Critical Current Noise Research Articles

A Josephson junction with h-BN tunnel barrier: observation of low critical current noise

Decoherence in quantum bits (qubits) is a major challenge for realizing scalable quantum computing. One of the primary causes of decoherence in qubits and quantum circuits based on superconducting Josephson junctions is the critical current fluctuation. Many efforts have been devoted to suppressing the critical current fluctuation in Josephson junctions. Nonetheless, the efforts have been hindered by the defect-induced trapping states in oxide-based tunnel barriers and the interfaces with superconductors in the traditional Josephson junctions. Motivated by this, along with the recent demonstration of 2D insulator h-BN with exceptional crystallinity and low defect density, we fabricated a vertical NbSe2/h-BN/Nb Josephson junction consisting of a bottom NbSe2 superconductor thin layer and a top Nb superconductor spaced by an atomically thin h-BN layer. We further characterized the superconducting current and voltage (I–V) relationships and Fraunhofer pattern of the NbSe2/h-BN/Nb junction. Notably, we demonstrated the critical current noise (1/f noise power) in the h-BN-based Josephson device is at least a factor of four lower than that of the previously studied aluminum oxide-based Josephson junctions. Our work offers a strong promise of h-BN as a novel tunnel barrier for high-quality Josephson junctions and qubit applications.

Low-frequency critical current noise in graphene Josephson junctions in the open-circuit gate voltage limit

We investigate critical current noise in short ballistic graphene Josephson junctions in the open-circuit gate-voltage limit within the McWorther model. We find flicker noise in a wide frequency range and discuss the temperature dependence of the noise amplitude as a function of the doping level. At the charge neutrality point we find a singular temperature dependence T^{-3}, strikingly different from the linear dependence expected for short ballistic graphene Josephson junctions under fixed gate voltage.

1/f critical current noise in short ballistic graphene Josephson junctions

Short ballistic graphene Josephson junctions sustain superconducting current with a non-sinusoidal current-phase relation up to a critical current threshold. The current-phase relation, arising from proximitized superconductivity, is gate-voltage tunable and exhibits peculiar skewness observed in high quality graphene superconductors heterostructures with clean interfaces. These properties make graphene Josephson junctions promising sensitive quantum probes of microscopic fluctuations underlying transport in two-dimensions. We show that the power spectrum of the critical current fluctuations has a characteristic 1/f dependence on frequency, f, probing two points and higher correlations of carrier density fluctuations of the graphene channel induced by carrier traps in the nearby substrate. Tunability with the Fermi level, close to and far from the charge neutrality point, and temperature dependence of the noise amplitude are clear fingerprints of the underlying material-inherent processes. Our results suggest a roadmap for the analysis of decoherence sources in the implementation of coherent devices by hybrid nanostructures.

Noise Properties of YBCO Nanostructures

Voltage noise measurements on close to optimally doped YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7-δ</sub> nanostructures have been performed. The measured resistance noise at temperature T = 96 K (above critical temperature T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> = 85 K) shows a quadratic dependence on the bias current, e.g., the voltage power spectral density S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</sub> αV <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Moreover, the normalized voltage noise S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</sub> /V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> is inversely proportional to the device volume. This is a clear indication that the noise is the result of an ensemble of independent resistive fluctuators, evenly distributed within the sample volume. For our structures, we obtain a product S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</sub> /V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> × Vol. = const. ≈6 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-33</sup> m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> /Hz resulting in a Hooge's parameter 3.4 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> , which is among the lowest reported in literature. At lower temperature, T = 2 K (well below T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> ) the total voltage fluctuations are given by the combined effect of critical current fluctuations and resistance fluctuations. For the critical current noise, we obtain a product S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</sub> /I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> × Vol. = const. ≈6 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-32</sup> m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> /Hz. The larger value of the relative critical current noise is most probably due to the fact that the critical current is determined by edge effects whereas the resistance is given by the total volume of the device.

