Among some of the current uses of dc superconducting quantum interference devices (SQUIDs) are qubit readouts and sensors for probing the properties of quantum materials. We present a gradiometric niobium SQUID design with state-of-the-art sensitivity in the femtotesla range, which can be tuned to specific readout requirements. The sensor is a next-generation fractional SQUID with a tightly optimized input coil and a combination of various measures known for restraining parasitic resonances and other detrimental effects. Our design combines the practical usefulness of well-defined pickup loops for well-defined imaging kernel and tunable probing applications with a fractionalization approach to reduce undesired inductances. In addition, our modeling predicts small dimensions for these planar sensors. These features make them of relevance for material studies and for the detection of magnetic fields in small volumes, e.g., as part of a cryogenic scanning quantum imaging apparatus for efficient diagnostics and quantum device readouts. This manuscript will benefit scientists and engineers working on quantum-computing technologies by clarifying potential general misconceptions about dc SQUID optimization alongside the introduction of the flexible compact dc SQUID design.
Among some of the current uses of dc superconducting quantum interference devices (SQUIDs) are qubit readouts and sensors for probing the properties of quantum materials. We present a gradiometric niobium SQUID design with state-of-the-art sensitivity in the femtotesla range, which can be tuned to specific readout requirements. The sensor is a next-generation fractional SQUID with a tightly optimized input coil and a combination of various measures known for restraining parasitic resonances and other detrimental effects. Our design combines the practical usefulness of well-defined pickup loops for well-defined imaging kernel and tunable probing applications with a fractionalization approach to reduce undesired inductances. In addition, our modeling predicts small dimensions for these planar sensors. These features make them of relevance for material studies and for the detection of magnetic fields in small volumes, e.g., as part of a cryogenic scanning quantum imaging apparatus for efficient diagnostics and quantum device readouts. This manuscript will benefit scientists and engineers working on quantum-computing technologies by clarifying potential general misconceptions about dc SQUID optimization alongside the introduction of the flexible compact dc SQUID design.
The direct current superconducting quantum in terference device (dc SQUID) sensor represents one of the most established applications of superconductor technology due to its sensitivity to magnetic flux. In this work, we present superconducting “fine-pitch” input coils with sub-micrometer parameters fabricated with electron beam lithography (EBL) that will be integrated into existing Nb/Al-AlOx/Nb-based SQUID sensor designs. The aim is to reduce inductive losses of the signal to-SQUID coupling without compromising the overall device layout. In a SQUID current sensor, maximization of the inductive coupling constant k between the signal input coil and the SQUID loop results in a low coupled energy sensitivity ϵc = ϵ/k2where ϵ is the intrinsic energy sensitivity. The fine-pitch coils are expected to increase the inductive coupling constant k as well as extend the range of input coil inductance for our existing devices. The SQUID energy sensitivity ϵ ∼ √CJJcan be lowered by reducing the Josephson junction (JJ) capacitance CJJ. We are developing a process, also based on EBL, to fabricate window-type JJs with sub-micrometer lateral size to obtain reduced JJ capacitances. Details concerning design aspects of the components, their fabrication and characterization results are provided in this paper.
We have designed and characterized a micro-SQUID with dispersive readout for use in low temperature scanning probe microscopy systems. The design features a capacitively shunted RF SQUID with a tunable resonance frequency from 5 to 12 GHz, micrometer spatial resolution, and integrated superconducting coils for local application of magnetic fields. The SQUID is operated as a nonlinear oscillator with a flux- and power-dependent resonance frequency. Measurements for device characterization and noise benchmarking were carried out at 4 K. The measured flux noise above 10 kHz at 4 K is 80 nΦ0 Hz−1∕2 at a bandwidth of 200 MHz. Estimations suggest that one can benefit from parametric gain based on inherent nonlinearity of the Josephson junction and reduce the flux noise to 30 nΦ0Hz–1∕2 at 100 mK, which corresponds to 10.6 μBHz–1∕2 for a magnetic moment located at the center of the pickup loop.Measuring the magnetic response of mesoscopic samples or mapping it vs. position for extended systems is effective methods for revealing the fundamental quantum properties of condensed matter systems. Over the past few decades, many advanced magnetic imaging schemes have been developed, including magnetic force microscopy,1 