Explore the vast range of titles available.

Unconventional superconductivity often emerges in close proximity to a magnetic instability. Upon suppressing the magnetic transition down to zero temperature by tuning the carrier concentration, pressure, or disorder, the superconducting transition temperature Tc acquires its maximum value. A major challenge is the elucidation of the relationship between the superconducting phase and the strong quantum fluctuations expected near a quantum phase transition (QPT) that is either second order (i.e. a quantum critical point) or weakly first order. While unusual normal state properties, such as non-Fermi liquid behavior of the resistivity, are commonly associated with strong quantum fluctuations, evidence for its presence inside the superconducting dome are much scarcer. In this paper, we use sensitive and minimally invasive optical magnetometry based on NV-centers in diamond to probe the doping evolution of the T = 0 penetration depth in the electron-doped iron-based superconductor Ba(Fe1−xCox)2As2. A non-monotonic evolution with a pronounced peak in the vicinity of the putative magnetic QPT is found. This behavior is reminiscent to that previously seen in isovalently-substituted BaFe2(As1−xPx)2 compounds, despite the notable differences between these two systems. Whereas the latter is a very clean system that displays nodal superconductivity and a single simultaneous first-order nematic-magnetic transition, the former is a charge-doped and significantly dirtier system with fully gapped superconductivity and split second-order nematic and magnetic transitions. Thus, our observation of a sharp peak in λ(x) near optimal doping, combined with the theoretical result that a QPT alone does not mandate the appearance of such peak, unveils a puzzling and seemingly universal manifestation of magnetic quantum fluctuations in iron-based superconductors and unusually robust quantum phase transition under the dome of superconductivity.

Non-invasive magnetic field sensing using optically-detected magnetic resonance of nitrogen-vacancy centers in diamond was used to study spatial distribution of the magnetic induction upon penetration and expulsion of weak magnetic fields in several representative superconductors. Vector magnetic fields were measured on the surface of conventional, elemental Pb and Nb, and compound LuNi2B2C and unconventional iron-based superconductors Ba1−x KxFe2As2 (x = 0.34 optimal hole doping), Ba(Fe1−x Cox)2As2 (x = 0.07 optimal electron doping), and stoichiometric CaKFe4As4, using variable-temperature confocal system with diffraction-limited spatial resolution. Magnetic induction profiles across the crystal edges were measured in zero-field-cooled and field-cooled conditions. While all superconductors show nearly perfect screening of magnetic fields applied after cooling to temperatures well below the superconducting transition, Tc, a range of very different behaviors was observed for Meissner expulsion upon cooling in static magnetic field from above Tc. Substantial conventional Meissner expulsion is found in LuNi2B2C, paramagnetic Meissner effect is found in Nb, and virtually no expulsion is observed in iron-based superconductors. In all cases, good correlation with macroscopic measurements of total magnetic moment is found.

While it is often thought that the geometric phase is less sensitive to fluctuations in the control fields, a very general feature of adiabatic Hamiltonians is the unavoidable dynamic phase that accompanies the geometric phase. The effect of control field noise during adiabatic geometric quantum gate operations has not been probed experimentally, especially in the canonical spin qubit system that is of interest for quantum information. We present measurement of the Berry phase and carry out adiabatic geometric phase gate in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. We manipulate the spin qubit geometrically by careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting Berry phase signal via spin echo interferometry. Our results show that control field noise at frequencies higher than the spin echo clock frequency causes decay of the quantum phase, and degrades the fidelity of the geometric phase gate to the classical threshold after a few (∼10) operations. This occurs inspite of the geometric nature of the state preparation, due to unavoidable dynamic contributions. We have carried out systematic analysis and numerical simulations to study the effects of the control field noise and imperfect driving waveforms on the quantum phase gate.

