Nutation Signals Research Articles

Longitudinal relaxation rate measurements for different signals unveiled by nutation spectroscopy: Application to the characterization of two arrangements experienced by water in a clay network.

Nutation consists in monitoring the motion of nuclear magnetization under the application of a radiofrequency (rf) field. With an appropriate amplitude of the rf field, the nutation frequency depends on the NMR relaxation times. This property offers the possibility of differentiating species having the same Larmor frequency but differing by their relaxation times. This may occur for the composite proton NMR signal of water in complex systems. Separate nutation signals are thus observed with the possibility of measuring their longitudinal relaxation times by simply applying a saturation hard pulse, followed by an evolution interval, prior to the nutation sequence. This novel experiment has been used for studying the two sites existing for water in two kaolinite samples (one hydrated after stabilization of several months and the other nonhydrated). It turns out that water in these two sites differs essentially by its transverse relaxation time. Moreover, recovery is surprisingly biexponential for these two signals. A proper analysis of results obtained by this saturation-recovery nutation experiment provides not only the specific longitudinal relaxation rates of water in these two sites but also information about the averaging which occurs at long evolution times. This is discussed with regard of the structure and organization of the clay network. In particular, from relaxation rates at short evolution times, it is shown that this network is mainly constituted of ordered platelets, with a relatively weak proportion of randomly distributed platelets.

Proton nutation spectroscopy. Application to the quantitation of water in a kaolinite sample.

Nutation consists in monitoring the motion of nuclear magnetization under the application of a radio-frequency field. Depending on the amplitude of the rf field, the nutation frequency may be sensitive to the two longitudinal and transverse relaxation rates R1 and R2, hence the possibility of differentiating species having the same resonance frequency in the laboratory frame (the Larmor frequency) but differing by their relaxation rates, as it may occur for the composite proton NMR signal of water in complex systems. Thus, Fourier transform of the nutation curve should provide separate peaks associated with the different species involved in a composite classical NMR signal. As nutation peaks may be close to zero frequency (or even at zero frequency), their full observation requires a complex Fourier transform. This implies a second nutation curve, de-phased by 90° with respect to the first one, achieved here by a second nutation experiment preceded by a 90° hard pulse. Eventually, more accurate parameters are obtained by a non-linear least-squares analysis of the simple nutation experiment. This methodology is applied to water in a natural clay (kaolinite) and reveals the unexpected presence of two peaks which can be characterized by the relaxation rates derived from the line-widths of the nutation signals.

基于激光章动的空间光到单模光纤的耦合方法

Based on the theory of mode-field matching, the relationship between coupling efficiency and jitter amplitude, radius ratio of Airy disk and single-mode fiber mode field is analyzed. In order to reduce the effect of random angle jitter on coupling efficiency, an automatic coupling scheme for making space light into single-mode fiber based on laser nutation is designed. The miss distance is calculated by data acquisition card and the offset voltage is output. The influence factors of algrithm precision and the relationship between laser nutation signal frequency and jitter frequency are analyzed. The feasibility of the algorithm is verified by Matlab simulation and experiments. Accuracy of miss distance angle is about 3 μrad obtained by experiment. The system feasibility is verified by space laser communication system. The coupling efficiency of the system is 67% when there is no disturbance, and it is improved by 6.5% when the disturbance is introduced and the control system is used to compensate the disturbance. The system response speed reaches 40 Hz. The coupling system is simple in structure and accurate in control algorithm. The controller signal processing speed is fast, and it has a great significance on the coupling of space light to single mode optical fiber. © 2016, Chinese Lasers Press. All right reserved.

Optical nutation in multilayered ellipsoidal quantum dots

The optical nutation signal of two and three ellipsoidal quantum dots (EQD) with finite confinement potential in the presence of polarized laser field is considered. In this regard, the effective-mass approximation within a perturbation scheme is used and the induced effective polarization of atoms in the multilayered ellipsoidal quantum dots is calculated for GaAs/GaAlAs/GaAs structure. The results showed that the optical nutation peak depends not only on the thickness of the intermediate layer but also on the ellipticity constant.

