Circular polarization excitation and detection in (14)N NQR

Circular polarization excitation and detection of (14)N NQR signal are reported. A theoretical model is presented in terms of fictitious spin-1/2 operators and is compared to experiments performed on a powder crystalline sample of RDX. It is shown that in spin-1 systems with finite asymmetry--unlike previously reported NMR and symmetric spin-3/2 NQR systems (Chen et al., J. Magn. Reson. 54, 324--327, 1983; Weber and Hahn, Phys. Rev. 120, 365--375, 1960)-the circular polarization nature of the signal is due to powder orientation effects in polycrystalline samples. Sensitivity improvements up to a factor of the square root of 2 are reported using the same hardware and switching modes from linear polarization to circular polarization; this also is shown to result from the polycrystalline nature of the samples.     

Operator structure of a nonquantum and nonclassical system

There exists a connection between the vectors of the Poincaré-sphere and the elements of the complex Hilbert space C². This latter space is used to describe spin-1/2 measurements. We use this connection to study the intermediate cases of a more general spin-1/2 measurement model which has no representation in a Hilbert space. We construct the set of operators of this general model and investigate under which circumstances it is possible to define linear operators. Because no Hilbert space structure is possible for these intermediate cases, it can be expected that no linear operators are possible and it is shown that under very plausible assumptions this is indeed the case.     

Entangling capabilities of symmetric two-qubit gates

Our work addresses the problem ofgenerating maximally entangled two spin-1/2 (qubit) symmetric states using NMR, NQR, Lipkin–Meshkov–Glick Hamiltonians. Time evolution of such Hamiltonians provides various logic gates which can be used for quantum processing tasks. Pairs of spin-1/2s have modelled a wide range of problems in physics. Here, we are interested in two spin-1/2 symmetric states which belong to a subspace spanned by the angular momentum basis {|j = 1, μ〉; μ = + 1, 0, ?1}. Our technique relies on the decomposition of a Hamiltonian in terms of SU(3) basis matrices. In this context, we define a set of linearly independent, traceless, Hermitian operators which provides an alternate set of SU(n) generators. These matrices are constructed out of angular momentum operators J _x , J _y , J _z . We construct and study the properties of perfect entanglers acting on a symmetric subspace, i.e., spin-1 operators that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power.     

Sensitivity enhancement of the central-transition signal of half-integer spin quadrupolar nuclei in solid-state NMR: features of multiple fast amplitude-modulated pulse transfer

Sensitivity enhancement of solid-state NMR spectrum of half-integer spin quadrupolar nuclei under both magic-angle spinning (MAS) and static cases has been demonstrated by transferring polarisation associated with satellite transitions to the central m=-1/2-->1/2 transition with suitably modulated radio-frequency pulse schemes. It has been shown that after the application of such enhancement schemes, there still remains polarisation in the satellite transitions that can be transferred to the central transition. This polarisation is available without having to wait for the spin system to return to thermal equilibrium. We demonstrate here the additional sensitivity enhancement obtained by making use of this remaining polarisation with fast amplitude-modulated (FAM) pulse schemes under both MAS and static conditions on a spin-3/2 and a spin-5/2 system. Considerable signal enhancement is obtained with the application of the multiple FAM sequence, denoted as m-FAM. We also report here some of the salient features of these multiple FAM sequences with respect to the nutation frequency of the pulses and the spinning frequency.     

Selective control of the states of multilevel quantum systems using nonselective rotation operators

We have calculated the sequences of nonselective rotation operators separated by intervals of free evolution that perform selective rotations between adjacent levels in systems with three, four, five, and six nonequidistant levels. We have numerically simulated the realization of the calculated sequences for quadrupole nuclei with corresponding spins controlled by intense nonselective radio-frequency (RF) pulses and investigated the dependences of the realization error on the parameters of external and internal interactions. To reduce the error when the RF field is not strong enough, we have found composite nonselective RF pulses consisting of five simple ones. We show that the error of the composite selective rotation operator can be reduced signifi- cantly in comparison to the error of a simple single selective pulse.     

Muon spin relaxation in spin gap state of BaVS3

Positive muon spin relaxation measurements were performed on a spin-1/2 system BaVS₃, which shows a metal-insulator transition at T_MI= 70 K. We found a marked muon-spin depolarization below T_X= 30 K without appreciable critical divergence. The possibility of muonium formation in the insulating state rather than electron spin freezing is discussed taking into account the quenching of V spins evidenced by ⁵¹V NMR and NQR measurements. This revised version was published online in August 2006 with corrections to the Cover Date.     

