Superconducting Quantum Interference Devices Inductance Research Articles

Observation of Broadband Entanglement in Microwave Radiation from a Single Time-Varying Boundary Condition.

Entangled pairs of microwave photons are commonly produced in the narrow frequency band of a resonator, which represents a modified vacuum density of states. We generate and investigate the entanglement of a stream of photon pairs, generated in a semi-infinite broadband transmission line, terminated by a superconducting quantum interference device (SQUID). A weak pump signal modulates the SQUID inductance, resulting in a single time-varying boundary condition, and we detect all four quadratures of the microwave radiation emitted at two different frequencies separated by 0.7GHz. Power calibration is done insitu, and we find positive logarithmic negativity and two-mode squeezing below the vacuum in the observed radiation, indicating entanglement.

The role of kinetic inductance on the performance of YBCO SQUID magnetometers

Inductance is a key parameter when optimizing the performance of superconducting quantum interference device (SQUID) magnetometers made from the high temperature superconductor YBa2Cu3O7−x (YBCO) because lower SQUID inductance L leads to lower flux noise, but also weaker coupling to the pickup loop. In order to optimize the SQUID design, we combine inductance simulations and measurements to extract the different inductance contributions, and measure the dependence of the transfer function VΦ and flux noise on L. A comparison between two samples shows that the kinetic inductance contribution varies strongly with film quality, hence making inductance measurements a crucial part of the SQUID characterization. Thanks to the improved estimation of the kinetic inductance contribution, previously found discrepancies between theoretical estimates and measured values of VΦ and could to a large extent be avoided. We then use the measurements and improved theoretical estimations to optimize the SQUID geometry and reach a noise level of = 44 fT/ for the best SQUID magnetometer with a 8.6 mm × 9.2 mm directly coupled pickup loop. Lastly, we demonstrate a method for reliable one-time sensor calibration that is constant in a temperature range of several kelvin despite the presence of temperature dependent coupling contributions, such as the kinetic inductance. The found variability of the kinetic inductance contribution has implications not only for the design of YBCO SQUID magnetometers, but for all narrow linewidth SQUID-based devices operated close to their critical temperature.

Effect of critical current spread on the noise performance of SQUID magnetometers: An experimental study

We investigate the noise performance dependence on the critical current spread of a fully integrated magnetometer based on superconducting quantum interference device (SQUID). In particular, we analyze the behavior of spectral density of magnetic field noise carrying out an experimental study on 200 magnetometers. The magnetic sensors consist of a superconducting flux transformer connected to a SQUID in a washer shape and include both a feedback coil for flux locked loop operation and an additional positive feedback circuit to increase the intrinsic voltage responsivity. A damping resistor in parallel to the SQUID inductance has been used in order to prevent both the degradation due to the non-optimal βL value and the washer resonances. Such sensors are often employed in magnetoencephalography or more in general in ultra-high sensitivity applications requiring the magnetic noise spectral density as low as 2 fT/√Hz in the white region.We will show that a SQUID critical current varying from 8 to 40 μA does not cause an evident degradation of the magnetometer sensibility. In addition, the magnetic field noise vs critical current indicates an optimal value of SQUID critical current of 20 μA. It corresponds to an inductance parameter βL of about 2 highlighting the effectiveness of the damping resistor in parallel to the SQUID inductance.

Geometric Dependence of Washer Inductance for NbN DC SQUIDs

Planar niobium nitride (NbN) dc superconducting quantum interference devices (SQUIDs) magnetometers were developed based on high-quality epitaxial NbN/AlN/NbN Josephson junctions for SQUID applications at higher operating temperatures. To improve the design of NbN dc SQUIDs, we measured the SQUID washer's inductance, which is a key SQUID parameter. A set of NbN dc SQUIDs with washers with different dimensions were implemented. The washer inductances were obtained from the periodic flux variation in the SQUIDs when a control current was injected directly into the SQUID washers; the results agree well with the ones calculated with a numerical simulation in InductEX software. We obtained an empirical expression to estimate the NbN SQUID inductance with washers with different geometric structures. Our results will be useful for designing NbN dc SQUID magnetometers in future.