Critical Current Spread and Thermal Noise in Bi-SQUID Cells and Arrays

We report on the detailed analysis of thermal noise, critical current spread, and parasitic elements influences on the bi-SQUID voltage response and its linearity. These results together with the results of our previous studies serve as a useful guidance in designing high-performance bi-SQUIDs and bi-SQUID arrays implemented in low-temperature superconductor or high-temperature superconductor for many applications such as linear low-noise amplifiers and high-sensitivity antennas.

Low-frequency critical current noise in Josephson junctions induced by temperature fluctuations

We demonstrate a spurious contribution to low-frequency critical current noise in Josephson junctions—normally attributed to charge trapping in the barrier—arising from temperature instabilities inherent in cryogenic systems. These temperature fluctuations modify the critical current via its temperature dependence. Cross-correlations between measured temperature and critical current noise in Al-AlOx-Al junctions show that, despite excellent temperature stability, temperature fluctuations induce observable critical current fluctuations. Particularly, because 1/f critical current noise has decreased with improved fabrication techniques in recent years, it is important to understand and eliminate this additional noise source.

Hawking Radiation and Nonequilibrium Quantum Critical Current Noise

The dynamical scaling of quantum critical systems in thermal equilibrium may be inherited in the driven steady state, leading to universal out-of-equilibrium behavior. This attractive notion has been demonstrated in just a few cases. We demonstrate how holography-a mapping between the quantum critical system and a gravity dual-provides an illuminating perspective and new results. Nontrivial out-of-equilibrium universality is particularly apparent in current noise, which is dual to Hawking radiation in the gravitational system. We calculate this in a two-dimensional system driven by a strong in-plane electric field and deduce a universal scaling function interpolating between previously established equilibrium and far-from-equilibrium current noise. Since this applies at all fields, out-of-equilibrium experiments no longer require very high fields for comparison with theory.

Optimal operating conditions of an entangling two-transmon gate

We identify the optimal operating conditions of an entangling two-qubit gate realized by capacitive coupling of two superconducting charge qubits in a transmission line resonator (the so-called ‘transmons’). We demonstrate that the sensitivity of the optimized gate to 1/f flux and critical current noise is suppressed to leading order. The procedure only requires a preliminary estimate of the 1/f noise amplitudes. No additional control or bias line beyond those used for the manipulation of individual qubits is needed. The proposed optimization is effective also in the presence of relaxation processes and of spontaneous emission through the resonator (Purcell effect).

1/f noise of Josephson-junction-embedded microwave resonators at single photon energies and millikelvin temperatures

We present measurements of 1/f frequency noise in both linear and Josephson-junction-embedded superconducting aluminum resonators in the low power, low temperature regime—typical operating conditions for superconducting qubits. The addition of the Josephson junction does not result in additional frequency noise, thereby placing an upper limit for fractional critical current fluctuations of 1×10−8 (1/Hz) at 1 Hz for sub-micron, shadow evaporated junctions. These values imply a minimum dephasing time for a superconducting qubit due to critical current noise of 40–1400 μs depending on qubit architecture. Occasionally, at temperatures above 50 mK, we observe the activation of individual fluctuators which increase the level of noise significantly and exhibit Lorentzian spectra.

Investigation of Current Noise in Underdamped Josephson Devices by Switching Current Measurements

Experimental measurements on critical current noise in underdamped niobium based Josephson devices by a technique based on the switching current measurements is reported. By sweeping the junction with a current ramp we measure the critical current switching as a function of the time using the standard time of flight technique. In such a way it is possible to obtain the critical current fluctuations ΔIc=Ic(t)-<Ic(t)> and the relative standard deviations which corresponds to the root square of the current fluctuation power. Pointing at the white noise fluctuations (above few Hz) and taking into account the physical frequency of the device, it is possible to evaluate the power spectral density of the critical current. The analysis has involved high quality underdamped Josephson junctions having an area ranging from (4x4) μm 2 to (40x40) μm 2 in the temperature range from 4.2 K to few tenth of mK. These measurement provide very useful information about the intrinsic noise of Josephson devices involving SQUIDs and qubits.

