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arXiv:1404.0534 · Review of Scientific Instruments

A near-field scanning microwave microscope based on a superconducting resonator for low power measurements

Sebastian E. de Graaf, Andrey V. Danilov, A. A. Adamyan, Sergey Kubatkin

Published Feb 1, 2013• 33 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/1.4792381

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In this thesis we use high-Q superconducting thin-film microwave resonators to interact with several types of quantum mechanical two-level systems. Such a resonator is used as the central building block in a cryogenic near-field scanning microwave microscope (NSMM) to reach a completely new regime of NSMM operation. In this regime where the superconducting resonator is only populated with a small number of photons, we demonstrate a capacitance sensitivity down to 64x10^(-21) Farad/rtHz and nanoscale resolution, which is sufficient to apply this scanning probe technique to quantum coherent objects. Such a 'coherent'-NSMM enables several new applications: for example to study the interaction of the NSMM probe with two-level defects in samples and to characterize artificial two-level systems (qubits), which eventually could lead to better understanding of decoherence mechanisms in superconducting quantum circuits. We demonstrate the ability to reach this regime in a sample consisting of a Cooper-pair box (CPB) weakly coupled to a superconducting resonator. In the strong driving regime we observe Landau-Zener-Stückelberg interference and we discover a new type of relaxation mechanism in the strongly driven CPBthat involves pair breaking and quasiparticle tunneling. It results in a recovered parity of the CPB and a population inversion of the dressed states. Not only does this demonstrate the applicability of NSMM for qubit characterization, but the quasiparticle mediated population inversion also becomes suitable for robust charge sensing in a scanning probe setup. To integrate the superconducting resonator onto our NSMM probe we develop a new type of resonator design - the fractal design - that have a very small external dipole moment allowing for a compact resonator. Another advantage of the fractal resonator is its resilience to magnetic fields. We show that the fractal resonator, after further optimization, can maintain quality factors above 10^5 in applied fields of more than 400 mT, something that becomes particularly useful for the interrogation of spin ensembles coupled to the resonator. We demonstrate that it is possible to detect down to 5x10^5 spins/rtHz in a very small volume coupled to a fractal resonator. Furthermore, the low dipole moment of the fractal resonator allows us to also introduce DC bias into the resonator without degrading its Q-factor. This is an important technological step that allows us to interact with new materials where spins can be quickly and locally manipulated using electric fields and we demonstrate the first steps in this direction with ensembles of manganese doped ZnO nanowires and frustrated molecular Cu spin triangles.The measurements achieve a very high sensitivity thanks to the Pound-Drever-Hall locking technique used. We develop this technique such that both resonance frequency and quality factor can be monitored with very high accuracy in real time. The demonstrated stability is ~30 Hz/rtHz for frequency readout and we can determine the Q-factor with a precision of 34 dB/rtHz.

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A micro-SQUID with dispersive readout for magnetic scanning microscopy

Foroughi, F., Mol, J.-M., T. Müller +3 more

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. 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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.

