Dipole Frequency Research Articles

Automatic generation of force fields and property surfaces for use in variational vibrational calculations of anharmonic vibrational energies and zero-point vibrational averaged properties

An automatic and general procedure for the calculation of geometrical derivatives of the energy and general property surfaces for molecular systems is developed and implemented. General expressions for an n-mode representation are derived, where the n-mode representation includes only the couplings between n or less degrees of freedom. The general expressions are specialized to derivative force fields and property surfaces, and a scheme for calculation of the numerical derivatives is implemented. The implementation is interfaced to electronic structure programs and may be used for both ground and excited electronic states. The implementation is done in the context of a vibrational structure program and can be used in combination with vibrational self-consistent field (VSCF), vibrational configuration interaction (VCI), vibrational Moller-Plesset, and vibrational coupled cluster calculations of anharmonic wave functions and calculation of vibrational averaged properties at the VSCF and VCI levels. Sample calculations are presented for fundamental vibrational energies and vibrationally averaged dipole moments and frequency dependent polarizabilities and hyperpolarizabilities of water and formaldehyde.

Structure determination of a membrane protein with two trans-membrane helices in aligned phospholipid bicelles by solid-state NMR spectroscopy.

The structure of the membrane protein MerFt was determined in magnetically aligned phospholipid bicelles by solid-state NMR spectroscopy. With two trans-membrane helices and a 10-residue inter-helical loop, this truncated construct of the mercury transport membrane protein MerF has sufficient structural complexity to demonstrate the feasibility of determining the structures of polytopic membrane proteins in their native phospholipid bilayer environment under physiological conditions. PISEMA, SAMMY, and other double-resonance experiments were applied to uniformly and selectively (15)N-labeled samples to resolve and assign the backbone amide resonances and to measure the associated (15)N chemical shift and (1)H-(15)N heteronuclear dipolar coupling frequencies as orientation constraints for structure calculations. (1)H/(13)C/(15)N triple-resonance experiments were applied to selectively (13)C'- and (15)N-labeled samples to complete the resonance assignments, especially for residues in the nonhelical regions of the protein. A single resonance is observed for each labeled site in one- and two-dimensional spectra. Therefore, each residue has a unique conformation, and all protein molecules in the sample have the same three-dimensional structure and are oriented identically in planar phospholipid bilayers. Combined with the absence of significant intensity near the isotropic resonance frequency, this demonstrates that the entire protein, including the loop and terminal regions, has a well-defined, stable structure in phospholipid bilayers.

Analysis of dispersion in dipole-FSS loaded hard rectangular waveguide

We investigate the properties of the dipole frequency selective surfaces-loaded rectangular waveguide. The analysis is carried out by using the method of moments together with an algorithm that solves for a multilayer structure in the spectral domain. The eigenmodes are determined by searching for resonant solutions. Dispersion diagrams obtained from this approach are compared with those generated by commercial software simulations. Experimental validation is also performed

Dipolar dynamic frequency shifts in multiple-quantum spectra of methyl groups in proteins: correlation with side-chain motion

Small deviations from the expected relative positions of multiplet components in double- and zero-quantum 1H-13C methyl correlation maps have been observed in spectra recorded on a 7-kDa protein. These dynamic frequency shifts (DFS) are the result of dipolar cross-correlations that derive from fields produced by the spins within the methyl groups. The shifts have been quantified and compared with values calculated from a Redfield analysis. Good agreement is noted between the signs of the predicted and experimentally observed relative shifts of lines in both F1 and F2 dimensions of spectra, as well as between the magnitudes of the calculated and observed shifts in the F2 (1H) dimension. The experimental DFS values show a reasonable correlation with 2H relaxation-derived measures of methyl side-chain dynamics, as expected from theory. This suggests that in cases where such shifts can be quantified, they can serve as qualitative measures of motion.

Spontaneous emission in the near field of two-dimensional photonic crystals

We show theoretically that photonic crystal membranes cause large variations in the spontaneous emission rate of dipole emitters, not only inside but also in the near field above the membranes. Our three-dimensional finite-difference time-domain calculations reveal an inhibition of more than five times and an enhancement of more than ten times for the spontaneous emission rate of emitters with select dipole orientations and frequencies. Furthermore, we demonstrate theoretically the potential of a nanoscopic emitter attached to the end of a glass fiber tip as a local probe for mapping the large spatial variations of the photonic crystal local radiative density of states. This arrangement is promising for on-command modification of the coupling between an emitter and the photonic crystal in quantum optical experiments.

