Saturation in hadamard NMR spectroscopy and its description by a correlation expansion

In broadband NMR spectroscopy excitation with pseudorandom binary amplitude or phase modulation permits the distribution of the excitation power over the entire data acquisition time while peak power requirements are kept low. For sufficiently low excitation power, the magnetization is the linear response of the spin system to its input. The transfer function of the linearly driven system is recovered with the fast Hadamard transform. It is identical to the FID signal in FT NMR. Increasing excitation levels produce distorted lineshapes resulting from linear processing of a nonlinear spin response. Spectra measured for different degrees of saturation are reproduced faithfully by a numerical solution of the Bloch equations including relaxation during excitation. The origin of the lineshape distortions is discussed on the basis of an expansion of the nonlinear response in terms of the linear response. This expansion is in good agreement with the Bloch equations for limited excitation levels. Its nonlinear response terms are generalized to account for connectivities in coupled spin systems.     

Theorie der Multipolrelaxation

The multipole resonance and relaxation is discussed starting with a general consideration of the quantum mechanical dynamics of spinsystems with arbitrary spinI. The irreversible entropy production as a function of the multipolarisations is calculated from the density operator, expanded in terms of a complete set of orthonormal multipole operators. By use of the methods of thermodynamics of irreversible processes one obtains relaxation equations, which are a generalization of the Bloch equations of pure magnetic dipole relaxation. They connect the time derivatives of the multipolarisations with affinities, which are defined by the expansion of the logarithmus of the density operator; for small multipolarisations the affinities are equal to the multipolarisations themselves. Relations for the relaxation matrix are discussed, especially a derivation is given for reciprocal relations between the relaxation coefficients. In the special case of spinI=1 the equations of quadrupole relaxation are studied for axial symmetry.     

General theory for the interference of two-photon and one-photon processes in semiconductor heterostructures

We develop a general theory for the dynamics of multi-photon processes in semiconductor heterostructures. The resulting effective multi-band Bloch equations describe the dynamics of electrons in the reduced set of bands between which the optical pulses induce quasi-resonant transitions. The model is specialized to the case of interfering one- and two-photon transitions across the band gap. The withdrawn bands are included as intermediate states for an effective interaction that is quadratic in the electromagnetic fields. The benefit of this perturbative approach is to lead to equations of motion for slowly varying quantities only, in the spirit of the rotating wave approximation. Coulomb interaction and relaxation can also easily be included. Finally, a general expression for the time dependent polarization current that is consistent with the approximations involved by the effective multi-band Bloch equations is derived.     

Quantum interference and population swapping in single quantum dots with V-type three-level

The quantum interference and Rabi oscillation of a V-type three-level system with two orthogonal sub-states in an elongated semiconductor quantum dot are discussed theoretically with optical Bloch equations when the system is driven by pulse-pair. Numerical calculations from the optical Bloch equations reveal that the quantum interference in the system is enhanced with the increasing of the energy decay or splitting. Furthermore, the populations swapping in two orthogonal sub-states can be realized though the direct transition is prohibited.     

简并四波混频信号的饱和效应

本文由光学Bloch方程和密度矩阵方程出发,研究了二能级系统共振型简并四波混频(DFWM)的饱和效应,给出了DFWM信号强度与泵浦光强度的函数关系.饱和泵浦光强的大小取决于纵向弛豫时间T1和横向弛豫时T2.对理论结果与相应实验进行了比较,表明二者符合得很好.     

Ultrasound propagation in dielectric glasses

The susceptibility of a two-level system coupled to a phonon heat bath is calculated by setting up its equation of motion and expanding the memory function (or self energy) and the inhomogeneity to second order in the coupling potential. Averaging over disorder yields attenuation and variation with temperature of sound velocity, which are compared to previous results obtained in the framework of the Bloch equations. The relaxation time approximation is avoided; there are new terms in both relaxation and resonant contributions.     