Spin 3/2 Zeeman perturbed NQR in the presence of slow sample rotation

Theoretical and experimental results are presented for the case of Zeeman perturbed nuclear quadrupole resonance (NQR) using spin-3/2 nuclei with a small Zeeman interaction, gammaB0, while the sample is very slowly rotated. It is found that the decay envelope for a simple two-pulse echo measurement can be strongly affected even though the sample may rotate only a few degrees or less during the course of the measurement. To lowest order the decay envelope can be described using a one dimensional function of the product of gammaB0, the rotation rate, and the square of the pulse spacing. Aside from an indirect and weak dependence on the quadrupole asymmetry parameter, eta, the result is independent of the NQR frequency. Identical results are expected for a stationary sample in a small rotating magnetic field. The effect seen here may be used to advantage to measure rotational motion, for example of particles in fluids, or may be an additional complication for some Zeeman perturbed NQR measurements, including some NQR detection and imaging methods.     

14N核四极共振的偏共振效应

用虚拟１／２自旋算符讨论了核四极共振（ＮＱＲ）中自旋Ｉ＝１的自旋系统对激发脉冲宽度和频率偏置的响应。用单脉冲和双脉冲来观测的核四极共振信号与理论预期相符合。此外还证明，若只考虑射频场在分子电场梯度（ＥＰＧ）张量主轴坐标系（ＰＡＳ）中的一个轴上的分量（即有效射频场分量）的作用，就可用ＮＭＲ矢量模型来处理Ｉ＝１的核自旋系统。 关键词：     

Finite pulse width artifact suppression in spin-1 quadrupolar echo spectra by phase cycling

A phase cycling scheme for suppressing spectral artifacts introduced in quadrupolar echo spectroscopy of spin-1 nuclei due to finite pulse width effects is presented. The phase cycling scheme is developed using the formalism of average Hamiltonian theory and fictitious spin-1 operators. A simulation and experiment on deuterated polyethelene is performed highlighting the spectral artifact introduced by finite pulse widths and successful removal with the proposed phase cycling scheme.     

Studies of molecular dynamics of thiazides by<Superscript>35</Superscript>Cl NQR spectroscopy and DFT calculation

Molecular dynamics of three derivatives of 1,2,4-benzothiadiazine-1,1-dioxide, hydrochlorothiazide (HCTZ), althiazide (ATZ) and chlorothiazide (CTZ), was studied by³⁵Cl nuclear quadrupole resonance (NQR) spectroscopy. The temperature dependence of the resonance frequency was analyzed within the 6 known standard models. The activation energies estimated from the temperature dependence of the³⁵Cl NQR frequency assuming the Bayer model were 1.07, 2.35 and 2.76 kJ/mol for HCTZ, ATZ and CTZ respectively, which confirms that HCTZ is less rigid than CTZ and ATZ is much more rigid than HCTZ, and suggests that the mechanism of relaxation is based on small amplitude librations. The characteristic temperatures estimated from the Bayer model, with that for CTZ (332.5 K) being much higher than for HCTZ (132.1 K), mean that the intermolecular interactions in CTZ are much stronger than in HCTZ, as suggested by the melting point of CTZ being higher than that for HCTZ. For ATZ the characteristic temperature (288 K) takes an intermediate value, which suggests that the intermolecular interactions in this compound are stronger than in HCTZ and weaker than in CTZ. A significant narrowing of the resonance³⁵Cl NQR line observed for all these compounds at room temperature, relative to that at the liquid nitrogen temperature, suggests an averaging of dipolar interactions as a result of fast rotation of nonquadrupole nuclei in the vicinity of the quadrupole nuclei, when 2πν_Qτ_c ≫ 1 (a rotation of the −NH₂ group in the direct neighborhood of the chlorine nuclei) or a change in the gradient orientation with its value preserved (which is equivalent to rotation of the quadrupole nucleus Cl). The influence of the rotations of the −NH₂ and −CH₂SCH₂CH=CH₂ groups (ATZ) or −CHCl₂ group (TCTZ) on the³⁵Cl NQR frequency was modelled by the B3LYP/6-31G^* method. The frequencies of the libration vibrations calculated from the temperature dependence of the NQR resonance frequency were compared with experimental ones and those implied by the density functional theory, infrared and Raman spectra. For HCTZ the anomalies in the temperature dependence of the³⁵Cl NQR frequency, the lack of hysteresis and small but notable changes in the slope and the jump in the frequency observed at 253 K which does not exceed 0.05 MHz suggest a second-order phase transition at 253 K.     

A Vanishing Theorem for Operators in Fock Space

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space, we show that rotation invariance implies the absence of terms which either create or annihilate only a single particle. We outline an application of this result in an operator theoretic renormalization analysis of Hamilton operators, which occur in non-relativistic qed.     

Experimental realization of a spin-1/2 triangular-lattice Heisenberg antiferromagnet

We report the results of magnetization and specific heat measurements on Ba{3}CoSb{2}O{9}, in which the magnetic Co{2+} ion has a fictitious spin 1/2, and provide evidence that a spin-1/2 Heisenberg antiferromagnet on a regular triangular lattice is actually realized in Ba{3}CoSb{2}O{9}. We found that the entire magnetization curve including the one-third quantum magnetization plateau is in excellent quantitative agreement with the results of theoretical calculations. We also found that Ba{3}CoSb{2}O{9} undergoes a three-step transition within a narrow temperature range.     