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Nano Letters•Aug 7, 2026•0 citations
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.
In this thesis we use high-Q superconducting thin-film microwave resonators to interact with several types of quantum mechanical two-level systems. Such a resonator is used as the central building block in a cryogenic near-field scanning microwave microscope (NSMM) to reach a completely new regime of NSMM operation. In this regime where the superconducting resonator is only populated with a small number of photons, we demonstrate a capacitance sensitivity down to 64x10^(-21) Farad/rtHz and nanoscale resolution, which is sufficient to apply this scanning probe technique to quantum coherent objects. Such a 'coherent'-NSMM enables several new applications: for example to study the interaction of the NSMM probe with two-level defects in samples and to characterize artificial two-level systems (qubits), which eventually could lead to better understanding of decoherence mechanisms in superconducting quantum circuits. We demonstrate the ability to reach this regime in a sample consisting of a Cooper-pair box (CPB) weakly coupled to a superconducting resonator. In the strong driving regime we observe Landau-Zener-Stückelberg interference and we discover a new type of relaxation mechanism in the strongly driven CPBthat involves pair breaking and quasiparticle tunneling. It results in a recovered parity of the CPB and a population inversion of the dressed states. Not only does this demonstrate the applicability of NSMM for qubit characterization, but the quasiparticle mediated population inversion also becomes suitable for robust charge sensing in a scanning probe setup. To integrate the superconducting resonator onto our NSMM probe we develop a new type of resonator design - the fractal design - that have a very small external dipole moment allowing for a compact resonator. Another advantage of the fractal resonator is its resilience to magnetic fields. We show that the fractal resonator, after further optimization, can maintain quality factors above 10^5 in applied fields of more than 400 mT, something that becomes particularly useful for the interrogation of spin ensembles coupled to the resonator. We demonstrate that it is possible to detect down to 5x10^5 spins/rtHz in a very small volume coupled to a fractal resonator. Furthermore, the low dipole moment of the fractal resonator allows us to also introduce DC bias into the resonator without degrading its Q-factor. This is an important technological step that allows us to interact with new materials where spins can be quickly and locally manipulated using electric fields and we demonstrate the first steps in this direction with ensembles of manganese doped ZnO nanowires and frustrated molecular Cu spin triangles.The measurements achieve a very high sensitivity thanks to the Pound-Drever-Hall locking technique used. We develop this technique such that both resonance frequency and quality factor can be monitored with very high accuracy in real time. The demonstrated stability is ~30 Hz/rtHz for frequency readout and we can determine the Q-factor with a precision of 34 dB/rtHz.
We describe the use of a cryogenic near-field scanning microwave microscope to image microwave electric fields from superconducting and normal-metal microstrip resonators. The microscope employs an open-ended coaxial probe and operates from 77 to 300 K in the 0.01–20 GHz frequency range with a spatial resolution of about 200 μm. We describe the operation of the system and present microwave images of Cu and Tl2Ba2CaCu2O8 microstrip resonators, showing standing wave patterns at the fundamental and second harmonic frequencies.
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.
Near field Scanning Microwave Microscopy (NSMM) is a scanning probe technique that non-invasively can obtain material properties on the nano-scale at microwave frequencies. While focus has been on developing room-temperature systems it was recently shown that this technique can potentially reach the quantum regime, opening up for applications in materials science and device characterization in solid state quantum information processing. In this paper we theoretically investigate this new regime of NSMM. Specifically we show that interaction between a resonant NSMM probe and certain types of two-level systems become possible when the NSMM probe operates in the (sub-) single photon regime, and we expect a high signal-to-noise ratio if operated under the right conditions. This would allow to detect single atomic material defects with energy splittings in the GHz range with nano-scale resolution, provided that individual defects in the material under study are well enough separated. We estimate that this condition is fulfilled for materials with loss tangents below tan δ ∼ 10(-3) which holds for materials used in today's quantum circuits and devices where typically tan δ < 10(-5). We also propose several extensions to a resonant NSMM that could improve sensitivity and functionality also for microscopes operating in a high power regime.
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.
Superconducting resonators are finding increasing applications in designing advanced quantum circuits for an ongoing sensing, metrology, and computing technological revolution. A detailed knowledge of the microscopic electromagnetic properties of superconducting resonators is directly relevant for their further improvements on circuitry design and device performance. Here, we introduce scanning-probe quantum microscopy to report nanoscale sensing of the microwave and static magnetic field environment of an on-chip niobium (Nb) superconducting resonator. Taking advantage of Rabi oscillation measurements, we show that microwave magnetic fields generated by the superconducting resonator mode can be utilized to achieve coherent control of a quantum spin sensor. We further visualize the static electromagnetic field response of the Nb resonator, showing magnetic field-induced formation, evolution, and depinning of superconducting vortices. Our results provide insights into future design, testing, and evaluation of solid-state superconducting resonators, highlighting the potential of quantum sensors as a local probe to investigate electromagnetic properties of superconducting quantum circuits.