Observation of High Coherence in Josephson Junction Qubits Measured in a Three-Dimensional Circuit QED Architecture

Superconducting quantum circuits based on Josephson junctions have made rapid progress in demonstrating quantum behavior and scalability. However, the future prospects ultimately depend upon the intrinsic coherence of Josephson junctions, and whether superconducting qubits can be adequately isolated from their environment. We introduce a new architecture for superconducting quantum circuits employing a three-dimensional resonator that suppresses qubit decoherence while maintaining sufficient coupling to the control signal. With the new architecture, we demonstrate that Josephson junction qubits are highly coherent, with T2 ∼ 10 to 20 μs without the use of spin echo, and highly stable, showing no evidence for 1/f critical current noise. These results suggest that the overall quality of Josephson junctions in these qubits will allow error rates of a few 10(-4), approaching the error correction threshold.

Critical current noise investigations in underdamped Josephson devices

An experimental investigation of the critical current noise in underdamped niobium based Josephson devices [junctions and Superconducting Quantum Interference Device (SQUID)] by a technique based on the switching current measurements is reported. By sweeping the junction with a current ramp we measure the critical current switching using the standard time of flight technique and analyze the data to extract the current noise. Measurements on Josephson junctions having an area ranging from (4 \ifmmode\times\else\texttimes\fi{} 4) to (40 \ifmmode\times\else\texttimes\fi{} 40) \ensuremath{\mu}m${}^{2}$ in the temperature range from 4.2 to 1.2 K are reported. The experimental results show a linear behavior of the current white noise from both the junction area and the temperature. These measurements provide very useful information about the intrinsic noise of Josephson devices involving SQUIDs and qubits.

Peak effect and dynamic melting transitions of driven vortex system in weakly disordered Josephson junction arrays

Using the resistively shunted junction model, we study the magnetic frustration induced dynamic melting transitions of a current-driven vortex system in two-dimensional weakly disordered Josephson juction arrays at zero temperature and very low temperatures. From the unified model simulations, we simultaneously obtain two kinds of dynamic melting transitions of the vortex flow, just below the vortex glass phase and above a dynamic melting threshold, respectively. The reenter pinned dilute vortex liquid behavior and the intrinsic quantum vortex liquid (QVL) phenomenon are also obtained, consistent with the recent experimental reports in disordered and superconducting MoGe films. The peak effect of critical current in the vortex glass is induced by intrinsic collective pinning effects in the plastic flow and the enhancement of critical current and voltage noise in the QVL phase arises from intrinsic quantum fluctuations in the moving vortex flow.

Experimental demonstration of a robust and scalable flux qubit

A novel rf-SQUID flux qubit that is robust against fabrication variations in Josephson junction critical currents and device inductance has been implemented. Measurements of the persistent current and of the tunneling energy between the two lowest lying states, both in the coherent and incoherent regime, are presented. These experimental results are shown to be in agreement with predictions of a quantum mechanical Hamiltonian whose parameters were independently calibrated, thus justifying the identification of this device as a flux qubit. In addition, measurements of the flux and critical current noise spectral densities are presented that indicate that these devices with Nb wiring are comparable to the best Al wiring rf-SQUIDs reported in the literature thusfar, with a $1/f$ flux noise spectral density at $1 $Hz of $1.3^{+0.7}_{-0.5} \mu\Phi_0/\sqrt{\text{Hz}}$. An explicit formula for converting the observed flux noise spectral density into a free induction decay time for a flux qubit biased to its optimal point and operated in the energy eigenbasis is presented.

High critical temperature superconductor Josephson junctions for quantum circuit applications

Recent findings of macroscopic quantum properties in high critical temperature superconductor (HTS) Josephson junctions (JJs) point toward the need to revise the role of zero energy quasi-particles in this novel superconductor. We will discuss the possibility of designing superconducting artificial atoms in a transmon configuration to study the low energy excitation spectra of HTS. We have engineered high quality grain boundary JJs on low dielectric constant substrates. By fabricating submicron junctions, we extract values of capacitance and Josephson critical current densities that satisfy the main transmon design requirements. Moreover, the measured critical current noise power extrapolated at 1 Hz gives a dephasing time of 25 ns, which indicates that the observation of macroscopic quantum coherent effects in HTS JJ is a feasible task.

