Flux Noise Research Articles

Continuous-variable electromechanical quantum thermal transistors

Abstract We present a scheme to realize quantum thermal transistor effects in a continuous-variable electromechanical system including two microwave cavities and one mechanical oscillator. The thermal noise fluxes between the quantum system and its baths are evaluated by quantum master equation. It is shown that the thermal noise flux at one microwave cavity as an emitter can be dissipated into the other as a collector by combining the heating Stokes and cooling anti-Stokes processes. The indirect energy transfers between the two microwave modes can be significantly amplified by small energy changes at the mechanical oscillator as the base. The extremely high amplification depends sensitively on the detunings of the two microwave modes, which provides a new tool for precision measurements. This study opens the door for constructing quantum thermal transistors using various continuous-variable systems and is well accessible based on current experimental techniques.

Methods in fluctuation (noise) spectroscopy and continuous analysis for high-throughput measurements

Abstract Fluctuation (noise) spectroscopy is widely used to investigate the low-frequency dynamics of charge carriers in condensed-matter systems, aiming to (i) improve the performance of micro- and nanoscale electronic devices and sensors, and (ii) use ‘noise as a signal’ in order to fundamentally investigate the microscopic motion and transitions of charge carriers coupled to the low-lying excitations in solids. Here, we focus on measurements of the ubiquitous 1 / f -type fluctuations, often composed by a superposition of (independent or correlated) two-level systems each giving rise to a Lorentzian spectrum, denoted random telegraph noise in the time domain. We briefly review the basic concepts of noise and fluctuations and give a comprehensive overview of state-of-the-art measuring techniques, using both commercially available signal analyzers and custom software in order to perform the spectral analysis of the recorded time signals, and critically evaluate their advantages and drawbacks. We describe how to use fast data acquisition devices in a cross-correlation setup providing additional quantitative information on the magnitude of uncorrelated instrument noise, and demonstrate the mathematical intricacies of extracting the noise spectra. We introduce a new method for high-throughput measurements by automated spectral analysis based on the concept of Continuous Analysis. We demonstrate the potential of this technique, working towards a FAIR data workflow, by measurements of magnetic flux noise within the hysteresis loop of ferromagnetic nanostructures.

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

Noise Scaling in SQUID Arrays

Abstract We numerically investigate the noise scaling in high-T_c commensurate 1D and 2D SQUID arrays. We show that the voltage noise spectral density in 1D arrays violates the scaling rule of ~1/N_p for the number N_p of Josephson junctions in parallel. In contrast, in 2D arrays with N_s 1D arrays in series, the voltage noise spectral density follows more closely the expected scaling behaviour of ~N_s/N_p. Additionally, we reveal how the flux and magnetic field rms noise spectral densities deviate from their expected ~(N_sN_p)^{-1/2} scaling and discuss their implications for designing low noise magnetometers.

Flux-pulse-assisted readout of a fluxonium qubit

Much attention has focused on the transmon architecture for large-scale superconducting quantum devices; however, the fluxonium qubit has emerged as a possible successor. With a shunting inductor in parallel to a Josephson junction, the fluxonium offers larger anharmonicity and stronger protection against dielectric loss, leading to higher coherence times as compared to conventional transmon qubits. The interplay between the inductive and Josephson energy potentials of the fluxonium qubit leads to a rich dispersive-shift landscape when tuning the external flux. Here, we propose to exploit the features in the dispersive shift to improve qubit readout. Specifically, we report on theoretical simulations showing improved readout times and error rates by performing the readout at a flux-bias point with large dispersive shift. We expand the scheme to include different error channels and show that with an integration time of 155 ns, flux-pulse-assisted readout offers about a 5-times improvement in the signal-to-noise ratio. Moreover, we show that the performance improvement persists in the presence of finite measurement efficiency combined with quasistatic flux noise and also when considering the increased Purcell rate at the flux-pulse-assisted readout point. We suggest a set of reasonable energy parameters for the fluxonium architecture that will allow for the implementation of our proposed flux-pulse-assisted readout scheme. Published by the American Physical Society 2024

Flux-tunable regimes and supersymmetry in twisted cuprate heterostructures

Van der Waals assembly allows for the creation of Josephson junctions in an atomically sharp interface between two exfoliated Bi2Sr2CaCu2O8+δ (Bi-2212) flakes that are twisted relative to each other. In a narrow range of angles close to 45°, the junction exhibits a regime where time-reversal symmetry can be spontaneously broken, and it can be used to encode an inherently protected qubit called flowermon. In this work, we investigate the physics emerging when two such junctions are integrated in a superconducting quantum interference device circuit threaded by a magnetic flux. We show that the flowermon qubit regime is maintained up to a finite critical value of the magnetic field, and, under appropriate conditions, it is protected against both charge and flux noise. For larger external fluxes, the interplay between the inherent twisted d-wave nature of the order parameter and the external magnetic flux enables the implementation of different artificial atoms, including a flux-biased protected qubit and a supersymmetric quantum circuit.

