Application of phase estimation algorithms to improve diamond spin magnetometry

Precision measurements of weak magnetic fields with nanoscale spatial resolution is an outstanding challenge in many fields including medicine, biology, material science and physical science. It has already been demonstrated that a single electronic spin formed by a defect color center in diamond, known as the nitrogen-vacancy (NV) center, can serve as a highly sensitive magnetometer with nanoscale resolution, even under ambient conditions. However, standard quantum sensing methods have significant drawbacks. These include the limited dynamic range due to quantum phase ambiguity, the non-linearity in sensitivity over the detectable field range, the requirement of prior knowledge of a working point for accurate deconvolution, etc. This thesis explores novel quantum control techniques such as the use of phase estimation algorithms (PEA) for magnetic field detection to address these issues. Unlike in the standard approach, PEA readout is linearly dependent on the field being sensed. PEA employed on oscillating (AC) magnetic fields can not only detect unknown field amplitudes but also allows detection of the field phase. The thesis also compares the performance of nonadaptive-PEA (NAPEA) with that of adaptive-PEA (QPEA) and conclude that NAPEA is superior to QPEA due to (a) better sensitivity on average, (b) consistency in sensitivity throughout the full field range, (c) comparatively less demanding measurement fidelity, and (d) for simplicity in its experimental realization. The techniques developed here can potentially have broad applicability to a wide variety of solid-state quantum systems and in the field of quantum control and measurement

Spatially-resolved study of the Meissner effect in superconductors using NV-centers-in-diamond optical magnetometry

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

Quantum phase transition inside the superconducting dome of Ba(Fe1-xCox)2As2 from diamond-based optical magnetometry

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 $\lambda (x)$ 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

Analysis of the London penetration depth in Ni-doped CaKFe4 As4

We report combined experimental and theoretical analysis of superconductivity in CaK(Fe1−xNix)4As4 (CaK1144) for x=0, 0.017, and 0.034. To obtain the superfluid density ρ=[1+ΔλL(T)/λL(0)]−2, the temperature dependence of the London penetration depth ΔλL(T) was measured by using a 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 λL(T≪Tc)≈λL(0) was measured by using MWR, λL(5K)≈170±20 nm, which agreed well with the NV centers in diamond optical magnetometry that gave λL(5K)≈196±12 nm, which agreed well with the NV centers in diamond optical magnetometry that gave λL(5K)≈196±12 nm. The experimental results are analyzed within the Eliashberg theory, showing that the superconductivity of CaK1144 is well described by the nodeless s± order parameter and that upon Ni doping the interband interaction increases

Nodeless multiband superconductivity in stoichiometric single-crystalline CaKFe4As4

Measurements of the London penetration depth Δλ(T) and tunneling conductance in single crystals of the recently discovered stoichiometric iron-based superconductor CaKFe4As4 (CaK1144) show nodeless, two-effective-gap superconductivity with a larger gap of about 6-10 meV and a smaller gap of about 1-4 meV. Having a critical temperature Tc,onset≈35.8 K, this material behaves similar to slightly overdoped (Ba1-xKx)Fe2As2 (e.g., x=0.54,Tc≈34 K), a known multigap s± superconductor. We conclude that the superconducting behavior of stoichiometric CaK1144 demonstrates that two-gap s± superconductivity is an essential property of high-temperature superconductivity in iron-based superconductors, independent of the degree of substitutional disorderWe thank A. Gurevich, D. D. Johnson, A. Kaminski, V. G. Kogan, and Lin-Lin Wang for useful discussions. This work was supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Science and Engineering Division. Ames Laboratory is operated for the US DOE by Iowa State University under Contract DE-AC02-07CH11358. The work in Madrid was supported by the Spanish Ministry of Economy and Competitiveness (FIS2014-54498-R and MDM-2014-0377), by the Comunidad de Madrid through program Nanofrontmag-CM (S2013/MIT-2850) by Axa Research Fund, FP7-PEOPLE-2013-CIG 618321, and the European Research Council (Grant Agreement No. 679080). Madrid's group also acknowledges SEGAINVEX-UAM. W.R.M. was funded by the Gordon and Betty Moore Foundation's EPiQS Initiative through Grant GBMF441

