We have fabricated a superconducting resonator capable of generating a strong microwave magnetic field in a small (100 μm) volume for low temperature magnetic resonance experiments. While the resonator was specifically developed for use at millikelvin temperatures in a dilution refrigerator, where the total cooling power is limited to a few hundred microwatts, it is also useful at temperatures up to 5 K. The resonator consists of a 220 μm diameter, 2-1/2 turn niobium coil resonating with a short section of niobium microstripline. At a resonance frequency of 3 GHz, the loaded Q of the resonator was 780. The field strength was characterized by performing electron spin nutations. Operating at 100 mK with 320 μW of dissipated power, the resonator generated a field of 4 G at a distance of 100 μm from the coil.
We have fabricated a superconducting resonator capable of generating a strong microwave magnetic field in a small (100 μm) volume for low temperature magnetic resonance experiments. While the resonator was specifically developed for use at millikelvin temperatures in a dilution refrigerator, where the total cooling power is limited to a few hundred microwatts, it is also useful at temperatures up to 5 K. The resonator consists of a 220 μm diameter, 2-1/2 turn niobium coil resonating with a short section of niobium microstripline. At a resonance frequency of 3 GHz, the loaded Q of the resonator was 780. The field strength was characterized by performing electron spin nutations. Operating at 100 mK with 320 μW of dissipated power, the resonator generated a field of 4 G at a distance of 100 μm from the coil.
We report on the design and performance of a cryogenic (300 mK) near-field scanning microwave microscope. It uses a microwave resonator as the near-field sensor, operating at a frequency of 6 GHz and microwave probing amplitudes down to 100 μV, approaching low enough photon population (N ∼ 1000) of the resonator such that coherent quantum manipulation becomes feasible. The resonator is made out of a miniaturized distributed fractal superconducting circuit that is integrated with the probing tip, micromachined to be compact enough such that it can be mounted directly on a quartz tuning-fork, and used for parallel operation as an atomic force microscope (AFM). The resonator is magnetically coupled to a transmission line for readout, and to achieve enhanced sensitivity we employ a Pound-Drever-Hall measurement scheme to lock to the resonance frequency. We achieve a well localized near-field around the tip such that the microwave resolution is comparable to the AFM resolution, and a capacitive sensitivity down to 6.4 × 10(-20) F/Hz, limited by mechanical noise. We believe that the results presented here are a significant step towards probing quantum systems at the nanoscale using near-field scanning microwave microscopy.
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.
Cooling microwave resonators to near the quantum ground state, crucial for their operation in the quantum regime, is typically achieved by direct device refrigeration to a few tens of millikelvin. However, in quantum experiments that require high operation power such as microwave-to-optics quantum transduction, it is desirable to operate at higher temperatures with non-negligible environmental thermal excitations, where larger cooling power is available. In this Letter, we present a radiative cooling protocol to prepare a superconducting microwave mode near its quantum ground state in spite of warm environment temperatures for the resonator. In this proof-of-concept experiment, the mode occupancy of a 10 GHz superconducting resonator thermally anchored at 1.02 K is reduced to 0.44±0.05 from 1.56 by radiatively coupling to a 70 mK cold load. This radiative cooling scheme allows high-operation-power microwave experiments to work in the quantum regime, and opens possibilities for routing microwave quantum states to elevated temperatures.
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.
Planar superconducting microwave resonators are commonly operated for various cryogenic applications, typically at frequencies between 2 and 15 GHz. But for certain applications, e.g. microwave spectroscopy to study the dynamics of charges and spins in solids, a wider spectral range is desired. Driving such microwave resonators at higher frequencies is challenging due to enhanced losses and reduced wavelength. Here we present superconducting stripline resonators operating at multiple frequencies as high as 50 GHz. These resonators are fabricated of Pb and can easily be adjusted to particular applications, including mK temperatures in a dilution refrigerator. Demonstrating such a resonator as a spectroscopic tool, we detect the superconducting transition of a Sn sample in a wide spectral range.
Abstract We systematically study the performance of compact lumped element planar microwave Nb70Ti30N (NbTiN) resonators operating at 5 GHz in external in-plane magnetic fields up to 440 mT, a broad temperature regime from 2.2 K up to 13 K, as well as mK temperatures. For comparison, the resonators have been fabricated on thermally oxidized and pristine, (001) oriented silicon substrates. When operating the resonators in the multi-photon regime at T = 2.2 K, we find internal quality factors Q int ≃ 2 × 105 for NbTiN resonators grown on pristine Si substrates. In addition, we investigate the Q-factors of the resonators on pristine Si substrates at millikelvin temperatures to assess their applicability for quantum applications. We find Q int ≃ 2 × 105 in the single photon regime and Q int ≃ 5 × 105 in the high power regime at T = 7 mK. From the excellent performance of our resonators over a broad temperature and magnetic field range, we conclude that NbTiN deposited on Si (100) substrates, where the surface oxide has been removed, constitutes a promising material platform for electron spin resonance and ferromagnetic resonance experiments using superconducting planar microwave resonators.