Nonlinear waves of the Hirota and the Maxwell Bloch equations in nonlinear optics

In this paper, considering the Hirota and the Maxwell–Bloch （H-MB） equations which are governed by femtosecond pulse propagation through a two-level doped fiber system, we construct the Darboux transformation of this system through a linear eigenvalue problem. Using this Daurboux transformation, we generate multi-soliton, positon, and breather solutions （both bright and dark breathers） of the H-MB equations. Finally, we also construct the rogue wave solutions of the above system.

Numerical solution to the Bloch equations:paramagnetic solutions under wideband continuous radio frequency irradiation in a pulsed magnetic field

A novel nuclear magnetic resonance （NMR） experimental scheme, called wideband continuous wave NMR （WB-CW-NMR）, is presented in this article. This experimental scheme has promising applications in pulsed magnetic fields, and can dramatically improve the utilization of the pulsed field. The feasibility of WB-CW-NMR scheme is verified by numerically solving modified Bloeh equations. In the numerical simulation, the applied magnetic field is a pulsed magnetic field up to 80 T, and the wideband continuous radio frequency （RF） excitation is a band-limited （0.68-3.40 GHz） white noise. ~lrthermore, the influences of some experimental parameters, such as relaxation time, applied magnetic field strength and wideband continuous RF power, on the WB-CW-NMR signal are analyzed briefly. Finally, a multi-channel system framework for transmitting and receiving ultra wideband signals is proposed, and the basic requirements of this experimental system are discussed. Meanwhile, the amplitude of the NMR signal, the level of noise and RF interference in WB-CW-NMR experiments are estimated, and a preliminary adaptive cancellation plan is given for detecting WB-CW-NMR signal from large background interference.

High-order harmonic generation of ZnO crystals in chirped and static electric fields

High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduced, the interference structure becomes obvious while the harmonic cutoff is not extended. Furthermore, the harmonic efficiency is improved when the static electric field is included. These phenomena are demonstrated by the classical recollision model in real space affected by the waveform of laser field and inversion symmetry. Specifically, the electron motion in k-space shows that the change of waveform and the destruction of the symmetry of the laser field lead to the incomplete X-structure of the crystal-momentum-resolved(k-resolved) inter-band harmonic spectrum. Furthermore, a pre-acceleration process in the solid four-step model is confirmed.

Topological horseshoe in nonlinear Bloch system

This paper demonstrates rigorous chaotic dynamics in nonlinear Bloch system by virtue of topological horseshoe and numerical method. It considers a properly chosen cross section and the corresponding Poincare map, and shows the existence of horseshoe in the Poincare map. In this way, a rigorous verification of chaos in the nonlinear Bloch system is presented.

Role of Bloch oscillation in high-order harmonic generation from periodic structure

The high-order harmonic generation from a model solid structure driven by an intense laser pulse is investigated using the semiconductor Bloch equations(SBEs). The main features of harmonic spectrum from SBEs agree well with the result of the time-dependent Schroodinger equation(TDSE), and the cut-off energy can be precisely estimated by the recollision model. With increasing the field strength, the harmonic spectrum shows an extra plateau. Based on the temporal population of electron and the time–frequency analysis, the harmonics in the extra plateau are generated by the Bloch oscillation. Due to the ultrafast time response of the Bloch electron, the generated harmonics provide a potential source of shorter isolated attosecond pulse.

Sensor design and implementation for a downhole NMR fluid analysis laboratory

This paper tries to build a multi-functional downhole nuclear magnetic resonance （NMR） fluid analysis laboratory that can evaluate fluid information in real time at reservoir conditions at a depth of several thousand meters. The aim is to monitor the pollution of the formation fluids and quantitatively evaluate NMR characteristics of the fluids. It focuses on the design of the structure and parameters of a sensor with zero stray fields. Two separate coils are designed to measure NMR characteristics of flowing or static fluids. A method is proposed to use the Bloch equation, to guide the optimization of the NMR sensor. Finally, the measured results confirm that the design is reasonable. There is a homogeneous static field （perpendicular to the axial direction） in the center of the sensor, and there are no stray external fields. The novel design of pre-polarization magnet improves the signal to noise ratio, while shortening the sensor length.