Analytical derivation of DC SQUID response

We consider voltage and current response formation in DC superconducting quantum interference device (SQUID) with overdamped Josephson junctions in resistive and superconducting state in the context of a resistively shunted junction (RSJ) model. For simplicity we neglect the junction capacitance and the noise effect. Explicit expressions for the responses in resistive state were obtained for a SQUID which is symmetrical with respect to bias current injection point. Normalized SQUID inductance (where Ic is the critical current of Josephson junction, L is the SQUID inductance, e is the electron charge and ℏ is the Planck constant) was assumed to be within the range l ≤ 1, subsequently expanded up to using two fitting parameters. SQUID current response in the superconducting state was considered for arbitrary value of the inductance. The impact of small technological spread of parameters relevant to low-temperature superconductor (LTS) technology was studied, using a generalization of the developed analytical approach, for the case of a small difference of critical currents and shunt resistances of the Josephson junctions, and inequality of SQUID inductive shoulders for both resistive and superconducting states. Comparison with numerical calculation results shows that developed analytical expressions can be used in practical LTS SQUIDs and SQUID-based circuits design, e.g. large serial SQIF, drastically decreasing the time of simulation.

Optimizing the spin sensitivity of grain boundary junction nanoSQUIDs—towards detection of small spin systems with single-spin resolution

We present an optimization study of the spin sensitivity of nano superconducting quantum interference devices (SQUIDs) based on resistively shunted grain boundary Josephson junctions. In addition the direct current SQUIDs contain a narrow constriction onto which a small magnetic particle can be placed (with its magnetic moment in the plane of the SQUID loop and perpendicular to the grain boundary) for efficient coupling of its stray magnetic field to the SQUID loop. The separation of the location of optimum coupling from the junctions allows for an independent optimization of the coupling factor and junction properties. We present different methods for calculating (for a magnetic nanoparticle placed 10 nm above the constriction) as a function of device geometry and show that those yield consistent results. Furthermore, by numerical simulations we obtain a general expression for the dependence of the SQUID inductance on geometrical parameters of our devices, which allows to estimate their impact on the spectral density of flux noise of the SQUIDs in the thermal white noise regime. Our analysis of the dependence of and on the geometric parameters of the SQUID layout yields a spin sensitivity of a few ( is the Bohr magneton) for optimized parameters, respecting technological constraints. However, by comparison with experimentally realized devices we find significantly larger values for the measured white flux noise, as compared to our theoretical predictions. Still, a spin sensitivity on the order of for optimized devices seems to be realistic.

Effects of magnetic nanoparticle films on the electrical characteristics of dc superconducting quantum interference devices

We evaluated the effects of Fe3O4 magnetic nanoparticle (NP) films on the electrical characteristics of superconducting quantum interference devices (SQUIDs) at 4.2 K to enhance the performance of superconducting circuits. The NP films were formed directly on the SQUIDs. For SQUIDs with 5-nm-NP films, the SQUID inductance increased almost linearly with the NP film thickness, reaching 19.7% at an NP film thickness of 990 nm. An increase in NP size from 5 to 20 nm reduced that in the SQUID inductance. On the other hand, no clear effects on the current–voltage characteristics of SQUIDs were observed for 5- and 10-nm-NP films, while the critical currents of some SQUIDs with 20-nm-NP films were reduced.

Planar SQUID magnetometer integrated with bootstrap circuitry under different bias modes

A planar superconducting quantum interference device (SQUID) magnetometer consisting of a parallel gradiometer SQUID with integrated input coils connected to an on-chip pickup loop was designed and fabricated in conventional niobium technology. SQUID bootstrap circuitry (SBC) incorporating suitable current and voltage feedbacks was also integrated into the design. For a SQUID inductance of Ls = 350 pH and a chip size of 5 × 5 mm2, the field resolution of the voltage-biased SQUID magnetometer reached <5 fT Hz−1/2 with the bootstrap circuit and an ordinary preamplifier. We also observed that the effective McCumber parameter βc of the junctions is influenced by the bias mode. Indeed, when the nominal junction βc was larger than unity, our SQUID magnetometer operated stably in the voltage bias mode. The device exhibited low noise even without SBC.