Optical nutation in GaAs/AlGaAs core-shell quantum dot

Optical nutation in GaAs/Al0.3Gao.7As core-shell quantum dot (CSQD) shined by femtosecond laser has been analyzed theoretically. The nutation signal intensity, arising due to photo-induced electronic transitions between ground state and first excitonic state, has been calculated using time dependent perturbation theory and rotational wave approximation. The dependency of the properties of optical nutation signal viz. its maximum amplitude and the oscillation frequency of the nutation signal has been studied at various CSQD's core radius and shell thickness.

Observation of infrared free-induction decay and optical nutation signals from nitrous oxide using a current modulated quantum cascade laser

Free induction decay (FID), optical nutation, and rapid passage induced signals in nitrous oxide, under both optically thin and optically thick conditions, have been observed using a rapid current pulse modulation, or chirp, applied to the slow current ramp of a quantum cascade (QC) laser. The variation in optical depth was achieved by increasing the pressure of nitrous oxide in a long path length multipass absorption cell. This allows the variation of optical depth to be achieved over a range of low gas pressures. Since, even at the highest gas pressure used in the cell, the chirp rate of the QC laser is faster than the collisional reorientation time of the molecules, there is minimal collisional damping, allowing a large macroscopic polarization of the molecular dipoles to develop. This is referred to as rapid passage induced polarization. The resultant FID signals are enhanced due to the constructive interference between the field within the gas generated by the slow ramp of the laser (pump), and that of the fast chirp of the laser (probe) signal generated by pulse modulation of the continuously operating QC laser. The FID signals obtained at large optical depth have not been observed previously in the mid-infrared regions, and unusual oscillatory signals have been observed at the highest gas pressures used.

Parameter-dependent optical nutation in PbSe/CdSe/ZnS quantum-dot

The eigenenergies and eigenfunctions of the spherical PbSe/CdSe/ZnS quantum-dot with the core-shell-shell structure and the electric dipole moment between the a1s state (the lowest state of the system) and b1p state (the lowest p state above the first potential) have been calculated by using the rotational wave approximation and the effective mass approximation. The optical nutation signal induced by the transition between these two energy levels has been calculated based on the optical Bloch equations. In particular, the influence of the core’s radius increasing and the CdSe shell’s thickness increasing has been investigated respectively. It is shown from the numerical calculation results that the optical nutation signals are dependent on the size and the structure of the quantum-dot. Moreover, the quantum size-dependent Rabi frequency has been analyzed.

Quantum size dependent optical nutation in CdSe/ZnS/CdSe quantum dot quantum well

The energy spectra and the optical nutation effect in CdSe/ZnS/CdSe quantum dot quantum well with core/shell/shell structure have been numerically studied and analyzed based on quantum theory and the effective mass approximation. For solving the uncertain coefficients A 0, A 1, B 0, B 1, A 2, B 2 and E, a new method has been used in the paper. It has been shown that the optical nutation signals of the CdSe/ZnS/CdSe quantum dot quantum well are dependent on the quantum size of the quantum dot quantum well and there exists an optimized condition for induced nutation signal, which is quite sensitive to the shells’ sizes of the QDQW with the core/shell/shell structure.

Dynamical measurements with a nuclear magnetic resonance force microscope

We report imaging and dynamical measurements using a H3e nuclear magnetic resonance force microscopy probe. Relaxation-time measurements and a one-dimensional image were obtained for H1 nuclei in a micron-scale crystal of (NH4)2SO4. The force detection was made possible by a small Permalloy magnet, which supplied a field gradient of 500 T/m. These experiments were performed in the sample-on-oscillator configuration at room temperature, where the oscillator had a resonance frequency of 1.5 kHz and a spring constant of 0.03 N/m. The proton magnetic moments underwent cyclic adiabatic inversions (CAIs) under the influence of a frequency-modulated rf field. Scanning the position of the magnet with respect to the sample provided a micron-scale image with a signal-to-noise ratio of 4.3. A spin nutation signal was also obtained; those data imply a rotating rf field of 14 G. Using a 90°-τ-180°-t-90°-CAI sequence, a spin echo was mapped out, with a full width at half maximum of 8 μs. We also discuss future applications of this instrument toward relaxation measurements of single-crystal MgB2 at low temperatures.

