High-Q Magnetic Levitation and Control of Superconducting Microspheres at Millikelvin Temperatures.

We report the levitation of a superconducting lead-tin sphere with 100 µm diameter (corresponding to a mass of 5.6 µg) in a static magnetic trap formed by two coils in an anti-Helmholtz configuration, with adjustable resonance frequencies up to 240 Hz. The center-of-mass motion of the sphere is monitored magnetically using a dc superconducting quantum interference device as well as optically and exhibits quality factors of up to 2.6×10^{7}. We also demonstrate 3D magnetic feedback control of the motion of the sphere. The setup is housed in a dilution refrigerator operating at 15 mK. By implementing a cryogenic vibration isolation system, we can attenuate environmental vibrations at 200 Hz by approximately 7 orders of magnitude. The combination of low temperature, large mass, and high quality factor provides a promising platform for testing quantum physics in previously unexplored regimes with high mass and long coherence times.

Magnetic vortex nucleation and annihilation in bi-stable ultra-small ferromagnetic particles.

Vortex-mediated magnetization reversal in individual ultra-small (∼100 nm) ferromagnetic particles at low temperatures is studied by nanoSQUID magnetometry. At zero applied bias field, the flux-closure magnetic state (vortex) and the quasi uniform configuration are bi-stable. This stems from the extremely small size of the nanoparticles that lies very close to the limit of single-domain formation. The analysis of the temperature-dependent (from 0.3 to 70 K) hysteresis of the magnetization allows us to infer the nature of the ground state magnetization configuration. The latter corresponds to a vortex state as also confirmed by electron holography experiments. Based on the simultaneous analysis of the vortex nucleation and annihilation data, we estimate the magnitude of the energy barriers separating the quasi single-domain and the vortex state and their field dependence. For this purpose, we use a modified power-law scaling of the energy barriers as a function of the applied bias field. These studies are essential to test the thermal and temporal stability of flux-closure states stabilized in ultra-small ferromagnets.

NanoSQUID Magnetometry on Individual As-grown and Annealed Co Nanowires at Variable Temperature.

Performing magnetization studies on individual nanoparticles is a highly demanding task, especially when measurements need to be carried out under large sweeping magnetic fields or variable temperature. Yet, characterization under varying ambient conditions is paramount in order to fully understand the magnetic behavior of these objects, e.g., the formation of nonuniform states or the mechanisms leading to magnetization reversal and thermal stability. This, in turn, is necessary for the integration of magnetic nanoparticles and nanowires into useful devices, e.g., spin-valves, racetrack memories, or magnetic tip probes. Here, we show that nanosuperconducting quantum interference devices based on high critical temperature superconductors are particularly well suited for this task. We have successfully characterized a number of individual Co nanowires grown through focused electron beam induced deposition and subsequently annealed at different temperatures. Magnetization measurements performed under sweeping magnetic fields (up to ∼100 mT) and variable temperature (1.4-80 K) underscore the intrinsic structural and chemical differences between these nanowires. These point to significant changes in the crystalline structure and the resulting effective magnetic anisotropy of the nanowires, and to the nucleation and subsequent vanishing of antiferromagnetic species within the nanowires annealed at different temperatures.

Coupling ultracold atoms to a superconducting coplanar waveguide resonator.

Ensembles of trapped atoms interacting with on-chip microwave resonators are considered as promising systems for the realization of quantum memories, novel quantum gates, and interfaces between the microwave and optical regime. Here, we demonstrate coupling of magnetically trapped ultracold Rb ground-state atoms to a coherently driven superconducting coplanar resonator on an integrated atom chip. When the cavity is driven off-resonance from the atomic transition, the microwave field strength in the cavity can be measured through observation of the AC shift of the atomic hyperfine transition frequency. When driving the cavity in resonance with the atoms, we observe Rabi oscillations between hyperfine states, demonstrating coherent control of the atomic states through the cavity field. These observations enable the preparation of coherent atomic superposition states, which are required for the implementation of an atomic quantum memory.

SQUID-based detection of ultra-low-field multinuclear NMR of substances hyperpolarized using signal amplification by reversible exchange.

