Abstract A superconducting quantum interference device with differential output or ‘DSQUID’ was previously proposed for operation in the presence of large common-mode signals. The DSQUID is the differential connection of two identical SQUIDs. Here we show that besides suppression of electromagnetic interference this device provides effective linearization of the DC SQUID voltage response. In the frame of the resistive shunted junction model with zero capacitance, we demonstrate that spur-free dynamic range of the DSQUID magnetic flux-to-voltage transfer function is higher than 100 dB while the total harmonic distortion of a signal is less than 10 −3 % with a peak-to-peak amplitude of a signal being a quarter of half flux quantum, 2Φ a = Φ 0 /8. Analysis of the DSQUID voltage response stability to a variation of circuit parameters shows that DSQUID implementation allows for highly linear magnetic flux-to-voltage transformation at the cost of a high identity of Josephson junctions and high-precision current supply.
Abstract A superconducting quantum interference device with differential output or ‘DSQUID’ was previously proposed for operation in the presence of large common-mode signals. The DSQUID is the differential connection of two identical SQUIDs. Here we show that besides suppression of electromagnetic interference this device provides effective linearization of the DC SQUID voltage response. In the frame of the resistive shunted junction model with zero capacitance, we demonstrate that spur-free dynamic range of the DSQUID magnetic flux-to-voltage transfer function is higher than 100 dB while the total harmonic distortion of a signal is less than 10 −3 % with a peak-to-peak amplitude of a signal being a quarter of half flux quantum, 2Φ a = Φ 0 /8. Analysis of the DSQUID voltage response stability to a variation of circuit parameters shows that DSQUID implementation allows for highly linear magnetic flux-to-voltage transformation at the cost of a high identity of Josephson junctions and high-precision current supply.
The dynamics and noise of a dc SQUID (the Superconducting Quantum Interference Device), with the McCumber parameter /spl beta//sub c/=2/spl pi/R/sup 2/l/sub c/C//spl Phi//sub 0/ close to the unity (where I/sub c/, R, C is the critical current, the shunt resistance and the capacitance of the Josephson junctions comprising the SQUID, respectively, /spl Phi//sub 0/=2.07 10/sup -15/ Wb is the magnetic flux quantum) integrated with a planar spiral input coil, have been experimentally studied. The length of the spiral input coil was chosen so as to match its /spl lambda//4 microwave resonance frequency to the plasma resonance frequency of the SQUID. The input coil resonance is found to enhance the overall quality factor Q of the Josephson oscillations in the SQUID and, as a result, to increase the dynamic resistance R/sub d/ and the gradient of the flux-to-voltage characteristics, /spl delta/V//spl delta//spl Phi/, without hysteresis. A dc SQUID with a loop inductance L=30.5 pH, /spl beta//sub c/=0.72, and a 6 turn input coil demonstrated a non-distorted quasi-sinusoidal flux-to-voltage transfer function with an exceptionally large modulation depth of 140 /spl mu/V peak-to-peak. The spectral density of the magnetic flux noise was as low as 3.5/spl times/10/sup -7/ /spl Phi//sub 0//Hz/sup 1/2/ in the double stage configuration, measured at a temperature 4.2 K using direct read out electronics. In combination with an intermediary transformer, the current resolution of the SQUID is as low as 1.25 pA/Hz/sup 1/2/ with an input coil inductance of 100 nH.
Superconducting double-loop interferometers (bi-SQUIDs) have been introduced to produce magnetic flux sensors specifically designed to exhibit an ultrahighly linear voltage response as a function of the magnetic flux. These devices are very important for quantum sensing and for signal processing of signals oscillating in the radio-frequency range of the electromagnetic spectrum. Here, we report an Al double-loop bi-SQUID based on proximitized mesoscopic Cu Josephson junctions. Such a scheme provides an alternative fabrication approach to conventional tunnel-junction-based interferometers, where the junction characteristics and, consequently, the magnetic-flux-to-voltage and magnetic-flux-to-critical-current device responses can be largely and easily tailored by the geometry of the metallic weak links. We discuss the performance of such sensors by showing a full characterization of the device switching current and voltage drop versus the magnetic flux for operation temperatures ranging from 30 mK to approximately 1K. The figures of merit of the transfer function and of the total harmonic distortion are also discussed. The latter provides an estimate of the linearity of the flux-to-voltage device response, which attains values as large as 45 dB. Such a result lets us foresee a performance already on par with that achieved in conventional tunnel-junction-based bi-SQUIDs arrays composed of hundreds of interferometers.