A voltage biased superconducting quantum interference device bootstrap circuit

We present a dc superconducting quantum interference device (SQUID) readoutcircuit operating in the voltage bias mode and called a SQUID bootstrap circuit(SBC). The SBC is an alternative implementation of two existing methods forsuppression of room-temperature amplifier noise: additional voltage feedback andcurrent feedback. Two circuit branches are connected in parallel. In the dc SQUIDbranch, an inductively coupled coil connected in series provides the bias currentfeedback for enhancing the flux-to-current coefficient. The circuit branch parallelto the dc SQUID branch contains an inductively coupled voltage feedback coilwith a shunt resistor in series for suppressing the preamplifier noise current byincreasing the dynamic resistance. We show that the SBC effectively reduces thepreamplifier noise to below the SQUID intrinsic noise. For a helium-cooled planarSQUID magnetometer with a SQUID inductance of 350 pH, a flux noise of about 3 μΦ0 Hz − 1/2 and a magnetic field resolution of less than 3 fT Hz − 1/2 were obtained. The SBC leads to a convenient direct readout electronics for a dc SQUIDwith a wider adjustment tolerance than other feedback schemes.

Epitaxial thick film high-Tc SQUIDs

Low-noise operation of superconducting quantum interference devices (SQUIDs) in magnetic fields requires high critical current and strong pinning of vortices in the superconducting electrodes and in the flux transformer. Crack-free epitaxial high-Tc dc-SQUID structures with a total thickness ?5 μm and a surface roughness determined by 30 nm high growth spirals were prepared with YBa2Cu3O7-x (YBCO) films on MgO substrates buffered by a SrTiO3/BaZrO3-bilayer. HRTEM demonstrated a high quality epitaxial growth of the films. The YBCO films and SQUID structures deposited on the buffered MgO substrates had a superconducting transition temperature Tc exceeding 91 K and critical current densities Jc > 3 MA/cm2 at 77 K up to a thickness ~5 μm. The application of thicker superconducting and insulator films helped us to increase the critical current and dynamic range of the multilayer high-Tc flux transformer and improve the insulation between the superconducting layers. An optimization of SQUID inductance allowed us to fabricate 8 mm SQUID magnetometers with SQUID voltage swings of ~60 μV and a field resolution of ~30 fT/√Hz at 77 K.

A Numerical Treatment of the rf SQUID: II. Noise Temperature

We investigate rf SQUIDs (Superconducting QUantum Interference Devices), coupled to a resonant input circuit, a readout tank circuit and a preamplifier, by numerically solving the corresponding Langevin equations. The quantity of interest is the noise temperature T N . We use an analytical expression T N0,opt, which is already optimized for the parameters of the input circuit, and vary the model parameters of the remaining circuit to minimize T N0,opt. We also compare T N0,opt to numerical simulations of the full circuit and find good agreement. The best device performance is obtained when β′ L ≡2π LI 0/Φ 0 is in the range 0.5–0.9; L is the SQUID inductance, I 0 the junction critical current and Φ 0 the flux quantum. For a tuned input circuit we find an optimal noise temperature T N0,opt≈3Tf/f c , where T, f and f c denote temperature, signal frequency and junction characteristic frequency, respectively. This value is close to the optimal noise temperatures obtained by approximate analytical theories carried out previously in the limit β′ L ≲1. We study the dependence of T N0,opt on various model parameters away from their optimum values, and often find much lower values of T N0,opt than predicted by the analytical theory. We finally discuss implications for devices that can be implemented experimentally.