scanning Hall probe microscopy,2 superconducting interference devices (SQUIDs),3,4 and NV center based magnetometry.5 The high sensitivity, low back action, and low power dissipation of SQUIDs make them attractive for many types of low temperature experiments. One classic example is the central role of scanning SQUID microscopy in tests of pairing symmetry of high-Tc cuprate superconductors.6 Other prominent applications are the thermodynamic characteristics of persistent currents in normal metal rings7 and proof of edge states in topological insulators in the quantum spin Hall regime.8A key performance for a SQUID is its flux sensitivity. Parametric amplification has been harnessed in nano-SQUIDs based on aluminum junctions9,10 in order to reduce the flux noise down to 30 nΦ0Hz–1∕2 with a bandwidth exceeding 60 MHz.10 Recent studies on parametric amplifiers and dispersive readout of superconducting qubits also harness the nonlinearity of the Josephson junction to boost sensitivity.11–13In scanning SQUID microscopy, signal sources often behave dipole-like, such as superconducting vortices in mesoscopic dots or currents in mesoscopic rings. Smaller SQUIDs provide better coupling to smaller samples which leads to higher spin sensitivity3,14 as the magnetic field of a dipole decreases with 1/r3. Various approaches have been pursued to reduce the size. The smallest nano-SQUID to date has been fabricated by evaporating Nb or Pb15 onto the apex of a sharp quartz tip reaching a loop diameter of below nm and a spin sensitivity of 0.38 μBHz−1/2 at tens of kHz bandwidth. Compared to such size-optimized devices, micro-SQUIDs fabricated using a standard Nb technique have the advantage of on-chip field coils and modulation coils,14 and can be operated at 4 K allowing for a wide range of applications. However, these come at the cost of larger pick-up loops of a few microns and a resulting poorer spin sensitivity of 200 μBHz−1/2 for a magnetic moment located at the center of the pickup loop.The limitation of large pickup loops was previously only overcome by devices with pickup loops defined by the focused-ion-beam,16 but has recently also been achieved by improvements in lithography and shown to offer better spatial resolution as well.17 Here, we present a scanning micro-SQUID which is based on the same fabrication technology incorporating another major advancement. Our design exploits the parametric amplification based on nonlinearities of the SQUID to boost sensitivity. The combination of a smaller pickup loop and parametric amplification of the signal leads to better spin sensitivity (10.6 μBHz−1/2) and higher bandwidth (200 MHz) compared to traditional DC micro-SQUIDs in which the flux sensitivity is mainly limited by internal dissipation.Our devices were fabricated at Hypres Inc. using planarized Nb/AlOx/Nb trilayer Josephson junction technology, including two planarized Nb layers with approximately 0.8 μm minimum feature size. The SQUID consists of a superconducting ring shunted by one Josephson junction with a designed critical current of 20 μA [Fig. 1(a)]. With this geometry, the SQUID is gradiometric, i.e., the effect of any homogeneous background magnetic field approximately cancels out. The smallest pickup loops implemented have an inner (outer) diameter of 1 μm (2 μm). The superconducting loop is shunted by an on-chip parallel-plate capacitor with amorphous silicon dioxide as dielectric which was designed to have a capacitance of 80 pF. The superconducting loop and the capacitor form a resonator with a flux dependent resonance frequency from 5 to 12 GHz. The pickup loops are placed on opposite corners of the parallel-plate capacitor at a distance of about 450 μm so that one loop can be located in close proximity to the sample while the other is kept far away from it. External fields can be applied to the sample by local single-turn field coils situated around each pickup loop. The field coils are fully integrated into the chip layout and can also be used to bias the SQUID at its most sensitive point. Compared to using additional modulation coils,14 this approach has the advantage of reducing the total device inductance, which leads to a higher sensitivity.18 In a scanning microscope, the field coil at the rear end (away from the sample) can be used to bias the SQUID or operate it in flux feedback such that resulting stray fields will not act on the sample, apart from a weak screening current through the pickup loop. The effective diameter of each coil is 7.5 μm, resulting in a mutual inductance of about 0.34 Φ0/mA (for the smallest pickup loop). The SQUID resonator is connected by an on-chip Z0 = 50 Ω coplanar waveguide (CPW) transmission line to the bonding pads. The two field coils are connected by two smaller CPWs to the bottom edge bonding pads [Fig. 1(c)], ending in two parallel-stripline waveguides running alongside the edges of the capacitor towards the respective field coils. Based on estimations, it should thus be possible to apply high frequency signals of at least several GHz to SQUID and sample.
