Measuring the geometric component of the transition probability in a two-level system

Topological Metamaterials

The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.

Verdazyl-ribose: A new radical for solid-state dynamic nuclear polarization at high magnetic field

Solid-state dynamic nuclear polarization (DNP) using the cross-effect relies on radical pairs whose electron spin resonance (ESR) frequencies differ by the nuclear magnetic resonance (NMR) frequency. We measure the DNP provided by a new water-soluble verdazyl radical, verdazyl-ribose, under both magic-angle spinning (MAS) and static sample conditions at 9.4 T, and compare it to a nitroxide radical, 4-hydroxy-TEMPO. We find that verdazyl-ribose is an effective radical for cross-effect DNP, with the best relative results for a non-spinning sample. Under non-spinning conditions, verdazyl-ribose provides roughly 2× larger 13C cross-polarized (CP) NMR signal than the nitroxide, with similar polarization buildup times, at both 29 K and 76 K. With MAS at 7 kHz and 1.5 W microwave power, the verdazyl-ribose does not provide as much DNP as the nitroxide, with the verdazyl providing less NMR signal and a longer polarization buildup time. When the microwave power is decreased to 30 mW with 5 kHz MAS, the two types of radical are comparable, with the verdazyl-doped sample having a larger NMR signal which compensates for its longer polarization buildup time. We also present electron spin relaxation measurements at Q-band (1.2 T) and ESR lineshapes at 1.2 and 9.4 T. Most notably, the verdazyl radical has a longer T1e than the nitroxide (9.9 ms and 1.3 ms, respectively, at 50 K and 1.2 T). The verdazyl electron spin lineshape is significantly affected by the hyperfine coupling to four 14N nuclei, even at 9.4 T. We also describe 3000-spin calculations to illustrate the DNP potential of possible radical pairs: verdazyl-verdazyl, verdazyl-nitroxide, or nitroxide-nitroxide pairs. These calculations suggest that the verdazyl radical at 9.4 T has a narrower linewidth than optimal for cross-effect DNP using verdazyl-verdazyl pairs. Because of the hyperfine coupling contribution to the electron spin linewidth, this implies that DNP using the verdazyl radical would improve at lower magnetic field. Another conclusion from the calculations is that a verdazyl-nitroxide bi-radical would be expected to be slightly better for cross-effect DNP than the nitroxide-nitroxide bi-radicals commonly used now, assuming the same spin-spin coupling constants.

Double electron-electron resonance with multiple non-selective chirp refocusing

A new approach to double electron-electron resonance (DEER) for distance determination involving nitroxide spin labels at dilute concentrations is presented. In general, DEER pulse sequences rely on double resonance between pump and observer spins excited by selective pulses at two distinct microwave frequencies. In the new approach abbreviated as nDEER, non-selective chirp pulses that refocus all relevant spin pairs are combined with DEER. This non-selective refocusing results in suppression of unmodulated contributions, such as the constant contribution as well as the background curvature due to inter-molecular spin partners in ordinary DEER data. Due to this dipolar attenuation effect, primary nDEER data are closer to the dipolar modulation of primary interest than ordinary DEER data. Restrictions of nDEER are that secondary information related to these unmodulated contributions becomes difficult to retrieve. Accordingly, incomplete deconvolution of the inter-molecular background prevents the application of nDEER to rigid spin pairs at high concentrations. A key advantage of nDEER is the high fidelity of the chirp refocusing pulses, which is important for nDEER schemes that incorporate dynamical decoupling to access longer distances. In this context, nDEER with Carr-Purcell (CP) pulse trains having N = 2 and N = 4 refocusing pulses are demonstrated. These CP nDEER sequences require a total of N + 2 pulses, which is less than the 2N + 1 pulses required for CP DEER schemes. The pump pulse position is incremented throughout the refocusing pulses, which restricts the minimum time increment to 96 ns on our spectrometer and therefore complicates application to distances below 3 nm. At Q-band frequencies, unwanted modulations related to pulse imperfections contribute only 3.5% relative to the principal nDEER modulation. Accordingly, there is no need for dedicated data reconstruction methods as in CP DEER methods.

