, in general, several phaseslip events are necessary to induce switching via a thermal runaway, there is indeed a regime of temperatures and currents in which a single event is sufficient. We carry out a detailed comparison of the results of the model with experimental measurements of the distribution of switching currents, and provide an explanation for the rather counter-intuitive broadening of the distribution width that is observed upon lowering the temperature. Moreover, we identify a regime in which the experiments are probing individual phase-slip events, and thus offer a way of unearthing and exploring the physics of nanoscale quantum tunneling of the one-dimensional collective quantum field associated with the superconducting order parameter.

We report measurements of switching current distribution ͑SWCD͒ from a phase-diffusion branch ͑PDB͒ to a quasiparticle-tunneling branch ͑QTB͒ as a function of temperature in a cuprate-based intrinsic Josephson junction. Contrary to the thermal-activation model, the width of the SWCD increases and the corresponding switching rate shows a nonlinear behavior with a negative curvature in a semilogarithmic scale with decreasing temperature down to 1.5 K. Based on the multiple-retrapping model, we quantitatively demonstrate that the frequency-dependent junction quality factor, representing the energy dissipation in a phase-diffusion regime, determines the observed temperature dependence of the SWCD and the switching rate. We also show that a retrapping process from the QTB to the PDB is related to the low-frequency limit damping.

Microwave response of S-shaped Bi 2 Sr 2 CaCu 2 O 8+x (BI-2212) micron-scale samples, in which the supercurrent was forced to flow perpendicular to the crystal layers, was investigated. A treatment with a focused ion beam allowed us to reduce the plasma frequency down to f p~5 GHz at T=0.3 K in naturally stacked Josephson junctions in a crystal. We observed Shapiro steps at frequencies as low as ~5 GHz. Well-developed zero-crossing Shapiro steps were observed at frequencies as low as ~10 GHz. They appeared as constant-voltage plateaus with a non-zero voltage occurring at zero bias current. We confirmed that zero-crossing Shapiro steps in the Bi-2212 stacked junctions can be observed when the irradiated frequency is sufficiently larger than f p . The observed high-order fractional steps in the microwave responses indicate that the interlayer-coupled Bi-2212 Josephson junctions have nonsinusoidal current-phase relation. Based on the temperature dependence of the steps we also showed that the 2 finite slope of the steps is due to the enhancement of the phase diffusion effect.

We study current-voltage (V-I) characteristics of short superconducting nanowires of length ∼ 100 nm exposed to microwave (MW) radiation of frequencies between 2 and 15 GHz. The radiation causes a decrease of the average switching current of the wire. This suppression of the switching current is modeled assuming that there is one-to-one correspondence between Little's phase slips, which are microscopic stochastic events induced by thermal and quantum fluctuations, and the experimentally observed switching events. We also find that at some critical power P * of the radiation a dissipative dynamic superconducting state occurs as an extra step on the V-I curve. It is identified as a phase slip center (PSC), which is essentially a deterministic and periodic in-time phase rotation. With the dependence of the switching currents and the standard deviations observed at the transitions: (i) from the supercurrent state to the normal state and (ii) from the supercurrent state to the PSC regime, we conclude that both of the two types of switching events are triggered by the same microscopic event, namely a single-phase slip. We show that the Skocpol-Beasley-Tinkham model is not applicable to our MW-driven PSCs, probably due to the tendency of the PSC to synchronize with the MW. Through the analysis of the switching current distributions at a sufficiently low temperature, we also present evidence that quantum phase slips play a role in switching events even under MWs.