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.
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.
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.
We present the driven response at T=30 mK of 6 GHz superconducting resonators constructed from capacitively-shunted three-dimensional (3D) aluminum nanobridge superconducting quantum interference devices (nanoSQUIDs). We observe flux modulation of the resonant frequency in quantitative agreement with numerical calculation and characteristic of near-ideal short weak-link junctions. Under strong microwave excitation, we observe stable bifurcation in devices with coupled quality factor (Q) ranging from 30–3500. Near this bias point, parametric amplification with >20 dB gain, 40 MHz bandwidth, and near quantum-limited noise performance is observed. Our results indicate that 3D nanobridge junctions are attractive circuit elements to realize quantum bits.
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.
Abstract We describe the theory and implementation of a dispersive magnetometer based on an aluminum nanoSQUID. The nanoSQUID consists of a superconducting loop interrupted by two variable-thickness weak-link nanobridge Josephson junctions. When the nanoSQUID is placed in parallel with a lumped-element capacitor, it acts as the inductive element in a resonant tank circuit. By performing microwave reflectometry on the circuit, the SQUID inductance can be measured, providing a sensitive meter of the flux threading the SQUID loop. In this review we provide the theoretical basis for the device, describe design and operation considerations, and present characterization results on several devices.
We characterize the flux sensitivity of a dispersive 3D aluminum nanobridge superconducting quantum interference device (SQUID) magnetometer as a function of applied in-plane magnetic field. In zero field, we observe an effective flux noise of 17 nΦ0/Hz1/2 with 25 MHz of bandwidth at 150 mK. Flux noise increased by less than a factor of three with parallel magnetic fields up to 61 mT. Operation in higher fields may be possible by decreasing the dimensions of the shunt capacitor in the magnetometer circuit. These devices are thus well suited for observing high-speed dynamics in nanoscale magnets, even in the presence of moderate bias magnetic fields.
Josephson junctions are the basis of superconducting qubits, amplifiers, and magnetometers. Historically, tunnel-style junctions have been most common. However, for some applications--those requiring a small, highly transparent, all-superconducting junction--nanobridge weak link junctions may be preferable. This thesis presents extensive characterization of aluminum nanobridge Josephson junctions. The junction behavior is simulated by numerically solving the Usadel equations. These simulations are then tested and confirmed via low- and microwave-frequency transport measurements. The data confirm that nanobridge junctions approach the ideal weak-link Josephson limit.Such a near-ideal junction can be used in a superconducting quantum interference device (SQUID) to form an ultra sensitive magnetometer. This thesis presents the first nanobridge-based dispersive SQUID magnetometer. The devices show near-zero dissipation, with bandwidth and sensitivity on par with the best reported results for any SQUID-based magnetometer. These magnetometers have several flexible modes of operation, allowing for optimization of sensitivity, bandwidth, or backaction. They also provide insight into the internal dynamics of dispersive measurement with nonlinear cavities, as the magnetometer backaction depends on the bias point and can readily be measured.Nanobridge junctions also provide a useful tool for diagnosing sources of decoherence in superconducting qubits. By replacing the usual tunnel junction with a nanobridge, the contribution of the junction to decoherence processes may be probed. In particular, the interaction of nanobridge junctions with quasiparticles provides information both about the junctions themselves and about quasiparticle generation and relaxation mechanisms. This thesis reports measurements of nonequilibrium quasiparticles trapping in phase-biased nanobridge junctions. By probing the quasiparticle-induced changes in resonant frequency of a high-Q nanoSQUID oscillator, one may measure the mean distribution of trapped quasiparticles and study its temperature dependence. These measurements also provide spectroscopy of the junctions' internal Andreev states and the dynamics of quasiparticle excitation and retrapping. The work presented here demonstrates the utility of nanobridge junctions as a tool for quantifying the population and distribution of quasiparticles in a superconducting circuit.