NbTiN SQUID-on-tip fabricated by self-aligned deposition using reactive DC magnetron sputtering

We fabricate superconducting quantum interference devices (SQUIDs) made of niobium-titanium nitride (NbTiN) thin films on the apex of sharp quartz capillaries. By incorporating reactive DC magnetron sputtering into the self-aligned deposition process for the SQUID-on-tip (SOT) fabrication, we produce NbTiN SOT devices with an effective diameter of ∼100 nm. The ø110 nm device has a superconducting transition temperature of 13.2 K, magnetic flux noise down to 0.7 μΦ0/Hz0.5 (4 K), and operating temperatures of 1.8–10 K. The developed technique enables the synthesis of nitride and other superconductors, thereby expanding the range of materials available for SOT devices.

Parity-spin superconducting qubit based on topological insulators

We propose to utilize two parity-protected qubits which are built based on superconductor/topological-insulator/superconductor (SC/TI/SC) Josephson junction to implement a parity-spin superconducting qubit. The SC/TI/SC Josephson junctions have identical Josephson potential, which is robust against fabrication variations and guarantees the reliable cos⁡2ϕ energy-phase relation for implementing a parity-protected qubit. By viewing the even and odd parity ground states of a single parity-protected qubit as spin- 12 states, we construct the logic qubit states using the total parity odd subspace of two parity-protected qubits, refereed to parity-spin qubit. This parity-spin qubit exhibits robustness against charge noise, similar to a singlet-triplet (S-T) qubit’s immunity to global magnetic field fluctuations. Meanwhile, the flux noise cannot directly couple two states with the same total parity and is significantly suppressed. Benefiting from the simultaneous protection from charge and flux noise, we demonstrate an enhancement of both T 1 and T 2 coherence times. Our work presents a TI-based approach to engineer symmetry-protected superconducting qubits.

Kinetic Inductance Traveling Wave Amplifier Designs for Practical Microwave Readout Applications

A Kinetic Inductance Traveling Wave Amplifier (KIT) utilizes the nonlinear kinetic inductance of superconducting films, particularly niobium titanium nitride (NbTiN), for parametric amplification. These amplifiers achieve remarkable performance in terms of gain, bandwidth, and compression power and frequently approach the quantum limit for noise. However, most KIT demonstrations have been isolated from practical device readout systems. Using a KIT as the first amplifier in the readout chain of an unoptimized microwave SQUID multiplexer coupled to a transition-edge sensor microcalorimeter, we see an initial improvement in the flux noise [1]. One challenge in KIT integration is the considerable microwave pump power required to drive the non-linearity. To address this, we have initiated efforts to reduce the pump power by using thinner NbTiN films and an inverted microstrip transmission line design. In this article, we present the new transmission line design, fabrication procedure, and initial device characterization—including gain and added noise. These devices exhibit over 10 dB of gain with a 3 dB bandwidth of approximately 5.5–7.25 GHz, a maximum practical gain of 12 dB, and typical gain ripple under 4 dB peak to peak. We observe an appreciable impedance mismatch in the NbTiN transmission line, which is likely the source of the majority of the gain ripple. Finally, we perform an initial noise characterization and demonstrate system-added noise of three quanta or less over nearly the entire 3 dB bandwidth.

Gottesman-Kitaev-Preskill State Preparation Using Periodic Driving.

The Gottesman-Kitaev-Preskill (GKP) code may be used to overcome noise in continuous variable quantum systems. However, preparing GKP states remains experimentally challenging. We propose a method for preparing GKP states by engineering a time-periodic Hamiltonian whose Floquet states are GKP states. This Hamiltonian may be realized in a superconducting circuit comprising a SQUID shunted by a superinductor and a capacitor, with a characteristic impedance twice the resistance quantum. The GKP Floquet states can be prepared by adiabatically tuning the frequency of the external magnetic flux drive. Wepredict that highly squeezed >11.9 dB (10.8dB) GKP magic states can be prepared on a microsecond timescale, given a quality factor of 10^{6} (10^{5}) and flux noise at typical rates.

Quantum analysis of a Mach–Zehnder interferometer with propagating a single photon Gaussian wave packet

In this paper, a Mach–Zehnder interferometer is analyzed with a single photon Gaussian wave packet at one of its input ports and vacuum state at the other input port. Various noises arising in the Mach–Zehnder interferometer such as photon flux noise and quadrature noise are mathematically analyzed. The effect of variation in device parameters on the power spectral density at the output ports of the Mach–Zehnder interferometer is studied. It is observed that the power spectral density of photon flux noise autocorrelation at the output ports of a Mach–Zehnder interferometer is a function of phase shift, whereas the power spectral density of quadrature noise autocorrelation at the output ports of a Mach–Zehnder interferometer is a function of frequency of a single photon wave packet and the phase shift. The analysis carried out in this paper will be helpful in understanding the quantum fluctuations in the design of quantum logic devices and circuits where the Mach–Zehnder interferometer is a core building block.