On a physical implementation of logical operators NOT and CNOT in a two-qubit quantum computer controlled by ultrashort optical pulses

It is shown that it is preferable to perform quantum computations on a system of two-level atoms with metastable states using optical dipole transitions that occur under the effect of ultrashort light pulses. It is suggested to measure the quantum information that is passed to qubits using Bloch, rather than pure, quantum states of two-level atoms. Moreover, the inversion of atoms can be used as the measure of quantum information. In order to describe the logical operators NOT and CNOT in the system of interacting two-level atoms (qubits), modified optical equations for the Bloch vectors of individual qubits are derived. These equations are solved in combination with field equations, without using the slowly varying amplitude approximation, for a small two-qubit system in the field of ultrashort intense optical pulses of arbitrary shape. A numerical analysis of the solution shows that it is possible to control the recording of information on individual qubits in a small quantum system of a dimension much smaller than the length of the optical wave by smoothly varying the irradiation conditions of qubits.     

射频场照射下多自旋体系弛豫的理论计算

根据Liouville-von Neumann方程，对射频场照射下多自旋体系的弛豫进行了理论描述，并用WBR理论推导出了体系的弛豫方程组，给出了各类弛豫速率的理论计算公式.在此基础上，编制了弛豫方程组数值解的计算程序，分别用此程序和Bloch方程计算了双自旋体系在不同情况下的稳态解，并对计算结果进行了简要的分析和讨论. 关键词： 核磁共振 弛豫 射频场 多自旋体系     

Modification of the domain wall structure and generation of submicron magnetic formations by local optical irradiation

Experimental and theoretical investigations are made of the generation of vertical Bloch lines in a magnetic iron garnet film exposed to pulsed optical radiation. High-speed photography and anisotropic dark-field microscopy are used to study characteristic features of the generation of Bloch lines and domain structure relaxation processes after the local action of a laser pulse. Optimum optical irradiation parameters to ensure the controlled generation of Bloch lines are established. A theoretical model is developed which links the generation of Bloch lines to the migration of domain walls induced by local changes in the distribution of the degaussing fields caused by a reduction in magnetization with temperature at the optical radiation focusing point. The experimental results indicate that the controlled formation of magnetic structures smaller than or of the order of 0.1 μm by local optical irradiation is quite feasible.     

光学Maxwell-Bloch方程的数值算法研究及其应用

建立了高准确度快速求解均匀展宽二能级体系光学Maxwell-Bloch耦合方程的数值算法.通过与特定条件得到的解析解的比较,验证了算法所具有的高收敛性和稳定性,并可保持算法的误差阶数,因此算法是可靠并实用的.应用该算法数值求解了一般条件下的MB方程,并由计算结果分析了失谐量、弛豫时间、初始光强对光脉冲在介质中的传播及对Bloch矢量演化的影响.所建立的数值算法对MB方程以及修正的这类偏微分方程组具有普适性.     

Dispersive optical bistability in a nonideal Fabry-Pérot cavity

A stability analysis is performed for optical bistability in a Fabry-Pérot cavity with mirrors of arbitrary transmission coefficient. The mixed absorptive and dispersive régime is covered. In order to describe the system we use the Maxwell0Bloch equations formulated in terms of slowly varying envelopes. Standing-wave effects are completely taken into account by refraining from a truncation of the harmonic expansions for the polarization and the inversion density. We represent the solutions of the linearized Bloch hierarchy in terms of Chebyshev polynomials depending on the stationary electric field envelopes. In this way, we reduce the stability problem to a four-dimensional set of linear differential equations. Together with a couple of boundary conditions these equations govern the spatial behaviour of the deviations of the forward and the backward electric field envelopes. Our final stability problem becomes much simpler in the uniform-field limit and in the adiabatic limit. If we choose the stationary backward electric field equal to zero we recover results that were derived earlier for the case of a ring cavity.     

Linear nonstationary optical dimensional resonances in atomic nanostructures

The existence of linear nonstationary optical resonances in a diatomic nanostructural object with a dipole-dipole atomic interaction has been proved. A new solution to the joint system of modified Bloch optical equations and nonlocal field equations is obtained for time intervals much shorter than the times of phase and energy relaxation. Formulas for effective polarizabilities of the object’s atoms, which have a set of dimensional resonances, are derived. The frequencies of these resonances significantly differ from the eigenfrequencies of the object’s atoms, and their properties depend on the interatomic distance, light-pulse duration, initial atomic inversions, and the orientation of the object’s axis relative to the direction of incidence of the external light wave.     