Ultra-low-field (ULF) nuclear magnetic resonance (NMR) is a promising spectroscopy method allowing for, e.g., the simultaneous detection of multiple nuclei. To overcome the low signal-to-noise ratio that usually hampers a wider application, we present here an alternative approach to ULF NMR, which makes use of the hyperpolarizing technique signal amplification by reversible exchange (SABRE). In contrast to standard parahydrogen hyperpolarization, SABRE can continuously hyperpolarize 1 H as well as other MR-active nuclei. For simultaneous measurements of 1 H and 19 F under SABRE conditions a superconducting quantum interference device (SQUID)-based NMR detection unit was adapted. We successfully hyperpolarized fluorinated pyridine derivatives with an up to 2000-fold signal enhancement in 19 F. The detected signals may be explained by two alternative reaction mechanisms. SABRE combined with simultaneous SQUID-based broadband multinuclear detection may enable the quantitative analysis of multinuclear processes.

Current-Phase Relation of Ballistic Graphene Josephson Junctions.

The current-phase relation (CPR) of a Josephson junction (JJ) determines how the supercurrent evolves with the superconducting phase difference across the junction. Knowledge of the CPR is essential in order to understand the response of a JJ to various external parameters. Despite the rising interest in ultraclean encapsulated graphene JJs, the CPR of such junctions remains unknown. Here, we use a fully gate-tunable graphene superconducting quantum intereference device (SQUID) to determine the CPR of ballistic graphene JJs. Each of the two JJs in the SQUID is made with graphene encapsulated in hexagonal boron nitride. By independently controlling the critical current of the JJs, we can operate the SQUID either in a symmetric or asymmetric configuration. The highly asymmetric SQUID allows us to phase-bias one of the JJs and thereby directly obtain its CPR. The CPR is found to be skewed, deviating significantly from a sinusoidal form. The skewness can be tuned with the gate voltage and oscillates in antiphase with Fabry-Pérot resistance oscillations of the ballistic graphene cavity. We compare our experiments with tight-binding calculations that include realistic graphene-superconductor interfaces and find a good qualitative agreement.

A high-resolution combined scanning laser and widefield polarizing microscope for imaging at temperatures from 4 K to 300 K.

Polarized light microscopy, as a contrast-enhancing technique for optically anisotropic materials, is a method well suited for the investigation of a wide variety of effects in solid-state physics, as, for example, birefringence in crystals or the magneto-optical Kerr effect (MOKE). We present a microscopy setup that combines a widefield microscope and a confocal scanning laser microscope with polarization-sensitive detectors. By using a high numerical aperture objective, a spatial resolution of about 240 nm at a wavelength of 405 nm is achieved. The sample is mounted on a 4He continuous flow cryostat providing a temperature range between 4 K and 300 K, and electromagnets are used to apply magnetic fields of up to 800 mT with variable in-plane orientation and 20 mT with out-of-plane orientation. Typical applications of the polarizing microscope are the imaging of the in-plane and out-of-plane magnetization via the longitudinal and polar MOKE, imaging of magnetic flux structures in superconductors covered with a magneto-optical indicator film via the Faraday effect, or imaging of structural features, such as twin-walls in tetragonal SrTiO3. The scanning laser microscope furthermore offers the possibility to gain local information on electric transport properties of a sample by detecting the beam-induced voltage change across a current-biased sample. This combination of magnetic, structural, and electric imaging capabilities makes the microscope a viable tool for research in the fields of oxide electronics, spintronics, magnetism, and superconductivity.

Tunable φ Josephson junction ratchet.

We demonstrate experimentally the operation of a deterministic Josephson ratchet with tunable asymmetry. The ratchet is based on a φ Josephson junction with a ferromagnetic barrier operating in the underdamped regime. The system is probed also under the action of an additional dc current, which acts as a counterforce trying to stop the ratchet. Under these conditions the ratchet works against the counterforce, thus producing a nonzero output power. Finally, we estimate the efficiency of the φ Josephson junction ratchet.

Model I-V curves and figures of merit of underdamped deterministic Josephson ratchets.

We propose simple models for the current-voltage characteristics of typical Josephson ratchets. We consider the case of a ratchet working against a constant applied counter force and derive analytical expressions for the key characteristics of such a ratchet: rectification curve, stopping force, input and output powers, and rectification efficiency. Optimization of the ratchet performance is discussed.

Local Electrical Imaging of Tetragonal Domains and Field-Induced Ferroelectric Twin Walls in Conducting SrTiO_{3}.