Shape oscillations in nondegenerate Bose gases: Transition from the collisionless to the hydrodynamic regime

We investigate collective oscillations of non-degenerate clouds of Rb-87 atoms as a function of density in an elongated magnetic trap. For the low-lying M=0 monopole-quadrupole shape oscillation we measure the oscillation frequencies and damping rates. At the highest densities the mean-free-path is smaller than the axial dimension of the sample, which corresponds to collisionally hydrodynamic conditions. This allows us to cover the cross-over from the collisionless to the hydrodynamic regime. The experimental results show good agreement with theory. We also analyze the influence of trap anharmonicities on the oscillations in relation to observed temperature dependencies of the dipole and quadrupole oscillation frequencies. We present convenient expressions to quantify these effects.

Spin manipulating stored1.85 GeV/cvector and tensor polarized spin-1 bosons

We recently studied the spin manipulation of $1.85\text{ }\text{ }\mathrm{GeV}/c$ vertically polarized deuterons stored in the COSY cooler synchrotron. We adiabatically swept an rf dipole's frequency through an rf-induced spin resonance and observed its effect on the deuterons' vector and tensor polarizations. After optimizing the resonance crossing rate and maximizing the rf dipole's voltage, we measured spin-flip efficiencies of $97\ifmmode\pm\else\textpm\fi{}1%$ and $98.5\ifmmode\pm\else\textpm\fi{}0.3%$ in two separate runs. We also confirmed at higher energy the striking behavior of the spin-1 tensor polarization recently found at IUCF.

1H/ 31P distance determination by solid state NMR in multiple-spin systems

The results of two techniques of dipolar recoupling, REDOR and CPMAS, are compared in the case of a coupled multiple-spin system. A fundamentally different behavior is observed for these two techniques. In REDOR, the terms associated with each interaction S– I k commute with each other and no truncation takes place so that each addition of spin I k causes a splitting with its dipolar frequency. In CPMAS, the flip-flop terms of the dipolar Hamiltonian do not commute with the dominant term from the strongly coupled spin pair so that the weak coupling terms from the neighboring spin I k are effectively truncated by the dominant pair interaction. Spin dynamics calculations are in agreement with the experimental data in a cubane shaped cluster.

Isotropic proton-detected local-field nuclear magnetic resonance in solids

A nuclear magnetic resonance method is presented which produces linear, isotropic proton-detected local-field spectra for INS spin systems in powdered samples. The method, heteronuclear isotropic evolution (HETIE), refocuses the anisotropic portion of the heteronuclear dipolar coupling frequencies by evolving the system under a series of specially designed Hamiltonians and evolution pathways. The theory behind HETIE is presented along with experimental studies conducted on a powdered sample of ferrocene, demonstrating the methodology outlined in this paper. Applications of HETIE for use in structure determination in the solid state are discussed.

Kohn’s theorem in a superfluid Fermi gas with a Feshbach resonance

We investigate the dipole mode in a superfluid gas of Fermi atoms trapped in a harmonic potential. According to Kohn's theorem, the frequency of this collective mode is not affected by an interaction between the atoms and is always equal to the trap frequency. This remarkable property, however, does not necessarily hold in an approximate theory. We explicitly prove that the Hartree-Fock-Bogoliubov generalized random phase approximation (HFB-GRPA), including a coupling between fluctuations in the density and Cooper channels, is consistent with both Kohn's theorem as well as Goldstone's theorem. This proof can be immediately extended to the strong-coupling superfluid theory developed by Nozi\'eres and Schmitt-Rink (NSR), where the effect of superfluid fluctuations is included within the Gaussian level. As a result, the NSR-GRPA formalism can be used to study collective modes in the BCS-BEC crossover region in a manner which is consistent with Kohn's theorem. We also include the effect of a Feshbach resonance and a condensate of the associated molecular bound states. A detailed discussion is given of the unusual nature of the Kohn mode eigenfunctions in a Fermi superfluid, in the presence and absence of a Feshbach resonance. When the molecular bosons feel a different trap frequency from the Fermi atoms, the dipole frequency is shown to depend on the strength of effective interaction associated with the Feshbach resonance.

Spin-Orbital Dynamics in the B-Phase of Superfluid Helium-3

We report numerical calculations on the spin–orbital dynamics of 3He-B within the formalism of Poisson brackets with the two-fluid model by Leggett and Takagi. We incorporate an additional orbital term in the equations for the spin–orbit dynamics which plays an important role at very low temperatures, when the damping of orbit dynamics is small. We also find that, under the relevant experimental conditions, the Brinkman–Smith mode is strongly modified by the orbital dynamics. The orbital momentum does not relax completely to the direction of magnetic field, but remains significantly deflected, particularly at very low temperatures, and precesses at the dipole–dipole frequency and nutate at the NMR frequency. We report numerical calculations of the spin–orbit dynamics in the spatially inhomogeneous case. We solved for the mode of precession near the walls of the experimental cell, which significantly deviates from that, obtained in theoretical calculations in previous publications. We also identified the mechanism of instability of homogeneous precession at very low temperatures, the exponential growth of textural-spin waves of the longitudinal mode of NMR.