Self-induced transparency of very short optical pulses

Solutions to a first order wave equation, appropriate to ultrashort optical pulse theory and to the optical undamped Bloch equations are presented. Detuning is shown to play essential role in the physical interpretation of these solutions. Related cases have been discussed by Courtens and by Lee. It is noted that the rotating wave approximation introduces strong restrictions on the range of validity of possible solutions. Pulses with Lorentzian shapes, while implied by the equations, appear to be without physical significance.     

Spectral Resolution and Inversion of the Bloch Equations with Relaxation

It is demonstrated that the linear Bloch equations, describing near-resonant excitation of two-level media with relaxation, can be resolved into a 3n-dimensional nonlinear system associated with a special spectral problem, generalizing the classical Zakharov–Shabat spectral problem. Remarkably, for n = 1 it is the well-known Lorenz system, and for n > 1 several such systems coupled with each other in a manner dependant on the excitation pulse. The unstable manifold of a saddle equilibrium point in this ensemble characterizes possible excitations of the spins from the initial equilibrium state. This enables us to get a straightforward geometric extension of the inverse scattering method to the damped Bloch equations and hence invert them, i.e., design frequency selective pulses automatically compensated for the effect of relaxation. The latter are essential, for example, in nuclear magnetic resonance and extreme nonlinear optics.      

Bloch equations with diffusion terms for rotational motion in fluids

The phenomenological Bloch equations for magnetic resonance are supplemented by terms for rotational diffusion in fluids. The equations are used to describe damping of magnetization components and the line shape of nonresonance absorption in parallel fields for ions with an anisotropic g factor and an effective spin of 1/2. In both cases, the contributions of the diffusion terms are comparable to the contribution from longitudinal and transverse relaxation times (T₁, T₂).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 42–46, January, 1973.The authors are indebted to B. M. Kozyrev for his interest in the work and discussions of the results.     

High-resolution nonlinear laser spectroscopy of exciton relaxation in GaAs quantum wells

This paper describes measurements of exciton relaxation in GaAs/AlGaAs quantum well structures based on high resolution nonlinear laser spectroscopy. The nonlinear optical measurements show that low energy excitons can be localized by monolayer disorder of the quantum well interface. We show that these excitons migrate between localization sites by phonon assisted migration, leading to spectral diffusion of the excitons. The frequency domain measurements give a direct measure of the quasi-equilibrium exciton spectral redistribution due to exciton energy relaxation, and the temperature dependence of the measured migration rates confirms recent theoretical predictions. The observed line shapes are interpreted based on solutions we obtain to modified Bloch equations which include the effects of spectral diffusion.     

Ensemble of asymmetric quantum dots in a cavity as a terahertz laser source

The possibility of establishing a terahertz laser generation at a transition between the dressed states formed by the interaction of an intense optical field with an ensemble of asymmetric quantum dots (QDs) in a high-Q terahertz cavity is discussed. It has been shown that the population inversion in the system of dressed states is achieved owing to spontaneous relaxation of the excited state of the QDs. The set of Maxwell–Bloch equations for the difference between dressed-state populations, polarization, and population of the cavity mode has been analyzed in the mean-field approximation. The lasing conditions have been clarified and the possibility of controlling the terahertz radiation intensity has been studied, including the case of an inhomogeneously broadened ensemble of QDs.     

Absorptive and dispersive optical profiles in fluctuating environments: A stochastic model

In this study, we determined the absorptive and dispersive optical profiles of a molecular system coupled with a thermal bath. Solvent effects were explicitly considered by modelling the non-radiative interaction with the solute as a random variable. The optical stochastical Bloch equations (OSBE) were solved using a time-ordered cumulant expansion with white noise as a correlation function. We found a solution for the Fourier component of coherence at the third order of perturbation for the nonlinear Four-wave mixing signal and produced analytical expressions for the optical responses of the system. Finally, we examined the behaviour of these properties with respect to the noise parameter, frequency detuning of the dynamic perturbation, and relaxation times.     

Optical zoomeron as a result of beatings of the internal modes of a Bragg soliton

A new solution of two-wave Maxwell-Bloch equations has been obtained analytically and numerically. It describes the propagation of an oscillating nonlinear optical solitary wave, or optical zoomeron, in a one-dimensional periodic resonant Bragg structure. It has been shown that the appearance of large oscillations in the velocity and total amplitude of Bloch modes of the pulse is caused by beating of internal modes of the perturbed Bragg soliton.