Microscopic model of critical current noise in Josephson-junction qubits: Subgap resonances and Andreev bound states

We propose a microscopic model of critical current noise in Josephson junctions based on individual trapping centers in the tunnel-barrier hybridized with electrons in the superconducting leads. We calculate the noise exactly in the limit of no on-site Coulomb repulsion. Our result reveals a noise spectrum that is dramatically different from the usual Lorentzian assumed in simple models. We show that the noise is dominated by sharp subgap resonances associated to the formation of pairs of Andreev bound states, thus providing a possible explanation for the spurious two-level systems (microresonators) observed in Josephson-junction qubits [R. W. Simmonds et al., Phys. Rev. Lett. 93, 077003 (2004).]. Another implication of our model is that each trapping center will contribute a sharp dielectric resonance only in the superconducting phase, providing an effective way to validate our results experimentally. We derive an effective Hamiltonian for a qubit interacting with Andreev bound states, establishing a direct connection between phenomenological models and the microscopic parameters of a Fermionic bath.

Temperature dependence of critical current fluctuations in Nb/AlOx/Nb Josephson junctions

We measured the low frequency critical current noise in Nb/AlOx/Nb Josephson junctions. Unshunted junctions biased above the gap voltage and resistively shunted junctions biased near the critical current Ic have been measured. For both, the spectral density of δIc/Ic, Sic(f), is proportional to 1/f, scales inversely as the area A and is independent of Jc≡Ic/A over a factor of nearly 20 in Jc. For all devices measured at 4.2 K, Sic(1 Hz)=2.0±0.4×10−12/Hz when scaled to A=1 μm2. We find that, from 4.2 to 0.46 K, Sic(f) decreases linearly with temperature.

Microscopic Model of Critical Current Noise in Josephson Junctions

We present a simple microscopic model to show how fluctuating two-level systems in a Josephson junction tunnel barrier of thickness L can modify the potential energy of the barrier and produce critical current noise spectra. We find low frequency 1/f noise that goes as L5. Our values are in good agreement with recent experimental measurements of critical current noise in Al/AlOx/Al Josephson junctions. We also investigate the sensitivity of the noise on the nonuniformity of the tunnel barrier.

Comparison of High Temperature Superconducting Gradiometers Using Flip Chip YBCO and TBCCO Antennas

To optimize our high-temperature superconducting (HTSC)-dc-SQUID gradiometric sensors with galvanically-coupled antennas, we investigated the performance of antennas on a separate substrate. These antennas are inductively coupled to a dc-SQUID-gradiometer in a flip-chip configuration. Different combinations of thin-film and substrate materials, including Tl <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Ba <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> CaCu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> _ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> (TBCCO) on Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> or LaAlO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> and YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7-x</sub> (YBCO) on SrTiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , were used to produce antennas with variable layouts. These were then characterized concerning their critical current densities, critical temperature, and noise properties to demonstrate their suitability for high-resolution magnetic measurements in a flip-chip configuration. Field gradient resolution and noise properties of multiple dc-SQUID gradiometer antenna combinations were determined and compared.

Microscopic origin of critical current fluctuations in large, small, and ultra-small area Josephson junctions

We analyze data on the critical current and normal-state resistance noise in Josephson junctions and argue that the noise in the critical current is due to a mechanism that is absent in the normal state. We estimate the noise produced by conventional two level systems in the insulating barrier and find that it agrees both in magnitude and in temperature dependence with the resistance fluctuations in the normal state but it is not sufficient to explain the critical current noise observed in large superconducting contacts. We propose a microscopic mechanism for the noise in the superconducting state in which the noise is due to electron tunneling between weak Kondo states at subgap energies. We argue that the noise produced by this mechanism gives temperature, area dependence, and intensity that agree with the data.