Magnetic sensors capable of detecting nanoscale volumes of spins allow for non-invasive, element-specific probing 1 , 2 , 3 . The error in such measurements is usually reduced by increasing the measurement time, and noise averaging the signal 4 , 5 . However, achieving the best precision requires restricting the maximum possible field strength to much less than the spectral linewidth of the sensor. Quantum entanglement and squeezing can then be used to improve precision (although they are difficult to implement in solid-state environments). When the field strength is comparable to or greater than the spectral linewidth, an undesirable trade-off between field strength and signal precision occurs 1 . Here, we implement novel phase estimation algorithms 6 , 7 , 8 on a single electronic spin associated with the nitrogen-vacancy defect centre in diamond to achieve an ∼8.5-fold improvement in the ratio of the maximum field strength to precision, for field magnitudes that are large (∼0.3 mT) compared to the spectral linewidth of the sensor (∼4.5 µT). The field uncertainty in our approach scales as 1/ T 0.88 , compared to 1/ T 0.5 in the standard measurement approach, where T is the measurement time. Quantum phase estimation algorithms have also recently been implemented using a single nuclear spin in a nitrogen-vacancy centre 9 . Besides their direct impact on applications in magnetic sensing and imaging at the nanoscale, these results may prove useful in improving a variety of high-precision spectroscopy techniques. Phase-estimation algorithms applied to single electronic spins in diamond allow weak magnetic fields to be measured with high sensitivity and a large dynamic range.

Unconventional superconductivity often emerges in close proximity to a magnetic instability. Upon suppressing the magnetic transition down to zero temperature by tuning the carrier concentration, pressure, or disorder, the superconducting transition temperature T c acquires its maximum value. A major challenge is the elucidation of the relationship between the superconducting phase and the strong quantum fluctuations expected near a quantum phase transition (QPT) that is either second order (i.e. a quantum critical point) or weakly first order. While unusual normal state properties, such as non-Fermi liquid behavior of the resistivity, are commonly associated with strong quantum fluctuations, evidence for its presence inside the superconducting dome are much scarcer. In this paper, we use sensitive and minimally invasive optical magnetometry based on NV-centers in diamond to probe the doping evolution of the T = 0 penetration depth in the electron-doped iron-based superconductor Ba(Fe 1− x Co x ) 2 As 2 . A non-monotonic evolution with a pronounced peak in the vicinity of the putative magnetic QPT is found. This behavior is reminiscent to that previously seen in isovalently-substituted BaFe 2 (As 1− x P x ) 2 compounds, despite the notable differences between these two systems. Whereas the latter is a very clean system that displays nodal superconductivity and a single simultaneous first-order nematic–magnetic transition, the former is a charge-doped and significantly dirtier system with fully gapped superconductivity and split second-order nematic and magnetic transitions. Thus, our observation of a sharp peak in λ ( x ) near optimal doping, combined with the theoretical result that a QPT alone does not mandate the appearance of such peak, unveils a puzzling and seemingly universal manifestation of magnetic quantum fluctuations in iron-based superconductors and unusually robust quantum phase transition under the dome of superconductivity.

We report combined experimental and theoretical analysis of superconductivity in CaK(Fe\\(_{1-x}\\)Ni\\(_x\\))\\(_4\\)As\\(_4\\) (CaK1144) for \\(x=\\)0, 0.017 and 0.034. To obtain the superfluid density, \\(\\rho=\\left(1+\\Delta \\lambda_L(T)/\\lambda_L(0) \\right)^{-2}\\), the temperature dependence of the London penetration depth, \\(\\Delta \\lambda_L (T)\\), was measured by using tunnel-diode resonator (TDR) and the results agreed with the microwave coplanar resonator (MWR) with the small differences accounted for by considering a three orders of magnitude higher frequency of MWR. The absolute value of \\(\\lambda_L (T \\ll T_c) \\approx \\lambda_L(0)\\) was measured by using MWR, \\(\\lambda_L (\\mathrm{5~K}) \\approx 170 \\pm 20\\) nm, which agreed well with the NV-centers in diamond optical magnetometry that gave \\(\\lambda_L (\\mathrm{5~K}) \\approx 196 \\pm 12\\) nm. The experimental results are analyzed within the Eliashberg theory, showing that the superconductivity of CaK1144 is well described by the nodeless s\\(_{\\pm}\\) order parameter and that upon Ni doping the interband interaction increases.