The energy sensitivity of a direct current (dc) superconducting quantum interference device (SQUID) can be improved if it is operated in a two-stage configuration. Employing this technique, a commercial dc SQUID system was modified and made competitive with other sensors especially designed for very low noise applications. We report the noise measurements performed in the temperature range 4.2 K–25 mK. At 4.2 K, the coupled energy sensitivity obtained with the two-stage dc SQUID was approximately ten times better than with a conventional readout electronics. The noise energy decreases linearly until approximately 300 mK, in good agreement with theoretical previsions. At lower temperature the hot-electron effect produces a saturation and the best energy sensitivity measured with open input coil is 35 ℏ.
The dc Superconducting Quantum Interference Device (dc-SQUID) is one of the most sensitive magnetic field sensors available. In this thesis we concentrate on its application as an amplifier. In this configuration, an input circuit of interest can be connected by means of a coupling coil. The intended application of our developed low-Tc SQUID amplifiers is the readout of the first spherical gravitational wave antenna MiniGRAIL. Using small-signal analysis as well as numerical simulations, we study the achievable signal-to-noise ratio of such sensors in practical measurements. Published theories and studies could be extended. Some interesting points treated are the influence of the often used negative feedback (flux-locked loop), an altered input impedance of the SQUID amplifier and the influence of back-action noise, which directly affects the object of interest. The altered operation of the SQUID due to the presence of the input circuit is studied in numerical experiments. Another important issue, the influence of integrated input coils on the dynamics of SQUIDs, is investigated theoretically and experimentally. The performance of our developed sensors is compared to numerical simulations on detailed models. The results give insights into the behavior, design and usage of dc-SQUIDs with integrated coils. For a SQUID with input inductances of 1.5 μH we reached a good coupled energy sensitivity of about 170 ¯h in a dilution refrigerator. Furthermore, we investigated the hot-electron effect. This effect typically limits the sensitivity of superconducting electronics at sub-Kelvin bath temperatures due to a weakened electron-phonon coupling. We performed heating experiments on thin-film resistors which are similar to the shunt resistors of the Josephson junctions used in our sensors. The suppression of the hot-electron effect via electronic thermal transport to attached cooling fins is investigated both experimentally, theoretically and numerically. The numerical technique turns out to be a useful tool for the thermal design of superconducting electronics.
An integrated magnetic nanosensor based on a niobium dc SQUID (superconducting quantum interference device) for nanoscale applications is presented. The sensor, having a washer shape with a hole of 200 nm and two Josephson-Dayem nanobridges of 80 nm × 100 nm, consists of a Nb(30 nm)/Al(30 nm) bilayer patterned by electron beam lithography (EBL) and shaped by lift-off and reactive ion etch (RIE) processes. The presence of the niobium coils, integrated on-chip and tightly coupled to the SQUID, allows us to easily excite the sensor in order to get the voltage-flux characteristics and to flux bias the SQUID at its optimal point. The measurements were performed at liquid helium temperature. A voltage swing of 75 µV and a maximum voltage-flux transfer coefficient (responsivity) as high as 1 mV/Φ(0) were directly measured from the voltage-flux characteristic. The noise measurements were performed in open loop mode, biasing the SQUID with a dc magnetic flux at its maximum responsivity point and using direct-coupled low-noise readout electronics. A white magnetic flux noise spectral density as low as 2.5 μΦ(0) Hz(-1/2) was achieved, corresponding to a magnetization or spin sensitivity in units of the Bohr magneton of 100 spin Hz(-1/2). Possible applications of this nanosensor can be envisaged in magnetic detection of nanoparticles and small clusters of atoms and molecules, in the measurement of nanoobject magnetization, and in quantum computing.
The authors have designed, fabricated, and measured a number of Nb-AlO/sub x/-Nb octagonal washer DC superconducting quantum interference devices (SQUIDs) and miniature DC SQUID susceptometers having minimum feature size down to 0.5 mu m. With SQUID inductance values on the order of 100 pH, typical noise performance is better than 1 mu Phi /sub 0// square root Hz. The small minimum feature size of input coils and pickup loop structures will facilitate tight coupling to a wide variety of systems ranging from submicron particles and structures to conventional approximately mu H input circuits. A single-washer SQUID with an 80-turn 0.5- mu m-linewidth, 630-nH input coil has user-friendly V- Phi (voltage-flux) curves and a coupled energy sensitivity of 20 h at 4.2 K. Susceptometers with pickup loops ranging from 20- mu m to 0.8- mu m across have very user-friendly V- Phi curves and a resolution of order 100 mu /sub B// square root Hz at 4.2 K for devices with the smallest loops.>