The effect of uncorrelatedness of inhomogeneous broadening on the formation of transient optical processes in multilevel systems

The correlation of inhomogeneous broadening at various frequency transitions in three-level systems is investigated, as is its effect on the intensity of a stimulated photon echo. It is shown that the correlation coefficient of inhomogeneous broadening at two different transitions and the response intensity of the stimulated photon echo depend on the parameter of the random interaction of an optical electron with a local field, as well as on the distribution width of additional frequency shifts owing to a partial fixation of transition energies. In this case, an insignificant variation of the correlation coefficient results in a considerable decrease in the response intensity.     

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.     

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.     

Coherent information storage with photon echoes produced by switching electric fields

We demonstrate modified photon echoes in Eu³⁺:Y₂SiO₅ by controlling the inhomogeneous broadening of the optical transition in Eu³⁺. These modified photon echoes are shown to be capable of storing phase and amplitude modulation.     

Laser frequency stabilization at 1.5 microns using ultranarrow inhomogeneous absorption profiles in Er:LiYF4

Single-frequency diode lasers have been frequency stabilized to 1.5 kHz Allan deviation over 0.05-50 s integration times, with laser frequency drift reduced to less than 1.4 kHz/min, using the frequency reference provided by an ultranarrow inhomogeneously broadened Er³⁺:⁴I_15/2→⁴I_13/2 optical absorption transition at a vacuum wavelength of 1530.40 nm in a low-strain LiYF₄ crystal. The 130 MHz full-width at half-maximum (FWHM) inhomogeneous line width of this reference transition is the narrowest reported for a solid at 1.5 μm. Strain-induced inhomogeneous broadening was reduced by using the single isotope ⁷Li and by the very similar radii of Er³⁺ and the Y³⁺ ions for which it substitutes. To show the practicability of cryogen-free cooling, this laser stability was obtained with the reference crystal at 5 K; moreover, this performance did not require vibrational isolation of either the laser or crystal frequency reference. Stabilization is feasible up to T=25 K where the Er³⁺ absorption thermally broadens to ∼500 MHz. This stabilized laser system provides a tool for interferometry, high-resolution spectroscopy, real-time optical signal processing based on spatial spectral holography and accumulated photon echoes, secondary frequency standards, and other applications such as quantum information science requiring narrow-band light sources or coherent detection.     

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.     

Optimum conditions for correlation of the temporal shape of an object pulse with a stimulated photon echo response in inhomogeneous external electric fields

We have studied the information locking effect and the effect of correlation of the shape of an object laser pulse with the shape of a stimulated photon echo response in the presence of external spatially inhomogeneous electric fields. We have shown that, for the transition ³H₄-³P₀ in a LaF₃:Pr³⁺ crystal, one can observe the effect of the correlation of the shape of an object laser pulse with the shape of a stimulated photon echo response and, depending on the scheme of the action of external spatially inhomogeneous electric fields, either the information locking effect or the information destroying effect.     

Photon echo in gases: From the non-Faraday rotation to unpolarized echo

A retrospective review of both theoretical and experimental works on photon echo in gases in the presence of longitudinal magnetic fields is presented from the viewpoint of new possibilities opened by this research for polarization echo spectroscopy of gases. The main attention is given to the physical scenario of the magnetic field’s effect on the properties of the photon echo. New results on the photon echo and stimulated photon echo in ytterbium vapor at the 1 ? 0 transition in the presence of the longitudinal magnetic field whose strength ranges from weak to strong are presented. Possible applications of the magnetic field effects for optical data storage and processing are analyzed.     

The correlation of inhomogeneous broadening and the efficiency of data locking in optical echo processors

The formation of responses of stimulated photon echo and the efficiency of data locking under the action of a spatially inhomogeneous electric field on a resonance medium are analyzed. It is shown that the action of a spatially inhomogeneous electric field on a resonance medium between the first and second excitation laser pulses leads to the reversible destruction of the phase memory of the medium, which manifests itself in a change in the time-frequency correlation of inhomogeneous broadening. The possibility of controlling the efficiency of data locking by varying the gradient of an external nonuniform electric field is considered.     

Photon echo relaxation in LaF3:Pr3+

We have observed deeply modulated photon echoes from Pr³⁺ ions in LaF₃ reflecting nuclear hyperfine interactions in both the ground ³H₄ and excited ³P₀ states. We infer splittings of 0.75 MHz for the ³P₀ state. Inhomogeneous broadening of the terminal levels is found to lead to echo modulation damping. A surprising concentration dependence of the photon echo relaxation rate is observed as well as a dramatically long-lived (3 min) stimulated photon echo.     

Quantum Memory with Natural Inhomogeneous Broadening in an Optical Cavity

We propose an efficient quantum memory scheme with natural inhomogeneous broadening in an asymmetric optical cavity. The scheme uses the strong rephasing pulses like traditional photon echo techniques rather than spectral holeburning, which enables us to have the potential implementation in a much broader range of material systems. In the condition of impedance matching to an optical cavity, we find that the input light pulse can be completely absorbed by an atomic ensemble. We also show that the quantum memory efficiency can be equal to unity even for a small optical depth of the atomic system.     