The lower critical magnetic field, \\(H_{c1}\\), of superconductors is measured by using ensembles of NV-centers-in-diamond optical magnetometry. The technique is minimally invasive, and has sub-gauss field sensitivity and sub-\\(\\mu\\)m spatial resolution, which allow for accurate detection of the vector field at which the vortices start penetrating the sample from the corners. Aided by the revised calculations of the effective demagnetization factors of actual cuboid - shaped samples, \\(H_{c1}\\) and the London penetration depth, \\(\\lambda\\), derived from \\(H_{c1}\\) can be obtained. We apply this method to three well-studied superconductors: optimally doped Ba(Fe\\(_{1-x}\\)Co\\(_{x}\\))\\(_2\\)As\\(_2\\), stoichiometric CaKFe\\(_4\\)As\\(_4\\), and high-\\(T_c\\) cuprate YBa\\(_2\\)Cu\\(_3\\)O\\(_{7-\\delta}\\). Our results are well compared with the values of \\(\\lambda\\) obtained using other techniques, thus adding another non-destructive and sensitive method to measure these important parameters of superconductors.

We present a detailed theoretical and numerical study discussing the application and optimization of phase estimation algorithms (PEAs) to diamond spin magnetometry. We compare standard Ramsey magnetometry, the non-adaptive PEA (NAPEA) and quantum PEA (QPEA) incorporating error-checking. Our results show that the NAPEA requires lower measurement fidelity, has better dynamic range, and greater consistency in sensitivity. We elucidate the importance of dynamic range to Ramsey magnetic imaging with diamond spins, and introduce the application of PEAs to time-dependent magnetometry.

We present an experimental method to perform dual-channel lock-in magnetometry of time-dependent magnetic fields using a single spin associated with a nitrogen-vacancy (NV) color center in diamond. We incorporate multi-pulse quantum sensing sequences with phase estimation algorithms to achieve linearized field readout and constant, nearly decoherence-limited sensitivity over a wide dynamic range. Furthermore, we demonstrate unambiguous reconstruction of the amplitude and phase of the magnetic field. We show that our technique can be applied to measure random phase jumps in the magnetic field, as well as phase-sensitive readout of the frequency.

Non-invasive magnetic field sensing using optically - detected magnetic resonance of nitrogen-vacancy (NV) centers in diamond was used to study spatial distribution of the magnetic induction upon penetration and expulsion of weak magnetic fields in several representative superconductors. Vector magnetic fields were measured on the surface of conventional, Pb and Nb, and unconventional, LuNi\\(_2\\)B\\(_2\\)C, Ba\\(_{0.6}\\)K\\(_{0.4}\\)Fe\\(_2\\)As\\(_2\\), Ba(Fe\\(_{0.93}\\)Co\\(_{0.07}\\))\\(_2\\)As\\(_2\\), and CaKFe\\(_4\\)As\\(_4\\), superconductors, with diffraction - limited spatial resolution using variable - temperature confocal system. Magnetic induction profiles across the crystal edges were measured in zero-field-cooled (ZFC) and field-cooled (FC) conditions. While all superconductors show nearly perfect screening of magnetic fields applied after cooling to temperatures well below the superconducting transition, \\(T_c\\), a range of very different behaviors was observed for Meissner expulsion upon cooling in static magnetic field from above \\(T_c\\). Substantial conventional Meissner expulsion is found in LuNi\\(_2\\)B\\(_2\\)C, paramagnetic Meissner effect (PME) is found in Nb, and virtually no expulsion is observed in iron-based superconductors. In all cases, good correlation with macroscopic measurements of total magnetic moment is found. Our measurements of the spatial distribution of magnetic induction provide insight into microscopic physics of the Meissner effect.