Transfer function and noise properties of YBa2Cu3O7−δ direct-current superconducting-quantum-interference-device magnetometers with resistively shunted inductances

We have investigated resistively shunted direct-coupled high-Tc dc superconducting quantum interference device (SQUID) magnetometers with four different inductances (50, 100, 150, and 200 pH). The SQUIDs were based on 200 nm thick YBa2Cu3O7−δ films deposited on bicrystal substrates with a 24° misorientation angle, and the shunt resistors were fabricated by masked ion damage. At T=77 K, good quantitative agreement was observed between the measured maximum voltage modulation depth ΔV and calculated values based on the theoretical predictions by Enpuku et al., whereas the white magnetic flux noise SΦ at 10 kHz of all four devices was found to be a factor of 2.3 higher than predicted. The lowest white magnetic field noise of 153 fT/Hz was obtained for the magnetometer with a SQUID inductance of 100 pH with an outer dimension of the pickup loop of just 2 mm.

YBaCuO/Co-doped PrBaCuO/YBaCuO ramp-edge junctions and their application to flip–flop circuits

We fabricated YBa 2 Cu 3 O 7− x /PrBa 2 Cu 2.8 Co 0.2 O 7− y /YBa 2 Cu 3 O 7− x ramp-edge Josephson junctions and measured their current–voltage ( I – V ) characteristics. Critical current ( I c ) and conductance ( G ) were evaluated as a function of the barrier layer thickness, and both of them exhibited a nearly exponential dependence. The decay parameters for I c and G were estimated to be 1.1 and 1.5 nm, respectively. We also examined superconducting quantum interference devices (SQUIDs) using this type of junction as a preliminary test for realizing oxide superconductive integrated circuits with high-speed operation. DC SQUIDs with direct-coupling control lines and no ground plane were fabricated and their loop inductance was evaluated. The obtained SQUID inductance ranged from 8 to 38 pH for a 4- μ m-wide, 3- to 12- μ m-long hole in a rectangular SQUID loop. In addition, a flip–flop circuit based on such a dc SQUID was fabricated. Both flux trapping and flux detrapping in the SQUID loop hole were confirmed when 1-ms-wide current pulses were injected into the SQUID loop.

Direct-Coupled High Tc DC Superconducting Quantum Interference Device Magnetometers on SrTiO3 Substrate: Theoretical Description and Comparison with Experiment

A comprehensive quantitative comparison between the measured performance of direct-coupled high Tc superconducting quantum interference device (SQUID) magnetometers with 30° bicrystal junctions and a numerical simulation is presented. It is shown that the characteristics of the SQUID magnetometer are considerably affected by resonances due to the large dielectric constant of the SrTiO3 substrate. In the realized magnetometer layout, the strip line resonance occurring in the SQUID inductance increases the voltage modulation depth and the output voltage noise of the SQUID, while the flux noise of the SQUID is nearly unchanged. It is also shown that the distortion of the voltage versus flux characteristic is caused by the LC resonance in the pickup loop of the magnetometer in combination with a capacitive feedback. Good agreement between experiment and simulation has been obtained.

Key components for the fabrication of flip-chip SQUID magnetometers and current sensors

We have prepared single layer washer-type dc superconducting quantum interference devices (SQUIDs), multilayer flux transformers and input coils as key components for flip-chip SQUID magnetometers and current sensors. The dc SQUIDs are prepared on a bicrystal substrate with a misorientation angle of . The maximum peak-to-peak flux modulated voltage amounts to typically for a SQUID inductance of 80 pH. flux transformers and input coils are prepared on a single crystal polished on both sides with dimensions mm. The preparation process of these structures involves the deposition of and layers by pulsed laser ablation and pattern definition by dry etching. The flip-chip magnetometers with 80 pH SQUIDs provide a field sensitivity equal to 2.6 nT whereas current sensors show a sensitivity equal to . The best value for the magnetic field resolution is 20 fT in the white noise region and 100 fT at 1 Hz with a corner at 10 Hz. Current resolution values are typically 40 pA in the white noise region.