We experimentally studied two important parameters of helium-cooled superconducting quantum interference devices (SQUIDs) in the voltage bias mode: the dynamic resistance Rd and the flux-to-current transfer coefficient ∂i/∂Φ, with different junction shunt resistors RJ. We investigated a voltage-biased SQUID using the direct readout current-to-voltage converter scheme involving an operational amplifier. At higher RJ, the flux-to-voltage conversion coefficient ∂V/∂Φ becomes sufficiently large to effectively suppress the room-temperature amplifier's noise without any need for additional feedback circuits. The McCumber parameter limits the rise of ∂V/∂Φ. We discuss the performance of voltage-biased SQUIDs at different effective McCumber parameters.
The dynamics and noise of a dc superconducting quantum interference device (SQUID) with the McCumber parameter βc=2πR2IcC/Φ0 close to the unity (where Ic, R, C are the critical current, the shunt resistance, and the capacitance of the Josephson junctions comprising the SQUID, respectively, and Φ0=2.07×10−15 Wb is the magnetic flux quantum) integrated with a planar spiral input coil have been experimentally studied. The length of the spiral input coil was chosen to match its λ/4 microwave resonance frequency to the plasma resonance frequency of the SQUID. The input coil resonance enhances the overall quality factor Q of the Josephson oscillations in the SQUID and, as a result, increases the dynamic resistance Rd and the gradient of the flux-to-voltage characteristics ∂V/∂Φ without hysteresis. This relaxes the tolerance for the βc parameter, simplifies the technological process, and improves the yield of devices. A dc SQUID with loop inductance L=31.4 pH, βc=0.72, and a six turn input coil has demonstrated a nondistorted quasisinusoidal flux-to-voltage transfer function with an exceptionally large modulation depth of approximately 140 μV peak-to-peak. A spectral density of the intrinsic magnetic flux noise as low as 3.5×10−7 Φ0/Hz1/2 has been measured in the double stage configuration at a temperature of 4.2 K using direct read-out electronics. This corresponds to the intrinsic energy resolution of ε=12.5h. In combination with an intermediary transformer, the current resolution of the SQUID is as low as 1.25 pA/Hz1/2 with an input coil inductance of 58 nH. The coupled energy resolution is εc=45h in the white noise region.
Recent experiments on superconducting flux qubits, consisting of a superconducting loop interrupted by Josephson junctions, have demonstrated quantum coherence between two different quantum states. The state of the qubit is measured with a superconducting quantum interference device (SQUID). Such measurements require the SQUID to have high resolution while exerting minimal backaction on the qubit. By designing shunts across the SQUID junctions appropriately, one can improve the measurement resolution without increasing the backaction significantly. Using a path-integral approach to analyze the Caldeira-Leggett model, we calculate the narrowing of the distribution of the switching events from the zero-voltage state of the SQUID for arbitrary shunt admittances, focusing on shunts consisting of a capacitance Cs and resistance Rs in series. To test this model, we fabricated a dc SQUID in which each junction is shunted with a thin-film interdigitated capacitor in series with a resistor, and measured the switching distribution as a function of temperature and applied magnetic flux. After accounting for the damping due to the SQUID leads, we found good agreement between the measured escape rates and the predictions of our model. We analyze the backaction of a shunted symmetric SQUID on a flux qubit. For the given parameters of our SQUID and realistic parameters for a flux qubit, at the degeneracy point we find a relaxation time of $113\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which limits the decoherence time to $226\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. Based on our analysis of the escape process, we determine that a SQUID with purely capacitive shunts should have narrow switching distributions and no dissipation.
Possible approaches to the creation of Josephson superconducting circuits with a high linearity of transformation of a magnetic signal into voltage and a wide dynamic range have been described. Realization of such circuit by the creation of a special spatial inhomogeneity in chains of Josephson junctions and connection of these chains into a differential circuit has been considered. A new method for linearizing the transfer function of a single two-junction superconducting quantum interference device, which is an elementary cell of the chain, by connecting to it an additional loop playing the role of a nonlinear transformer of the magnetic flux has been described. For both approaches, the basic analytical expressions describing the synthesized circuits are presented. The data on numerical calculation and experimental measurements of samples produced on the basis of niobium technology with the critical current density of Josephson junctions of 4.5 kA/cm 2 are reported. The approaches developed in the work can serve as a basis for the creation of highly efficient gigahertz superconducting amplifiers for cellular and satellite communications and can be applied for improving the characteristics of SQUID-based devices.