We demonstrate electrical mapping of tetragonal domains and electric field-induced twin walls in SrTiO_{3} as a function of temperature and gate bias utilizing the conducting LaAlO_{3}/SrTiO_{3} interface and low-temperature scanning electron microscopy. Conducting twin walls appear below 105 K, and new twin patterns are observed after thermal cycling through the transition or on electric field gating. The nature of the twin walls is confirmed by calculating their intersection angles for different substrate orientations. Numerous walls formed when a large side- or back-gate voltage is applied are identified as field-induced ferroelectric twin walls in the paraelectric tetragonal matrix. The walls persist after switching off the electric field and on thermal cycling below 105 K. These observations point to a new type of ferroelectric functionality in SrTiO_{3}, which could be exploited together with magnetism and superconductivity in a multifunctional context.

Quantitative nanoscale vortex imaging using a cryogenic quantum magnetometer.

Microscopic studies of superconductors and their vortices play a pivotal role in understanding the mechanisms underlying superconductivity. Local measurements of penetration depths or magnetic stray fields enable access to fundamental aspects such as nanoscale variations in superfluid densities or the order parameter symmetry of superconductors. However, experimental tools that offer quantitative, nanoscale magnetometry and operate over large ranges of temperature and magnetic fields are still lacking. Here, we demonstrate the first operation of a cryogenic scanning quantum sensor in the form of a single nitrogen-vacancy electronic spin in diamond, which is capable of overcoming these existing limitations. To demonstrate the power of our approach, we perform quantitative, nanoscale magnetic imaging of Pearl vortices in the cuprate superconductor YBa2Cu3O7-δ. With a sensor-to-sample distance of ∼10 nm, we observe striking deviations from the prevalent monopole approximation in our vortex stray-field images, and find excellent quantitative agreement with Pearl's analytic model. Our experiments provide a non-invasive and unambiguous determination of the system's local penetration depth and are readily extended to higher temperatures and magnetic fields. These results demonstrate the potential of quantitative quantum sensors in benchmarking microscopic models of complex electronic systems and open the door for further exploration of strongly correlated electron physics using scanning nitrogen-vacancy magnetometry.

Sensitivity of ultracold atoms to quantized flux in a superconducting ring.

We report on the magnetic trapping of an ultracold ensemble of (87)Rb atoms close to a superconducting ring prepared in different states of quantized magnetic flux. The niobium ring of 10 µm radius is prepared in a flux state n Φ(0), where Φ(0)=h/2e is the flux quantum and n varying between ±6. An atomic cloud of 250 nK temperature is positioned with a harmonic magnetic trapping potential at ∼18 µm distance below the ring. The inhomogeneous magnetic field of the supercurrent in the ring contributes to the magnetic trapping potential of the cloud. The induced deformation of the magnetic trap impacts the shape of the cloud, the number of trapped atoms, as well as the center-of-mass oscillation frequency of Bose-Einstein condensates. When the field applied during cooldown of the chip is varied, the change of these properties shows discrete steps that quantitatively match flux quantization.

Conductivity and magnetoresistance of La0.7Ce0.3MnO(3-δ) thin films under photoexcitation.

La0.7Ce0.3MnO3 thin films of different thicknesses, degrees of CeO2-phase segregation and oxygen deficiency, grown on SrTiO3 single crystal substrates, were comparatively investigated with respect to both their spectral and temperature-dependent photoconductivity (PC) and their magnetoresistance (MR) behaviour under photoexcitation. While as-grown films were insensitive to optical excitation, oxygen reduction appeared to be an effective way to decrease the film resistance, but the film thickness was found to play a minor role. However, from the evaluation of the spectral behaviour of the PC and the comparison of the MR of the LCeMO/substrate-samples with a bare substrate under illumination we find that the photoconductivity data reflects not only contributions from (i) photogenerated charge carriers in the film and (ii) carriers injected from the photoconductive substrate (as concluded from earlier works), but also (iii) a decisive parallel photoconduction in the SrTiO3 substrate. Furthermore--also by analyzing the MR characteristics--the unexpected occurence of a strong electroresistive effect in the sample with the highest degree of CeO2 segregation and oxygen deficiency could be attributed to the electroresistance of the SrTiO3 substrate as well. The results suggest a critical reconsideration and possibly a reinterpretation of several previous photoconductivity and electroresistance investigations of manganite thin films on SrTiO3.

The Mn(2+)/Mn(3+) state of La0.7Ce0.3MnO3 by oxygen reduction and photodoping.

