Stimulated photon echo under excitation by incoherent and coherent pulses

Excitation of stimulated photon echo by two incoherent pulses obtained from one source and one coherent pulse is considered. The dependence of the average amplitude of stimulated echo on the parameters of noise pulses is determined. The results can be used for analysis of the corresponding algorithm of excitation of stimulated spin echo, as well as in calculations of characteristics of the signal processors based on the phenomena of photon and spin echoes.     

Excitation of photon echo by noise pulses

The excitation of photon echo by noise pulses that are formed by modulation of the carrying frequency with Gauss noise is modeled. The modeling is based on optical Bloch equations the solution of which for noise pulse realizations is constructed by their stepwise approximation. In terms of the formalism of state transfer matrices, the two- and three-pulse excitation modes are analyzed. The complex envelopes of the primary and stimulated echo responses are determined. In the linear (low-level-signal) mode, the shape of the two-pulse echo corresponds to that of the time delayed and inverted noise pulse. The boundary of the linear mode, upon exceeding of which distortions of the shape of the noise pulse become noticeable, is determined. The shape of the stimulated (three-pulse) echo in the linear mode corresponds to that of the autocorrelation function of the noise pulse realization. Upon passage beyond the boundary of the linear mode, the shape of the three-pulse echo corresponds either to the cross-correlation function of distorted noise pulses (with different intensities) or to the autocorrelation function of distorted pulses (with the same intensities). The modeled photon echo excitation modes can be used in photon echo processors to process signals in the light range.     

在双色场中使用相干叠加态来提高高次谐波的发射

本文提出了一种在双色场中使用相干叠加态来提高高次谐波发射效率的方法. 我们首先通过在800nm基本激光脉冲上添加一束控制激光脉冲在理论上得到双色合成激光场;其次,通过求解一维含时薛定谔方程,计算得到了体系处于不同初始态时的高次谐波谱,并结合时频分布图对其微观机理进行分析. 计算结果表明,使用相干叠加态作为体系的初始态,通过调节两束激光的相对相位可以有效实现提高高次谐波的发射效率的目的.     

在双色场中使用相干叠加态来提高高次谐波的发射

本文提出了一种在双色场中使用相干叠加态来提高高次谐波发射效率的方法.我们首先通过在800 nm基本激光脉冲上添加一束控制激光脉冲在理论上得到双色合成激光场;其次,通过求解一维含时薛定谔方程,计算得到了体系处于不同初始态时的高次谐波谱,并结合时频分布图时其微观机理进行分析.计算结果表明,使用相干叠加态作为体系的初始态,通过调节两束激光的相对相位可以有效实现提高高次谐波的发射效率的目的.     

Photon Echo from Localized Excitons in Semiconductor Nanostructures

An overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.     

Stochastic excitation of a stimulated spin echo

The excitation of a stimulated spin echo by two coherent pulses of Gaussian white noise and a δ-function-like radio pulse is studied. The mean value of the complex envelope of the echo is obtained by solving the Bloch equations. The behavior of the mean value of the envelope of the stimulated echo is investigated for a Lorentzian shape of the inhomogeneously broadened absorption line. It is shown that in an excitation regime which is linear for noise pulses the envelope corresponds to the Fourier transform of the line-shape function. Nonlinear distortions of the mean value of the envelope of a stimulated echo can arise outside the linear excitation regime. Zh. Tekh. Fiz. 67, 100–104 (October 1997)     

Excitation of the spin density and current by coherent light pulses in quantum wells

We study the orbital and spin dynamics of charge carriers induced by non-overlapping linearly polarized light pulses in semiconductor quantum wells. It is shown that such an optical excitation with coherent pulses leads to a spin orientation of photocarriers and an electric current. The effects are caused by the interference of optical transitions driven by individual pulses. The distribution of carriers in the spin and momentum spaces depends on the crystallographic orientation of quantum wells and can be efficiently controlled by the pulse polarizations, time delay and phase shift between the pulses, as well as an external magnetic field.     

