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.
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.
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 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.
We describe a dispersive nanoSQUID (nanoscale superconducting quantum interference device) magnetometer comprised of two variable thickness aluminum weak-link Josephson junctions shunted in parallel with an on-chip capacitor. This arrangement forms a nonlinear oscillator with a tunable 4–8 GHz resonant frequency with a quality factor Q = 30 when coupled directly to a 50 Ω transmission line. In the presence of a near-resonant microwave carrier signal, a low frequency flux input generates sidebands that are readily detected using microwave reflectometry. If the carrier excitation is sufficiently strong, then the magnetometer also exhibits parametric gain, resulting in a minimum effective flux noise of 30 n Φ 0 Hz −1/2 with 20 MHz of instantaneous bandwidth. If the magnetometer is followed with a near-quantum-noise-limited Josephson parametric amplifier, we can increase the bandwidth to 60 MHz without compromising sensitivity. This combination of high sensitivity and wide bandwidth with no on-chip dissipation makes this device ideal for local sensing of spin dynamics, both classical and quantum.
Abstract An analysis of the measurement of the magnetic flux in superconducting qubits based on RF SQUIDs was carried out with an 800 MHz bandwidth low-power-consumption cryogenic high-electron-mobility transistor amplifier. The preliminary experimental results obtained at temperatures 2 K and 4 K for RF SQUIDs in hysteretic, and in two non-hysteretic, regimes with a pump frequency of about 30 MHz are discussed. Parameters of RF SQUIDs in the hysteretic and non-hysteretic modes are analyzed within the framework of the resistively and capacitively shunted junction model for Josephson junctions. Its sensitivity at a temperature of 30 mK and frequency band (speed) are calculated and optimized to read the states of a flux qubit used as a single microwave photon counter. It is shown that an RF SQUID, operated in an adiabatic non-hysteretic mode for qubit readout, allows us to minimize its back-action effect and the dark count rate. This is due to the absence of Josephson generation, the small amplitude of the resonator electromagnetic field, and the selection of the pump frequency that does not coincide with the characteristic frequencies of the flux qubit.
Digital superconducting quantum interference devices (SQUIDs) based on single-flux quantum (SFQ) logic have attractive characteristics such as wide dynamic ranges and high slew rates. However, the resolution of a typical digital SQUID is limited by SFQ feedback. To realize lower magnetic field noise by magnetometers using digital SQUIDs, we have adopted two feedback combinations: one, utilizing the SFQ input/output for a main loop and the other, using a mutually coupled loop. The main loop receives direct Φ0feedback and subflux quantum feedback Φ0/n, where n is an integer from the mutually coupled loop. The flux resolution for the digital SQUID shows improvement with increasing n and reaches below 40 mΦ0at n = 210; however, the slew rate decreases with increasing n and reaches 1.22 × 106Φ0/s at fc= 1.25 GHz and n = 210. For a magnetometer using a digital SQUID with a pickup loop, we confirmed a magnetic field noise of less than 100 fT/√Hz with a signal bandwidth of 1 MHz for operation frequency fcof 20 GHz.
There is currently fundamental and technological interest in measuring and manipulating nanoscale magnets, particularly in the quantum coherent regime. To observe the dynamics of such systems one requires a magnetometer with not only exceptional sensitivity but also high gain, wide bandwidth, and low backaction. We demonstrate a dispersive magnetometer consisting of a two-junction superconducting quantum interference device (SQUID) in parallel with an integrated, lumped-element capacitor. Input flux signals are encoded as a phase modulation of the microwave drive tone applied to the magnetometer, resulting in a single quadrature voltage signal. For strong drive power, the nonlinearity of the resonator results in quantum limited, phase sensitive parametric amplification of this signal, which improves flux sensitivity at the expense of bandwidth. Depending on the drive parameters, the device performance ranges from an effective flux noise of 0.29 $\ensuremath{\mu}{\ensuremath{\Phi}}_{0}$Hz${}^{\ensuremath{-}1/2}$ and 20 MHz of signal bandwidth to a noise of 0.14 $\ensuremath{\mu}{\ensuremath{\Phi}}_{0}$Hz${}^{\ensuremath{-}1/2}$ and a bandwidth of 0.6 MHz. These results are in excellent agreement with our theoretical model.