A two-dimensional isotropic quantum antiferromagnet with unique disordered ground state

We continue the study of valence-bond solid antiferromagnetic quantum Hamiltonians. These Hamiltonians are invariant under rotations in spin space. We prove that a particular two-dimensional model from this class (the spin-3/2 model on the hexagonal lattice) has a unique ground state in the infinite-volume limit and hence no Néel order. Moreover, all truncated correlation functions decay exponentially in this ground state. We also characterize all the finite-volume ground states of these models (in every dimension), and prove that the two-point correlation function of the spin-2 square lattice model with periodic boundary conditions has exponential decay.     

Tensor formulation of spin-1 and spin-2 fields

Spin projection operators which constitute a resolution of the identity in the space of second rank tensor wave functions are constructed. These projectors are then used to establish Lagrangian quantum field theories for free massive particles with spin-1 (two equivalent formulations) and spin-2.     

Symmetry breaking by instantons in supergravity

The non-zero modes of different spin operators on the background of a self-dual gravitational instanton are all related by global supersymmetry transformations and completely cancel in the one-loop term, which is determined entirely by the zero modes. We derive the number of zero modes of each spin. In an asymptotically locally Euclidean self-dual instanton there are 2τ $\text{spin}\text{-}\text{3}\text{2}$ zero modes and 3τ spin-2 zero modes, where τ is the Hirzebruch signature. Up to 3 of the spin-2 zero modes (depending on boundary conditions) may correspond to global rotations. The $\text{spin}\text{-}\text{3}\text{2}$ zero modes break the U(1) chiral symmetry and give rise to helicity-changing amplitudes. Together with the spin-2 zero modes they determine the trace anomaly or scaling behaviour. We can compare our results with the perturbation theory predictions for the axial vector current and trace anomalies in K3, the unique compact self-dual gravitational instanton, because in this case there are no boundary terms. We obtain agreement.     

Kitaev模型与拓扑量子相变

文章通过在一种准一维路径上引入自旋算符的约当-维格纳（Jordan—Wigner）变换，证明了Kitaev自旋模型完全等价于一个不含任何非物理自由度的自由Majorana费米子模型。通过对偶变换，进一步证明了这个系统中存在的量子相变可用非定域的拓扑序参量来描述；并且，这些非定域的拓扑序参量在对偶空间变成为定域的朗道类型的序参量。文章作者的工作揭示了传统的量子相变和拓扑量子相变的内在关系，扩展了朗道二级相变理论的适用范围。     

A study of continuous-wave two-frequency NQR

A simple continuous-wave parallel to pulse version of a multifrequency nuclear quadrupole resonance (NQR) device was constructed and tested: two orthogonal radio-frequency (RF) fields were applied simultaneously at two suitable frequencies to a multilevel quadrupole probe (I⋝1). A modified superregenerative NQR oscillator-detector (SRO) was utilized. An additional coil and RF source were used to irradiate the sample at the second frequency. After tuning the SRO to a chosen NQR line, the signal proportional to the population difference of the corresponding pair of energy levels was monitored. When another suitable transition was saturated simultaneously, sharing one level with the monitored line, the corresponding population change was also reflected in the first signal intensity change. The phenomenon was examined for Sb nuclei in Sb₂S₃ powder at room temperature.     

Exact solutions of an Ising spin chain with a spin-1 impurity

An exact solution of a single impurity model is hard to derive since it breaks translation invariance symmetry. We present the exact solution of the spin-1/2 transverse Ising chain imbedded by a spin-1 impurity. Using the hole decomposition scheme, we exactly solve the spin-1 impurity in two subspaces which are generated by a conserved hole operator.The impurity enlarges the energy deformation of the ground state above a pure transverse Ising system without impurity.The specific heat coefficient shows a small anomaly at low temperature for finite size. This indicates that the impurity can tune the ground state from a magnetic impurity space to a non-magnetic impurity space, which only exists for spin-1impurity comparing with spin-1/2 impurity and a pure transverse Ising chain without impurity. These behaviors essentially come from adding impurity freedom, which induces a competition between hole and fermion excitation depending on the coupling strength with its neighbor and the single-ion anisotropy.     

Ground state phase diagram of a spin-2 antiferromagnet on the square lattice

We use the vertex state model approach to construct optimum ground states for a large class of quantum spin-2 antiferromagnets on the square lattice. Optimum ground states are exact ground states of the model which minimize all local interaction operators. The ground state contains two continuous parameters and exhibits a second order phase transition from a disordered phase with exponentially decaying correlation functions to a Néel ordered phase. The behaviour is very similar to that of the corresponding ground state of a quantum spin-3/2 model on the hexagonal lattice, which has been investigated in an earlier paper. Received 8 April 1999