Stimulated spin echo upon excitation with pseudorandom pulses

Different regimes of excitation of a stimulated spin echo by pseudorandom pulses and short coherent delta-shaped pulses are considered. Radio pulses phase-shifted by a 127-element M sequence are used as pseudorandom signals. The shape of the complex envelope of the stimulated echo is simulated in linear and nonlinear regimes with respect to the phase-shifted pulses. It is demonstrated that the excitation pulses can be described by correlation functions. Appropriate conditions are determined under which the amplitude of the stimulated echo can be greater than the amplitude corresponding to the classical algorithm used for exciting a stimulated echo by three delta-shaped pulses. The results obtained can be used for analyzing the formation of a stimulated photon echo.     

磁共振现代射频脉冲理论在非均匀场成像中的应用

在磁共振非均匀场成像中，传统的射频脉冲导致回波信号的衰减.为了减小和消除这种磁共振信号的衰减，在讨论了经典理论的基础上根据非线性动力学中的逆散射理论和Shinnar-Le Roux方法导出了用于非均匀场成像的射频脉冲设计方法.模拟结果表明，采用逆散射理论和Shinnar-Le Roux方法优化的脉冲序列可以明显提高信号的信噪比. 关键词： 磁共振成像 射频脉冲 非线性系统     

Coherent transients in the femtosecond photoassociation of ultracold molecules

We demonstrate the photoassociation of ultracold rubidium dimers using coherent femtosecond pulses. Starting from a cloud of ultracold rubidium atoms, electronically excited rubidium molecules are formed with shaped photoassociation pump pulses. The excited state molecules are projected with a time-delayed probe pulse onto molecular ion states which are detected in a mass spectrometer. Coherent transient oscillations of the excited state population are observed in the wings of the pump pulse, in agreement with the time-dependent solution of the Schr?dinger equation of the excitation process.     

Simulation of coherent responses of resonant media excited by a series of ultrashort laser pulses

A technique for the numerical simulation of coherent optical responses of the photon echo type formed in resonance media with strong inhomogeneous broadening under the action of femtosecond laser pulses is developed. This approach is based on solving the Maxwell-Bloch equations using the finite-difference time-domain (FDTD) method without application of a fast rotating field and slowly varying envelope approximations. The method can be used to simulate coherent responses in different resonance media with a complex structure of energy levels. The technique was validated using the example of describing experiments on narrowing a photon echo pulse and femtosecond echo processing.     

三能级原子与少周期脉冲串作用中的相干布居捕获

研究了少周期脉冲串作用下三能级原子中的布居转移和相干布居捕获现象.在非旋波近似的情况下求解了密度矩阵方程.研究结果表明在等时间间隔的锁相脉冲作用下,系统能级的布居逐步转移并积累,系统基态相干也逐步积累.在满足脉冲重复频率为基态能级频差的整数分之一倍时,三能级系统和频率梳中两梳齿频率成分作用形成相干布居捕获现象,原子暗态布居值达到最大,介质对脉冲透明.在适当选取少周期脉冲参量的情况下,在0.5个ns的时间内三能级系统相干性演化到最大后到达稳态,相干布居捕获发生.与脉宽为100个fs的多周期脉冲相比,少周期脉冲串在介质中建立相干布居捕获的时间缩短两个数量级.由于频率梳中与三能级系统发生作用的梳频成份有相同的频移,相干布居捕获的条件双光子共振仍然满足.因而,当两基态能级频率差较大时,如果选取少周期脉冲载波频率为系统能级1至2和1至3的传输频率之和的一半ω=(ω₁+ω₂)/2,室温下原子热运动的引起的多普勒频移并不会破坏相干布居捕获.     

Echo spectroscopy and quantum stability of trapped atoms

We investigate the dephasing of ultra cold 85Rb atoms trapped in an optical dipole trap and prepared in a coherent superposition of their two hyperfine ground states by interaction with a microwave pulse. We demonstrate that the dephasing, measured as the Ramsey fringe contrast, can be reversed by stimulating a coherence echo with a pi pulse between the two pi / 2 pulses, in analogy to the photon echo. We also demonstrate that "echo spectroscopy" can be used to study the quantum dynamics in the trap even when more than 10(6) states are thermally populated and to study the crossover from quantum to classical dynamics.     