Achieving 99.9% Proton Spin-Flip Efficiency At Higher Energy With A Small rf Dipole

We recently used a new ferrite rf dipole to study spin flipping of a 2.1 GeV/c vertically polarized proton beam stored in the COSY Cooler Synchrotron in Jülich, Germany. We swept the rf dipole's frequency through an rf-induced spin resonance to flip the beam's polarization direction. After determining the resonance's frequency, we varied the frequency range, frequency ramp time, and number of flips. At the rf dipole's maximum strength and optimum frequency range and ramp time, we measured a spin-flip efficiency of 99.92+/-0.04%. This result, along with a similar 0.49 GeV/c IUCF result, indicates that, due to the Lorentz invariance of an rf dipole's transverse integralBdl and the weak energy dependence of its spin-resonance strength, an only 35% stronger rf dipole should allow efficient spin flipping in the 100 GeV BNL RHIC Collider or even the 7 TeV CERN Large Hadron Collider.

3D Frequency domain BEM for solving dipolar gradient elastic problems

A three dimensional (3D) boundary element method (BEM) for treating time harmonic problems in linear elastic structures exhibiting microstructure effects is presented. These microstructural effects are taken into account with the aid of the dipolar gradient elastic theory, which is the simplest dynamic version of Mindlin’s generalized elastic theory. A variational statement is established to determine all possible classical and non-classical (due to gradient terms) boundary conditions of the general boundary value problem. The dipolar gradient frequency domain elastodynamic fundamental solution is explicitly derived and used to construct the boundary integral representation of the solution with the aid of a reciprocal integral identity. In addition to a boundary integral representation for the displacement, a boundary integral representation for its normal derivative is also necessary for the complete formulation of a well posed problem. Surface quadratic quadrilateral boundary elements are employed and the discretization is restricted only to the boundary. The solution procedure is described in detail. A numerical example serves to illustrate the method and demonstrate its accuracy

Data analysis procedures for pulse ELDOR measurements of broad distance distributions

The reliability of procedures for extracting the distance distribution between spins from the dipolar evolution function is studied with particular emphasis on broad distributions. A new numerically stable procedure for fitting distance distributions with polynomial interpolation between sampling points is introduced and compared to Tikhonov regularization in the dipolar frequency and distance domains and to approximate Pake transformation. Distance distribution with only narrow peaks are most reliably extracted by distance-domain Tikhonov regularization, while frequency-domain Tikhonov regularization is favorable for distributions with only broad peaks. For the quantification of distributions by their mean distance and variance, Hermite polynomial interpolation provides the best results. Distributions that contain both broad and narrow peaks are most difficult to analyze. In this case a high signal-to-noise ratio is strictly required and approximate Pake transformation should be applied. A procedure is given for renormalizing primary experimental data from protein preparations with slightly different degrees of spin labelling, so that they can be compared directly. Performance of all the data analysis procedures is demonstrated on experimental data for a shape-persistent biradical with a label-to-label distance of 5 nm, for a [2]catenane with a broad distance distribution, and for a doubly spin-labelled double mutant of plant light harvesting complex II

Spin manipulation of1.94 GeV/cpolarized protons stored in the COSY cooler synchrotron

We recently studied spin flipping of a $1.94\text{ }\text{ }\mathrm{GeV}/c$ vertically polarized proton beam at COSY in J\"ulich, Germany. We swept an rf-dipole's frequency through an rf-induced spin resonance to flip the beam's polarization direction. After determining the resonance's frequency, we varied the dipole's strength, frequency range, and frequency ramp time. At the rf-dipole's maximum strength, and optimum frequency range and ramp time, we measured a spin-flip efficiency of $99.3%\ifmmode\pm\else\textpm\fi{}0.1%$. This result indicates that an rf dipole may allow efficient spin flipping in high energy proton rings.