Quantum phase transition inside the superconducting dome of Ba(Fe1-xCox)2As2 from diamond-based optical magnetometry

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 $\lambda (x)$ 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.</p

Measuring the Lower Critical Field of Superconductors Using Nitrogen-Vacancy Centers in Diamond Optical Magnetometry

The lower critical magnetic field, H-c1, of superconductors is measured by optical magnetometry using ensembles of nitrogen-vacancy centers in diamond. The technique is minimally invasive and allows accurate detection of the vector magnetic field with subgauss sensitivity and submicrometer spatial resolution. These capabilities are used for detailed characterization of the first vortex penetration into superconducting samples from the corners. Aided by the revised calculations of the effective demagnetization factors of actual cuboid-shaped samples, these measurements provide precise determination of H-c1 and the related absolute value of the London penetration depth, lambda. We apply this method to three well-studied superconductors: optimally doped Ba(Fe1-xCox)(2)As-2, stoichiometric CaKFe4As4, and the high-T-c cuprate YBa2Cu3O7-delta. Our results compared well with the values of lambda obtained with other techniques, thus adding another noninvasive and sensitive method to measure these important parameters of superconductors.</p

Spatially-resolved study of the Meissner effect in superconductors using NV-centers-in-diamond optical magnetometry

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.</p

Nodeless multiband superconductivity in stoichiometric single-crystalline CaKFe4 As4

Measurements of the London penetration depth Δλ(T) and tunneling conductance in single crystals of the recently discovered stoichiometric iron-based superconductor CaKFe4As4 (CaK1144) show nodeless, two-effective-gap superconductivity with a larger gap of about 6–10 meV and a smaller gap of about 1–4 meV. Having a critical temperature Tc,onset≈35.8 K, this material behaves similar to slightly overdoped (Ba1−xKx)Fe2As2 (e.g., x=0.54,Tc≈34 K), a known multigap s± superconductor. We conclude that the superconducting behavior of stoichiometric CaK1144 demonstrates that two-gap s± superconductivity is an essential property of high-temperature superconductivity in iron-based superconductors, independent of the degree of substitutional disorder.This article is published as Cho, Kyuil, A. Fente, S. Teknowijoyo, M. A. Tanatar, K. R. Joshi, N. M. Nusran, T. Kong, W. R. Meier, U. Kaluarachchi, I. Guillamon, H. Suderow, S. L. Bud’ko, P. C. Canfield, and R. Prozorov. "Nodeless multiband superconductivity in stoichiometric single-crystalline CaKFe4 As4." Physical Review B 95, no. 10 (2017): 100502. DOI: 10.1103/PhysRevB.95.100502. Posted with permission.</p

Analysis of the London penetration depth in Ni-doped CaKFe4 As4

We report combined experimental and theoretical analysis of superconductivity in CaK(Fe1-xNix)(4) As-4 (CaK1144) for x = 0, 0.017, and 0.034. To obtain the superfluid density rho = [1 + Delta lambda(L)(T)/lambda(K)(0)](-2), the temperature dependence of the London penetration depth Delta lambda(L)(T) was measured by using a 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 << T-c) approximate to lambda(L)(0) was measured by using MWR, lambda(L)(5 K) approximate to 170 +/- 20 nm, which agreed well with the NV centers in diamond optical magnetometry that gave lambda(L)(5 K) 196 +/- 12 nm. The experimental results are analyzed within the Eliashberg theory, showing that the superconductivity of CaK1144 is well described by the nodeless s(+/-) order parameter and that upon Ni doping the interband interaction increases.</p