Films of cerium-doped LaMnO3, which has been intensively discussed as an electron-doped counterpart to hole-doped mixed-valence lanthanum manganites during the past decade, were analyzed by x-ray photoemission spectroscopy with respect to their manganese valence under photoexcitation. The comparative analysis of the Mn 3s exchange splitting of La0.7Ce0.3MnO3 (LCeMO) films in the dark and under illumination clearly shows that both oxygen reduction and illumination are able to decrease the Mn valence towards a mixed 2+/3+ state, independently of the film thickness and the degree of CeO2 segregation. Charge-injection from the photoconductive SrTiO3 substrate into the Mn eg band with carrier lifetimes in the range of tens of seconds and intrinsic generation of electron-hole pairs within the films are discussed as two possible sources of the Mn valence shift and the subsequent electron doping.

Phase retrapping in a pointlike φ Josephson junction: the butterfly effect.

We consider a φ Josephson junction, which has a bistable zero-voltage state with the stationary phases ψ = ±φ. In the nonzero voltage state the phase "moves" viscously along a tilted periodic double-well potential. When the tilting is reduced quasistatically, the phase is retrapped in one of the potential wells. We study the viscous phase dynamics to determine in which well (-φ or +φ) the phase is retrapped for a given damping, when the junction returns from the finite-voltage state back to the zero-voltage state. In the limit of low damping, the φ Josephson junction exhibits a butterfly effect-extreme sensitivity of the destination well on damping. This leads to an impossibility to predict the destination well.

Reversal mechanism of an individual Ni nanotube simultaneously studied by torque and SQUID magnetometry.

Using an optimally coupled nanometer-scale SQUID, we measure the magnetic flux originating from an individual ferromagnetic Ni nanotube attached to a Si cantilever. At the same time, we detect the nanotube's volume magnetization using torque magnetometry. We observe both the predicted reversible and irreversible reversal processes. A detailed comparison with micromagnetic simulations suggests that vortexlike states are formed in different segments of the individual nanotube. Such stray-field free states are interesting for memory applications and noninvasive sensing.

Ferromagnetic planar Josephson junction with transparent interfaces: a φ junction proposal.

We calculate the current-phase relation of a planar Josephson junction with a ferromagnetic weak link located on top of a thin normal metal film. Following experimental observations we assume transparent superconductor-ferromagnet interfaces. This provides the best interlayer coupling and a low suppression of the superconducting correlations penetrating from the superconducting electrodes into the ferromagnetic layer. We show that this Josephson junction is a promising candidate for experimental φ junction realization.

Experimental evidence of a φ Josephson junction.

We demonstrate experimentally the existence of Josephson junctions having a doubly degenerate ground state with an average Josephson phase ψ=±φ. The value of φ can be chosen by design in the interval 0<φ<π. The junctions used in our experiments are fabricated as 0-π Josephson junctions of moderate normalized length with asymmetric 0 and π regions. We show that (a) these φ Josephson junctions have two critical currents, corresponding to the escape of the phase ψ from -φ and +φ states, (b) the phase ψ can be set to a particular state by tuning an external magnetic field, or (c) by using a proper bias current sweep sequence. The experimental observations are in agreement with previous theoretical predictions.

Deterministic Josephson vortex ratchet with a load.

We investigate experimentally a deterministic underdamped Josephson vortex ratchet-a fluxon particle moving along a Josephson junction in an asymmetric periodic potential. By applying a sinusoidal driving current, one can compel the vortex to move in a certain direction, producing an average dc voltage across the junction. Being in such a rectification regime, we also load the ratchet, i.e., apply an additional dc bias current I(dc) (counterforce) which tilts the potential so that the fluxon climbs uphill due to the ratchet effect. The value of the bias current at which the fluxon stops climbing up defines the strength of the ratchet effect and is determined experimentally. This allows us to estimate the loading capability of the ratchet, the output power, and the efficiency. For the quasistatic regime we present a simple model which delivers straightforward analytic expressions for the above-mentioned figures of merit.

Josephson junction with a magnetic-field tunable ground state.

We consider an asymmetric 0-π Josephson junction consisting of 0 and π regions of different lengths L(0) and L(π). As predicted earlier this system can be described by an effective sine-Gordon equation for the spatially averaged phase ψ so that the effective current-phase relation of this system includes a negative second harmonic ∝sin(2ψ). If its amplitude is large enough, the ground state of the junction is doubly degenerate ψ=±φ, where φ depends on the amplitudes of the first and second harmonics. We study the behavior of such a junction in an applied magnetic field H and demonstrate that H induces an additional term ∝Hcosψ in the effective current-phase relation. This results in a nontrivial ground state tunable by magnetic field. The dependence of the critical current on H allows for revealing the ground state experimentally.