Wideband frequency-swept excitation in pulsed EPR spectroscopy

Excitation of electron spins with monochromatic rectangular pulses is limited to bandwidths that are smaller than the spectral widths of most organic radicals and much smaller than the spectral widths of transition and rare earth metal ions. With frequency-swept pulses, bandwidths of up to 800MHz have previously been attained for excitation and detection of spin packets at frequencies of about 9.6GHz and bandwidths of up to 2.5GHz in a polarization transfer experiment at frequencies of about 34GHz. The remaining limitations, mainly due to resonator bandwidth and due to pulse length restrictions are discussed. Flip angles for state-space rotations on passage of a transition can generally be computed from the critical adiabaticity by the Landau-Zener-Stückelberg-Majorana expression. For hyperbolic secant pulses, the Demkov-Kunike model describes excitation for spin packets within and outside the sweep range. Well within the sweep range, the Bloch-Siegert phase shift is proportional to critical adiabaticity to a very good approximation. Because of the dependence of both flip angle and coherence phase on critical adiabaticity, it is advantageous to use pairs of amplitude and frequency modulation functions that provide such offset-independent adiabaticity. Compensation for the resonator response function should restore offset-independent adiabaticity. Whereas resonance offsets and Bloch-Siegert phase can be refocused at certain pulse length ratios, phase dispersion in coupled spin systems cannot generally be refocused. Based on the bandwidth limitations that arise from spin dynamics, requirements are derived for a spectrometer that achieves precise spin control over wide bands. The design of such a spectrometer and hardware characterization by EPR experiments are discussed.

EPR-correlated dipolar spectroscopy by Q-band chirp SIFTER

Frequency-swept chirp pulses uniformly excite the nitroxide spectrum at Q-band frequencies, which allows for acquisition of two-dimensional spectra correlating the dipolar spectrum to the EPR spectrum.

Perturbation of nuclear spin polarizations in solid state NMR of nitroxide-doped samples by magic-angle spinning without microwaves

We report solid state (13)C and (1)H nuclear magnetic resonance (NMR) experiments with magic-angle spinning (MAS) on frozen solutions containing nitroxide-based paramagnetic dopants that indicate significant perturbations of nuclear spin polarizations without microwave irradiation. At temperatures near 25 K, (1)H and cross-polarized (13)C NMR signals from (15)N,(13)C-labeled L-alanine in trinitroxide-doped glycerol/water are reduced by factors as large as six compared to signals from samples without nitroxide doping. Without MAS or at temperatures near 100 K, differences between signals with and without nitroxide doping are much smaller. We attribute most of the reduction of NMR signals under MAS near 25 K to nuclear spin depolarization through the cross-effect dynamic nuclear polarization mechanism, in which three-spin flips drive nuclear polarizations toward equilibrium with spin polarization differences between electron pairs. When T1e is sufficiently long relative to the MAS rotation period, the distribution of electron spin polarization across the nitroxide electron paramagnetic resonance lineshape can be very different from the corresponding distribution in a static sample at thermal equilibrium, leading to the observed effects. We describe three-spin and 3000-spin calculations that qualitatively reproduce the experimental observations.