Influence of disorder on electrically and optically detected electron spin nutation

A numerical study of the influence of disorder in semiconductors on spin-Rabi nutation observed with pulsed electrically or optically detected magnetic-resonance techniques (pEDMR and pODMR, respectively) is presented. It is shown that transient nutation signals of disordered spin ensembles differ from ordered ensembles as inhomogeneously broadened Land\'e-factor distributions are presented. In contrast to ordered systems, the magnitudes of spin-Rabi nutation and spin-Rabi beat nutation change significantly with a strong dependence of their ratio on the correlation of the Land\'e factors within the nearest-neighbor spin pairs. An interpretation of these results is given and their application for the investigation of disorder using pEDMR and pODMR is discussed.

10.1007/s11448-008-3003-3

The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ωrf is close to the Rabi frequency ω1 in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ɛ are accompanied by higher-frequency oscillations at frequencies nωrf and nωrf ± ɛ, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ɛ on the sign of the detuning ω1 − ωrf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ωrf + ɛ increases, while the amplitude at the difference frequency ωrf − ɛ decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E′1 centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.

Effect of the Bloch-Siegert shift on the frequency responses of Rabi oscillations in the case of nutation resonance

The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ωrf is close to the Rabi frequency ω1 in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ɛ are accompanied by higher-frequency oscillations at frequencies nωrf and nωrf ± ɛ, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ɛ on the sign of the detuning ω1 − ωrf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ωrf + ɛ increases, while the amplitude at the difference frequency ωrf − ɛ decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E′1 centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.

Optical nutation induced by transition between levels inside and outside the well in acore–shell CdSe/ZnS quantum dot

The energy eigenvalues and eigenfunctions of a core–shell CdSe/ZnS quantum dot structurehave been obtained under an effective-mass approximation. The electric transition dipolemoment induced by the 1s (inside the well)–1s (outside the well) transition has beencalculated. The optical nutation signal induced by the transition has been calculatednumerically based on the optical Bloch equations. In particular, the influence of the sizevariation of the core’s radius and the shell’s thickness has been studied. It has been shownfrom the results that the optical nutation signal is sensitive to the size and structure, andthat there is an optimal structure and size for the optical nutation phenomenon. Thequantum size dependent Rabi frequency and intensity of the optical nutation are alsodiscussed.

Quantum size dependent optical nutation in a core-shell CdSe/ZnS quantum dot

The energy eigenvalues and eigenfunctions have been obtained for a core-shell CdSe/ZnS quantum dot structure under effective-mass approximation. The electric transition dipole moment is calculated for the 1s–2s electronic transition. The optical nutation signal of the transition of electrons has been calculated numerically based on optical Bloch equations. Particularly, we have investigated the quantum size, the core's radius and the shell's thickness, dependent optical nutation. It is shown from calculation results that the optical nutation signal is sensitive to the size and structure change. And the reasons for the variation of the Rabi frequency have been discussed based on the theory of the quantum size confined effect (QSCE).

Dressed state EPR nutations of E1′ centers in neutron-irradiated quartz

Dressed state electron paramagnetic resonance (EPR) nutations of E 1′ centers in neutron-irradiated crystalline quartz are observed using, in addition to the continuous microwave field 2 B 1 cos ( ω t ) and the pulse of longitudinal magnetic field, a linearly polarized RF field 2 B 2 cos ( ω rf t ) along the static magnetic field. The dressed nutation of the frequency ω 2 = γ B 2 is detected when the RF field frequency, ω rf, is near the frequency of bare spin nutation ω 1 = γ B 1 ( γ is the electron gyromagnetic ratio). Our results give evidence for the line-narrowing effect associated with the dressed nutation and the amplitude asymmetry of the left ( ω 1− ω 2) and right ( ω 1+ ω 2) components in Fourier spectra of observed nutation signals.

Optical Nutation in Cold 85Rb Atoms

We have observed optical nutation in cold 85Rb atoms with a negligible Doppler broadening. The optical nutation of a two-level atom arranged by optical pumping has been studied as a function of detuning frequency and Rabi frequency. The change of the nutation signal caused by magnetic substate degeneracy has also been observed for σ and π excitations. This can be explained by optical nutation beatings from different transition probabilities among magnetic sublevels. Absolute transition probabilities with σ and π transitions and a branching ratio between them have been measured.