Selective excitation,coherent control,and attosecond spectrochronography of electron subshells in atomic systems

Optical field waveforms with an ultrabroad spectrum and a tailored phase are shown to enable selective excitation, coherent control, and attosecond spectrochronography of electron subshells in many-electron atomic systems. Analysis of the evolution of the density matrix of electron subshells in an atomic system driven by an ultrashort light pulse shows that the interference of different quantum pathways of electron dynamics plays a key role in the buildup of the nonlinear-optical response of such a system. Our analysis suggests a method whereby the attosecond dynamics of individual electron subshells in atoms can be coherently controlled with ultrashort laser pulses.     

Multiband Adiabatic Inversion Pulses

The conditions necessary to obtain multiple adiabatic population inversion at different frequencies in a two-level system are defined. It is shown how any pulse that produces adiabatic inversion in a single frequency band can be modified to become a multiband adiabatic inversion pulse. Using Floquet formalism, the interaction between the different inversion bands is described and shown to create effective nonlinear irradiation fields. By controlling the reference phase of the single-inversion-frequency-band pulses, these effective irradiation fields can be minimized or canceled. These pulses can be used for multiple selective excitation or selective population inversion in coherent spectroscopy. NMR experiments confirming the theoretical predications are shown. The experimental results agree very well with the theoretical predictions.     

Analysis of effect of excitation pulse characteristics on numerical simulation of reverse saturable absorption

We present the results of analysis of rate equations for reverse saturable absorption (RSA) process to understand the applicability and probable errors in using only time dependence of the excitation pulse as against both space and time dependence in numerical simulations of rate equations. We have considered a three-level approximation of the five-level rate equations under nano-second laser pulse excitations. The population density, nonlinear absorption and transmission have been calculated and compared for different approximations and for different excitation pulse spatial shapes. We show that the neglect of spatial characteristics of the excitation pulses in the rate equation analysis can lead to considerable errors in the numerical simulations of RSA in case of excitation fluences below the fluence for saturation of transmission.     

Effect of the Excitation Radiation Coherence on Oscillations of the Photon Echo Intensity

The physical reasons for observing the splitting of optical lines several orders of magnitude smaller than the spectral width of a laser pulse are investigated. A theory of coherent and incoherent photon echo (PE) in an external static magnetic field and in the presence of a pulsed magnetic field, which causes oscillations of the PE intensity, is elaborated. It is shown that the periods of oscillations in the echo intensity, the echo duration, and the dimensions of the regions in the inhomogeneous line, where the excited ions are coherent, do not depend on the degree of coherence of the laser pulse and on the external static magnetic field. As follows from the theory, in the case of the coherent excitation of the echo, the amplitude of the intensity oscillations is independent of the external static magnetic field if the inhomogeneous line is symmetric. It is shown that the amplitude of the oscillations at the incoherent excitation of the echo is equal to the autocorrelation function of the distribution function of the transition frequency along the inhomogeneous line with the argument equal to the Zeeman splitting of the optical line in the external magnetic field. In this case, the experimental values of the oscillation amplitude are in good agreement with the calculated values of the autocorrelation function for the total inhomogeneous line in LuLiF₄:Er³⁺ (⁴I_15/2?F_9/2 transition). In the same way, the autocorrelation function has been obtained for YLiF₄:Er³⁺ on the same transition.     

Diffusion and relaxation effects in general stray field NMR experiments

We analyze the evolution of magnetization following any series of radiofrequency pulses in strongly inhomogeneous fields, with particular attention to diffusion and relaxation effects. When the inhomogeneity of the static magnetic field approaches or exceeds the strength of the RF field, the magnetization has contributions from different coherence pathways. The diffusion or relaxation induced decay of the signal amplitude is in general nonexponential, even if the sample has single relaxation times T(1), T(2) and a single diffusion coefficient D. In addition, the shape of the echo depends on diffusion and relaxation. It is possible to separate contributions from different coherence pathways by phase cycling of the RF pulses. The general analysis is tested on stray field measurements using two different pulse sequences. We find excellent agreement between measurements and calculations. The inversion recovery sequence is used to study the relaxation effects. We demonstrate two different approaches of data analysis to extract the relaxation time T(1). Finite pulse width effects on the timing of the echo formation are also studied. Diffusion effects are analyzed using the Carr--Purcell--Meiboom--Gill sequence. In a stray field of a constant gradient g, we find that unrestricted diffusion leads to nonexponential signal decay versus echo number N, but within experimental error the diffusion attenuation is still only a function of g(2)Dt(3)(E)N, where t(E) is the echo spacing.