Theory for cross effect dynamic nuclear polarization under magic-angle spinning in solid state nuclear magnetic resonance: the importance of level crossings

We present theoretical calculations of dynamic nuclear polarization (DNP) due to the cross effect in nuclear magnetic resonance under magic-angle spinning (MAS). Using a three-spin model (two electrons and one nucleus), cross effect DNP with MAS for electron spins with a large g-anisotropy can be seen as a series of spin transitions at avoided crossings of the energy levels, with varying degrees of adiabaticity. If the electron spin-lattice relaxation time T(1e) is large relative to the MAS rotation period, the cross effect can happen as two separate events: (i) partial saturation of one electron spin by the applied microwaves as one electron spin resonance (ESR) frequency crosses the microwave frequency and (ii) flip of all three spins, when the difference of the two ESR frequencies crosses the nuclear frequency, which transfers polarization to the nuclear spin if the two electron spins have different polarizations. In addition, adiabatic level crossings at which the two ESR frequencies become equal serve to maintain non-uniform saturation across the ESR line. We present analytical results based on the Landau-Zener theory of adiabatic transitions, as well as numerical quantum mechanical calculations for the evolution of the time-dependent three-spin system. These calculations provide insight into the dependence of cross effect DNP on various experimental parameters, including MAS frequency, microwave field strength, spin relaxation rates, hyperfine and electron-electron dipole coupling strengths, and the nature of the biradical dopants.

Non-cyclic geometric phase of nuclear quadrupole resonance signals of powdered samples

The non-cyclic geometric phase of ¹⁴N and ³⁵Cl NQR signals induced by the character of trajectory of nuclear magnetization motion upon pulse r.f. excitation of powdered samples is studied. Analytical expressions for the geometric phases of NQR signals of the nuclei of spins I=1 and 3/2 upon nuclear magnetization rotation induced by means of r.f. pulses with frequency detuned from the resonance and for any impulse duration for a separate crystallite are obtained. It is shown that the geometric phase recorded for the signal from a powdered sample at Δω=0 can be different from zero and can oscillate upon changes in duration of the r.f. excitation pulse. An alternative variant of the nutation experiment aimed at obtaining the asymmetry parameter η from locations of frequency singularities in the nutation phase spectrum for nuclei of spin I=3/2 in powder substances is proposed.

Increasing 14N NQR signal by 1H-14N level crossing with small magnetic fields

NQR detection of materials, such as TNT, is hindered by the low signal-to-noise ratio at low NQR frequencies. Sweeping small (0-26 mT) magnetic fields to shift the (1)H NMR frequency relative to the (14)N NQR frequencies can provide a significant increase of the (14)N NQR signal-to-noise ratio. Three effects of (1)H-(14)N level crossing are demonstrated in diglycine hydrochloride and TNT. These effects are (1) transferring (1)H polarization to one or more of the (14)N transitions, including the use of an adiabatic flip of the (1)H polarization during the field sweep, (2) shortening the effective (14)N T(1) by the interaction of (1)H with the (14)N transitions, (3) "level transfer" effect where the third (14)N (spin 1) energy level or other (14)N sites with different NQR frequency are used as a reservoir of polarization which is transferred to the measured (14)N transition by the (1)H. The (14)N NQR signal-to-noise ratio can be increased by a factor of 2.5 for one (14)N site in diglycine hydrochloride (and 2.2 in TNT), even though the maximum (1)H frequency used in this work, 111 6 kHz, is only 30% larger than the measured (14)N frequencies (834 kHz for diglycine hydrochloride and 843 kHz for TNT).

170 nm nuclear magnetic resonance imaging using magnetic resonance force microscopy

We demonstrate one-dimensional nuclear magnetic resonance imaging of the semiconductor GaAs with 170 nm slice separation and resolve two regions of reduced nuclear spin polarization density separated by only 500 nm. This was achieved by force detection of the magnetic resonance, magnetic resonance force microscopy (MRFM), in combination with optical pumping to increase the nuclear spin polarization. Optical pumping of the GaAs created spin polarization up to 12 times larger than the thermal nuclear spin polarization at 5K and 4T. The experiment was sensitive to sample volumes of 50 microm(3) containing approximately 4 x 10(11)71 Ga/Hz. These results demonstrate the ability of force-detected magnetic resonance to apply magnetic resonance imaging to semiconductor devices and other nanostructures.