Radio frequency SQUIDs operating at 77 K with 1 GHz lumped-element tank circuits

We have developed a matching scheme for the operation of a rf superconducting quantum interference device (SQUID) with a lumped-element tank circuit at pumping frequencies up to 1 GHz. This conventional LC resonant circuit is inductively coupled to a matching coil, which is connected to the 50 Ω transmission line. We characterized the flux noise of high-temperature rf SQUIDs at resonant frequencies between 221 and 950 MHz. At about 900 MHz, we obtained the white flux noise of about 14.6 μφ0/Hz with a SQUID inductance LS=150 pH and 20 μφ0/Hz with LS=260 pH. Several of such tank circuits can be driven in parallel or in series with only one cable.

Large Inductance Superconducting Quantum Interference Device Magnetometer for Magnetoencephalography Measurement

The characteristics of the low T c dc superconducting quantum interference devices (SQUIDs) having a large inductance of 1 nH were investigated. The degradation of the modulation voltage due to the large inductance parameter β L was recovered by damping the SQUID inductance with a resistor having twice the junction resistance. The modulation voltage of 20 µ V was close to the value given by the computer simulation. The value of the measured flux noise, using a dc bias flux-locked-loop with a cooled tank circuit, of 21 µΦ0/√ Hz was about 8 times larger than the theoretical value. The flux noise at the white region increased to 39 µΦ0/√ Hz after removing the tank circuit, but because of the improved flux transfer efficiency from the input coil to the SQUID a white field noise of about 10 fT/√ Hz was obtained using a second order axial gradiometer. A clear auditory evoked field was observed using the large β L SQUID magnetometer which was directly coupled to the amplifier.

Performance of YBa2Cu3O7−δ direct current SQUIDS with high-resistance step-edge junctions

We measured the performance of dc superconducting quantum interference devices (SQUIDs) fabricated from YBa2Cu3O7−δ films as a function of the SQUID inductance, L, and normal resistance, Rn, of step-edge Josephson junctions and compared it to theoretical expectations. A process for adjusting critical currents and obtaining high normal resistances of junctions has been developed. All measurements were performed in liquid nitrogen, i.e., at 77 K. We could obtain controllably normal resistances of 5–10 Ω per junction at critical currents of 20–50 μA. A spectral density of white flux noise of SΦ1/2=2.5μΦ0/√Hz was obtained with a dc SQUID having L=50 pH, Rn=7 Ω per junction, βL=0.5 and ∂V/∂Φ=110 μV/Φ0. The best magnetic field resolution at 1 kHz was 20 fT/√Hz, with L=150 pH.

High-T c superconductor/normal-metal/superconductor edge junctions and SQUIDs with integrated groundplanes

Epitaxial, high-Tc superconductor/normal-metal/superconductor (SNS) edge-geometry weak links and superconducting quantum interference devices (SQUIDs) have been fabricated with integrated YBa2Cu3O7 (YBCO) groundplanes and SrTiO3 insulators, using a process which incorporates six epitaxial layers. The SNS edge junctions were produced using off-axis sputtered films and Co-doped-YBCO normal metal interlayers. These devices show excellent performance with typical critical current-resistance (IcRn) products of 500–800 μV for 100–150 Å thick normal metal layers at 65 K, and 1-σ critical current density ( Jc) spreads as small as 12%. SNS SQUIDs incorporating groundplanes exhibit voltage modulation of up to 130 μV at 65 K and 40 μV at 77 K. SQUID inductance measurements indicate microstrip inductance values of 1 pH per square at 65 K.

High- SQUID magnetometers for biomagnetic measurements

We have designed and fabricated three types of high- SQUID (superconducting quantum interference device) magnetometers based on step-edge Josephson junctions using three different concepts of coupling magnetic flux into the SQUID: (i) a single pickup loop galvanically coupled to the SQUID, (ii) a flux transformer inductively coupled to the SQUID and (iii) a multiloop pickup loop used directly as the SQUID inductance. On a substrate we achieved an effective flux capture area of and for the inductively coupled and multiloop devices, respectively. Due to the low white noise levels of for the inductively coupled magnetometer and for the multiloop device high quality magnetocardiograms were recorded inside a magnetically shielded room without signal averaging.