Radiation forces on a three-level atom in the high-order Bessel beams

The general expressions of the average dissipative and dipole forces acting on a A-configuration three-level atom in an arbitrary light field are derived by means of the optical Bloch equations based on the atomic density matrix elements, and the general properties of the average dissipative and dipole forces on a three-level atom in the linearly-polarized high-order Bessel beams （HBBs） are analysed. We find a resonant property （with two resonant peaks） of the dissipative force and a non-resonant property （with two pairs of non-resonant peaks） of the dipole force on the three-level atom, which are completely different from those on the two-level atom. Meanwhile we find a saturation effect of the average dissipative force in the HBB, which comes from the saturation of the upper-level population. Our study shows that the general expressions of the average dissipative and dipole forces on the three-level atom will be simplified to those of the two-level atom under the approximation of large detuning. Finally, we study the axial and azimuthal Doppler cooling of atoms in ID optical molasses composed of two counter-propagating HBBs and discuss the azimuthal influence of the HBB on the Doppler cooling limit. We also find that the Doppler limit of atoms in the molasses HBB is slightly below the conventional Doppler limit of hГ/（2kB） due to the orbital angular momentum lh of the HBB.

Effect of Lorentz local field correction on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (PNA) molecules

This paper investigates the effect of Lorentz local field correction （LFC） on the propagation of ultrashort laser pulses in a para-nitroaniline molecular medium under resonant and nonresonant conditions by solving numerically the full-wave Maxwell-Bloch equations beyond slowly-varying envelope approximation and rotating-wave approximation. The effect of the LFC is considerably obvious when pulses with large areas propagate in the dense molecular medium. In the case of resonance, the group velocity of the sub-pulses split from the incident pulse along propagation is severely decreased by the LFC, especially for the latest sub-pulse. However, in the case of nonresonance, the influence of the LFC on the temporal evolution of the pulse is less obvious and lacks homogeneity with an increase in incident pulse area, propagation distance and molecular density.

Atomic Spin Polarization Controllability Analysis:A Novel Controllability Determination Method for Spin-Exchange Relaxation-Free Co-Magnetometers

This paper investigates the atomic spin polarization controllability of spin-exchange relaxation-free co-magnetometers(SERFCMs).This is the first work in the field of controllability analysis for the atomic spin ensembles systems,whose dynamic behaviors of spin polarization are described by the Bloch equations.Based on the Bloch equations,a state-space model of the atomic spin polarization for SERFCM is first established,which belongs to a particular class of nonlinear systems.For this class of nonlinear systems,a novel determination method for the global state controllability is proposed and proved.Then,this method is implemented in the process of controllability analysis on the atomic spin polarization of an actual SERFCM.Moreover,a theoretically feasible and reasonable solution of the control input is proposed under some physical constraints,with whose limitation of realistic conditions,the controller design can be accomplished more practically and more exactly.Finally,the simulation results demonstrate the feasibility and validation of the proposed controllability determination method.

Improving the intensity and efficiency of compressed echo in rare-earth-ion-doped crystal

We investigate the intensity and efficiency of a compressed echo, which is important in arbitrary waveform generation（AWG）. A new model of compressed echo is proposed based on the optical Bloch equations, which exposes much more detailed parameters than the conventional model, such as the time delay of the chirp lasers, the nature of the rare-earth-iondoped crystal, etc. According to the novel model of compressed echo, we find that reducing the time delay of the chirp lasers and scanning the lasers around the center frequency of the inhomogeneously broadened spectrum, while utilizing a crystal with larger coherence time and excitation lifetime can improve the compressed echo＇s intensity and efficiency. The theoretical analysis is validated by numerical simulations.

Nonstandard finite-difference schemes for the two-level Bloch model

In this paper, we present splitting schemes for the two-level Bloch model. After proposing two ways to split the Bloch equation, we show that it is possible in each case togenerate exact numerical solutions of the obtained sub-equations. These exact solutionsinvolve matrix exponentials which can be expensive to compute. Here, for 2×2 matriceswe develop equivalent formulations which reduce the computational cost. These splittingschemes are nonstandard ones and conserve all the physical properties (Hermicity, positiveness and trace) of Bloch equations. In addition, they are explicit, making effectivetheir implementation when coupled with the Maxwell’s equations.