Nontidal oceanic excitation of nutation and diurnal/semidiurnal polar motion revisited

A new 7.5‐yearlong time series of hourly estimates of nontidal ocean angular momentum, representing signals forced by 6‐hourly surface atmospheric pressure and winds including those forced by the atmospheric tides, is used to assess the influence of a dynamic ocean on nutation and on diurnal and semidiurnal polar motions. Using available atmospheric angular momentum data, we estimate the total excitation by the dynamically coupled atmosphere‐ocean system and compare it to that of the atmosphere alone. In case of the retrograde diurnal excitation, significant contributions are found for the retrograde annual, prograde annual, and prograde semiannual nutations and for the constant offset of the celestial pole. For the prograde annual nutation corresponding to the retrograde S1 component of excitation, the atmosphere‐ocean model does not improve the agreement with VLBI observations beyond that obtained using the atmosphere model alone. We also considered separately an irregular contribution to nutation, which can excite both the free core nutation signal and other broadband variability. The irregular component of the atmosphere‐ocean model is found to be significantly correlated with that derived from the atmosphere model. For the prograde diurnal component of excitation, which contributes to polar motion, the only nonnegligible effect (∼9 microarc seconds (μas)) is associated with the prograde S1 harmonic. The only significant component of the semidiurnal excitation found is the elliptical oscillation S2 in polar motion with major semiaxis of 9 μas, but this estimate is uncertain because the 6‐hourly atmospheric fields used to force the ocean do not properly resolve semidiurnal signals. In any case, this contribution is much smaller than that from the S2 ocean gravitational tide.

Optical coherent transient effects in magnetoactive GaAs/AlGaAs quantum well structure

The effect of an external magnetic field on optical coherent transient phenomena has been analyzed for semiconductor quantum well structures (QWS). The Lüttinger Hamiltonian is used to incorporate the complex valence band structure which is modified due to the application of the magnetic field. We have considered a GaAs/AlGaAs QWS with magnetic field applied in the direction perpendicular to the plane of the well. We get two quantum levels due to confinement, and doubly degenerate heavy-hole and light-hole bands corresponding to each quantum level, thus leading to eight hole subbands. This results in an 8×8 Hamiltonian in an appropriately chosen basis. Energy eigenvalues and eigenvectors have been calculated by numerically diagonalizing the above Hamiltonian. The absorption characteristics and the optical coherent transient phenomena have been studied by solving the effective semiconductor Bloch equations in the weak excitation regime. The polarization induced in conjunction with the results obtained by solving the modified Lüttinger Hamiltonian has been used to analyze the transient characteristics. We observe a blueshift in transition energy with an increase in magnetic field. The features are changed dramatically when one includes band mixing. The crossing of subbands in the absence of band-mixing effects changes over to anticrossing behavior when band mixing is included. Multiple oscillations are observed in the optical nutation signal that can be attributed to band-mixing effects. Absorption spectra also show a significant blueshift with an increase in magnetic field and additional peaks appear when band mixing is included.

Second-Order Echo Signals in Two-Pulse Delayed Nutation

Nonstationary magnetic nutation signals of the second-order echo that occur during the effect of a resonance radiofrequency pulse of length t2 on a two-level inhomogeneously broadened spin system preliminarily excited by a pulse of length t1 < t2 have been studied theoretically. It has been found that in contrast to the delayed nutation echo whose formation is attributed to the restoration of the longitudinal magnetization that arose by the end of the first pulse, these signals result from the “reversal” in time of three effective signals of free precession generated after the termination of the first pulse. The theoretical results are in good agreement with the experimental data obtained in NMR of protons in glycerin. A conclusion on the validity of the theorem of coherent transient processes occurring in two-level systems in the presence of an exciting field is drawn.

Transient NQR signals in the effective field of multipulse trains

This paper is a theoretical analysis of time-dependent nutation and echo signals in the effective field of multipulse trains in NQR. The results of experimental investigations of the same aspects were reported in earlier papers. The various features of dipole-dipole interactions in three-level quadrupole spin systems are discussed. It is shown that, in contrast to NMR, the dipole Hamiltonian in the interaction representation determined by the quadrupole Hamiltonian contains only three diagonal components of the dipole-dipole interaction tensor. On the other hand, the strong inhomogeneous broadening characteristic of NQR hinders exact measurement of these components by ordinary methods. The theoretical analysis suggests that the decay of the echo-signal envelope in the effective field of multipulse trains is determined solely by the dipole relaxation time, which serves as justification of a new experimental method used in measuring the characteristics of the dipole-dipole interaction tensor in spin systems with an inhomogeneously broadened spectrum.