Ferromagnetism of 2D Solid3He Investigated by SQUID NMR

Pulsed NMR measurements have been performed on 3He films adsorbed on an exfoliated graphite sample of area 2 m2. The spectrometer is constructed using a DC SQUID with additional positive feedback, operating in flux locked loop mode with a bandwidth of 3.4 MHz. The input circuit, is a superconducting flux transformer, and so is intrinsically broadband. This spectrometer can therefore operate from typical frequencies used in conventional NMR down to otherwise inaccessible low kHz frequencies. With this system studies at the “ferromagnetic anomaly” have been undertaken at frequencies from 2 kHz to 100 kHz (0.06 to 3.09 mT), with the static magnetic field oriented normal to the nominal direction of the graphite platelets. At 50 and 100 kHz, measurements of the susceptibility are fit by high temperature series expansions between 100 mK and 5 mK, to determine an exchange constant J=1.86 mK. Below 1.3 mK the dipolar frequency shift increases linearly with temperature down to 0.3 mK, extrapolating to 10 kHz, close to our calculated value of 9.6 kHz, for fully polarised spins with an assumed lattice spacing of 0.392 nm for the second layer solid. Below 1.5 mK, a significant field dependence to the magnetisation and dipolar frequency shift appears at fields comparable to the characteristic dipolar field, below which the equilibrium alignment of the magnetization is field dependent. Assuming the frequency shift, in applied fields of 1.54 and 3.09 mT, to be proportional to the sample polarisation we find that it is not possible to fit the observed temperature dependence by 2D ferromagnetic spin-wave theory, with a consistent set of parameters for both fields. The theory is applied in the range 0.15>T/J>0.5, takes into account the Zeeman gap and finite system size, and includes the k=0 spin wave term. At present, the data provide no unambiguous evidence for a finite ordering temperature induced by the anisotropic dipolar interaction.

Superfluid dynamics of a Bose–Einstein condensate in a periodic potential

We investigate the superfluid properties of a Bose–Einstein condensate (BEC) trapped in aone-dimensional periodic potential. We study, both analytically (in the tight binding limit)and numerically, the Bloch chemical potential, the Bloch energy and the Bogoliubovdispersion relation, and we introduce two different, density dependent, effective masses andgroup velocities. The Bogoliubov spectrum predicts the existence of sound waves, andthe arising of energetic and dynamical instabilities at critical values of the BECquasi-momentum which dramatically affect its coherence properties. We investigate thedependence of the dipole and Bloch oscillation frequencies in terms of an effective massaveraged over the density of the condensate. We illustrate our results with severalanimations obtained solving numerically the time-dependent Gross–Pitaevskiiequation.

Dynamics of a trapped Bose Einstein condensate in the presence of a one-dimensional optical lattice

We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential. We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential. We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of 'small' amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap ('insulator' regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.

Out-of-Phase Stimulated Electron Spin−Echo Appearing in the Evolution of Spin-Correlated Photosynthetic Triplet-Radical Pairs

A strong out-of-phase stimulated electron spin-echo is observed for the Q A - radical in the spin-correlated triplet-radical pair 3 PQ A - in photosynthetic bacterial reaction centers. The formation of this echo is shown tobe induced by spin polarization of Q A - and by decay of the triplet state. The out-of-phase and in-phase echoes show deep envelope modulation induced by electron-electron dipole interaction between the partners in the pair. The analysis of this modulation provides dipolar frequencies. The interspin distance in 3 PQ A - is shown to be the same as in the radical pair P + Q A -. This new type of experiment appears to be widely applicable for the study of chemical reactions and intermolecular distances in solids.

Dipole radiation in a one-dimensional photonic crystal. II. TM polarization.

As in a recent paper [I. Alvarado-Rodríguez, P. Halevi, and Adán S. Sánchez, Phys. Rev. E 63, 056613 (2001); 65, 039901(E) (2002)], we study the power emitted by an oscillating dipole in a superlattice (SL) modeled by means of a periodic distribution of Dirac-delta functions (Dirac-comb SL). However, while in the aforementioned paper the radiation was restricted to the transverse electric (TE) polarization mode, here we focus our attention on the transverse magnetic (TM) mode. Employing the same methodology, again we find that the power spectra are dominated by slope discontinuities. These occur - if at all - at the band edges for on-axis propagation, depending on the dipole's position and orientation. The largest enhancement or inhibition is present for normalized frequencies such that (omegad/c) less, similar 2pi; here, omega is the dipole frequency, c is the speed of light in vacuum, and d is the distance between the barriers. For substantial values of the grating strength considerable enhancement or suppression of the radiated power (in comparison to the free-space value) is obtained. We also find that the power emitted by a gas of randomly oriented dipoles exhibits slope discontinuities at all band edges for on-axis propagation. In comparison with the TE polarization case, the TM polarization exhibits several different qualitative features.