Inverse estimation of heat flux and temperature field for a nonlinear heat transfer system using step-renewed two-stage Kalman filter

Inverse estimation of the thermal input and states is a useful tool for the monitoring of a thermal system. Nonlinear heat transfer is a quite common issue in this kind of problem. As the thermal properties are temperature-dependent, it is difficult to inversely estimate the input and temperature field. To deal with this problem, a step-renewed scheme is adopted into the weighted optimal two-stage Kalman filter (WOTSKF), forming step-renewed WOTSKF (SR-WOTSKF). This strategy is a marching method, without solving the Jacobian matrix in extended Kalman filter. The feasibility of dealing with the nonlinear inverse heat transfer problem is implemented by comparing WOTSKF and SR-WOTSKF. Then, the weighting factor, initial guess of the input heat flux and measurement noise are changed to investigate their effects on the simultaneous estimation results of heat flux and temperature field. It is found that when the weighting factor is 0.95, the relative error of the estimated heat flux using SR-WOTSKF is approximately 2.73% which is much lower than that using WOTSKF. Results using SR-WOTSKF demonstrate that the estimation results are independent of the initial guess and the estimated heat flux can track the exact one in a short period. An incorrect initial guess causes the initial estimation error of the temperature and heat flux and it makes no sense to following period. When the standard deviations of the measurement noise are adopted as 0.01, 0.10, 0.50 and 1.00, the mean relative error of the heat flux is 2.73%, 4.79%, 7.71% and 9.43%, demonstrating the strong robustness of SR-WOTSKF to resist the measurement noise.

Robust Predictive Current Control of PMSG Wind Turbines with Sensor Noise Suppression

Model predictive control (MPC) is an efficient and multi-functional control scheme for synchronous permanent magnet generators (PMSGs). However, the effective management of traditional MPC depends on precise system models. Multiple uncertainties of permanent magnet flux, motor inductance, filter inductance and parameter measurement noise will limit MPC’s performance. The conventional linear extended state observer (ESO) can perform robust predictive control of the ultralocal model of the PMSG system to cope with parameter mismatches. However, the ESO is limited in balancing disturbance rejection with measurement noise attenuation. Since the amplification of high-frequency noise pollution can lead to both poor control performance and system instability, this challenge is of significant importance. To solve the problem, a new hybrid parallel cascaded ESO (PCESO) model-free predictive control framework is proposed using the three-level neutral-point-clamped (NPC) power electronic converter, on both the machine side and grid side. Analytical discussions of the time and frequency domain characteristics of the PCESO demonstrate its superior characteristics over the ESO. The proposed method can effectively balance parameter mismatch, disturbance rejection and high-frequency noise suppression. Finally, the effectiveness of the proposed method, under uncertainties of parameter mismatches, measurement noise and permanent magnet flux, is verified through real-time hardware-in-the-loop tests on a back-to-back grid-tied PMSG interfaced with an NPC power converter.

Evolution of 1/f Flux Noise in Superconducting Qubits with Weak Magnetic Fields.

The microscopic description of 1/f magnetic flux noise in superconducting circuits has remained an open question for several decades despite extensive experimental and theoretical investigation. Recent progress in superconducting devices for quantum information has highlighted the need to mitigate sources of qubit decoherence, driving a renewed interest in understanding the underlying noise mechanism(s). Though a consensus has emerged attributing flux noise to surface spins, their identity and interaction mechanisms remain unclear, prompting further study. Here, we apply weak in-plane magnetic fields to a capacitively shunted flux qubit (where the Zeeman splitting of surface spins lies below the device temperature) and study the flux-noise-limited qubit dephasing, revealing previously unexplored trends that may shed light on the dynamics behind the emergent 1/f noise. Notably, we observe an enhancement (suppression) of the spin-echo (Ramsey) pure-dephasing time in fields up to B=100 G. With direct noise spectroscopy, we further observe a transition from a 1/f to approximately Lorentzian frequency dependence below 10Hz and a reduction of the noise above 1MHz with increasing magnetic field. We suggest that these trends are qualitatively consistent with an increase of spin cluster sizes with magnetic field. These results should help to inform a complete microscopic theory of 1/f flux noise in superconducting circuits.

Model for 1/f flux noise in superconducting aluminum devices: Impact of external magnetic fields

Superconducting quantum interference devices and related circuits made of aluminum are known to display 1/ω flux noise, where ω is frequency. A recent experiment showed that the application of an external magnetic field in the 10–100 G range changed the noise to a single Lorentzian peaked at ω = 0. Here, it is shown that a model based on independent impurity spin flips with coexisting cross and direct mechanisms of spin relaxation may explain these experiments. The model shows that application of an external magnetic field can be used to reduce the impact of flux noise in qubits.

Fabrication of Nb and MoGe SQUID-on-tip probes by magnetron sputtering

We demonstrate the fabrication of scanning superconducting quantum interference devices (SQUIDs) on the apex of sharp quartz scanning probes—known as SQUID-on-tip probes—using conventional magnetron sputtering. We produce and characterize SQUID-on-tips made of both Nb and MoGe with effective diameters ranging from 50 to 80 nm, magnetic flux noise down to 300 nΦ0/Hz, and operating fields as high as 2.5 T. Compared to the SQUID-on-tip fabrication techniques used until now, including thermal evaporation and collimated sputtering, this simplified method facilitates experimentation with different materials, potentially expanding the functionality and operating conditions of these sensitive nanometer-scale scanning probes.

Design and Fabrication of Two-stage SQUID for Transition Edge Sensor

The X-ray transition edge sensor (TES) modeled by calorimeter is extremely sensitive to temperature changes when operating at a voltage bias in the temperature region, and is widely used for the detection of particles and photons from submicron frequency to gamma rays. Superconducting quantum interference device (SQUID) is the key to TES current signal readout, we have designed a two-stage SQUID amplifier circuit. First-stage sensor SQUID uses first-grade gradiometer with high input mutual inductance about 176.2 , it increases the coupling sensitivity with the TES detector and has stronger resistance to external interference. Second-stage SQUID array(SSA) adopts 32 single SQUIDs in series, which has low magnetic flux noise and high magnification. We have verified the characteristics of this two-stage circuit and demonstrated that it has a lower magnetic flux noise.

The Role of Atmospheric Noise in Decadal SST Variability

Abstract A substantial role for atmospheric noise in simulations of decadal internal variability of SST is demonstrated by a comparison of a multicentury climate model control and a corresponding interactive ensemble (IE) simulation. The IE is designed to reduce atmospheric noise in the heat flux, wind stress, and freshwater flux at the air–sea interface. This comparison suggests that nearly all SST variability on decadal time scales is forced by internal atmospheric variability. The results are examined to determine the relative roles of atmospheric surface heat flux noise and ocean dynamics in the decadal volume-averaged heat budget of the upper ocean. The regional heat budgets in two regions, the South Pacific and the midlatitude North Atlantic, show the net atmospheric surface heat flux to be approximately in equilibrium with the ocean dynamics forcing. The IE and control results are used in the equilibrium heat budget approximation to infer the atmospheric heat flux response to SST, as well as the time series of the control atmospheric noise surface heat flux and ocean dynamics forcings for several regions. The South Pacific region SST is found to be primarily forced by the atmospheric noise surface heat flux and the North Atlantic region SST is forced by the ocean dynamics. Similar strengths for the atmospheric heat flux noise and ocean dynamics forcing, with an interdecadal atmospheric heat flux noise time scale and a centennial ocean dynamics time scale, are found for an Atlantic multidecadal variability region SST.

Highly Sensitive Tunable Magnetometer Based on Superconducting Quantum Interference Device

In the present article, experimental results regarding fully integrated superconducting quantum interference devices (SQUID), including a circuit to tune and optimize the main sensor device characteristics, are reported. We show the possibility of modifying the critical current of a SQUID magnetometer in liquid helium by means of a suitable heating circuit. This allows us to improve the characteristics of the SQUID sensor and in particular to optimize the voltage-magnetic flux characteristic and the relative transfer factor (responsivity) and consequently to also improve the flux and magnetic field noise. It is also possible to reset the SQUID sensor in case of entrapment of magnetic flux, avoiding taking it out of the helium bath. These results are very useful in view of most SQUID applications such as those requiring large multichannel systems in which it is desirable to optimize and eventually reset the magnetic sensors in a simple and effective way.

Tunable Superconducting Flux Qubits with Long Coherence Times

In this work, we study a series of tunable flux qubits inductively coupled to a coplanar waveguide resonator fabricated on a sapphire substrate. Each qubit includes an asymmetric superconducting quantum interference device which is controlled by the application of an external magnetic field and acts as a tunable Josephson junction. The tunability of the qubits is typically $\pm 3.5$ GHz around their central gap frequency. The measured relaxation times are limited by dielectric losses in the substrate and can attain $T_{1}\sim 8 \mu s$. The echo dephasing times are limited by flux noise even at optimal points and reach $T_{2E}\sim 4 \mu s$, almost an order of magnitude longer than state of the art for tunable flux qubits.