A remark on coherent Raman beats in an inhomogeneous broadened system

We have pointed out that coherent Raman beats (CRB) in a three-level system with inhomogeneous broadening of optical transition do not suffer from power broadening and AC Stark shift due to the probe laser field if the sublevel coherence from which the CRB are stimulated is prepared over a sufficiently wide frequency range of the inhomogeneous broadening.     

Modulation of the shape of the photon echo pulse by a pulsed magnetic field: Zeeman splitting in LuLiF4:Er3+ and YLiF4:Er3+

A spectroscopy method has been proposed involving a change in the time shape of the echo signal in the presence of a perturbation, which splits the frequencies of the transitions of two or more ion subgroups of the echo-active ions. This method has been applied to optical systems in which the Zeeman effect is manifested. The ion transition frequencies of ions are switched by a weak pulsed magnetic field acting during the time of the radiation of the photon echo pulse. The modulation of the photon echo signal shape was observed in LuLiF₄:Er³⁺ and YLiF₄:Er³⁺. The time interval between the two nearest minima corresponds to the accumulated phase of the electric dipole moment ?? and makes it possible to determine the difference of the g factors of the ground and excited ⁴ F _9/2(I) states of the Er³⁺ ion in the LuLiF₄ the YLiF₄ matrices for the known amplitude of the pulsed magnetic field. It has been shown that the echo response of the system can be programmed by the weak magnetic field pulses.     

三价铕离子配合物的激光光谱研究

利用高灵敏度的时间辨激光光谱技术研究了在配位场作用下Ｅｕ＾３＾＋的直接激发与发特性。Ｅｕ＾３＾＋的直接激发光谱（特别是７Ｆ０－５Ｄ０的超灵敏跃迁）及其发射光谱随不同的配合物的变化，同时观测到与配位对称性及配位强度有联系的７Ｆ１－５Ｄ０磁偶极跃 迁的分裂。在对７Ｆ０－５Ｄ０跃迁共振与非共振的１０ｐｓ激光脉冲的激励下，都可以立即观察到５Ｄ０－７ＦＪ（Ｊ＝２，３，４）的发射，说明Ｅｕ＾３＾＋的５Ｄ０能态     

Photon echo in the presence of a magnetic field: New prospects for data accumulation and processing

The possibility for echo signal switching-off and the switching of echo polarization between the ±45° positions is demonstrated for the photon echo (PE) and stimulated photon echo (SPE) generated in Yb vapor at the (6s6p)³ P ₁ ? (6s ²)¹ S ₀ transition by two pulses of the resonant linearly polarized radiation at appropriate experimental parameters in the weak magnetic field limit. The experimental data are in qualitative agreement with the theoretical analysis and the calculations made for the 1 ? 0 transition. The strong magnetic field limit leads to unpolarized PE and SPE signals generated by linearly polarized radiation pulses. The possibility of the generation of a long-lived echo in ytterbium vapor due to the magnetic field induced mixing of the upper working level with the metastable level is discussed. The results can be employed for the optical data storage and processing.     

非晶纳米发光材料(Y,Eu)2O3-SiO2发射光谱的分析研究

EXAFS测定表明sol-gel方法制备的纳米非晶(Y,Eu)₂O₃-SiO₂发光材料中,发光中心Eu³⁺的局域环境和晶态X₂型Y₂SiO₅Eu中Eu³⁺离子的局域环境相似。以此结构为依据,用M. F. Reid的方案计算了晶场迭加模型中的能级参数及光谱强度参数,并得到了与实验结果基本一致的理论光谱图.     

Effect of the translational velocity of active particles on the properties of a photon echo

The photon echo method was used to detect an increase in the relaxation rate in the vibrational-rotational transition of fluoromethane in ¹³CH₃F gas and a ¹³CH₃F-argon mixture upon an increase in the velocity of active particles. For a photon echo in the 0–1 transition in a Yb + Xe mixture, the dependence of the relaxation parameters on the direction of the translational velocity of Yb leads to qualitative changes and a collision photon echo arises.     

Oscillations of the photon echo intensity in a pulsed magnetic field: Zeeman splitting in LiLuF<Subscript>4</Subscript>:Er<Superscript>3+</Superscript>

A method of high-resolution time-resolved optical spectroscopy using oscillations of the photon echo intensity in the presence of a perturbation, which splits the optical frequencies of the transitions of two or more ion subgroups, has been proposed and demonstrated. This method has been applied to systems in which the Zee-man effect is manifested. The transition frequencies of ions are switched by a pulsed magnetic field. Oscillations of the photon echo intensity were observed in LiLuF₄:Er³⁺ and LiYF₄:Er³⁺. The first minimum corresponding to the accumulated phase of the electric dipole moment π/2 is reached in the pulsed magnetic field with an amplitude of ～2 G at a duration of 30 ns. The Zeeman splitting in this field is ～10 MHz, which is much less than the laser spectral width (0.15 Å ～ 9 GHz). The g factor of the ⁴ F _9/2(I) excited state of the Er³⁺ ion in the LiLuF₄ matrix has been determined in zero magnetic field. The comparison with the g-factor value found from the measurement of the absorption spectrum in a magnetic field of 8 kG has been performed.     

超低温下掺Er3+玻璃的相干拍频调制效应研究

采用非相干光时延四波混频(TDFWM-IL)实验装置,在7K温度下,利用波长为800 nm的飞秒脉冲激光,观测到掺Er3+玻璃的光子回波效应,发现信号随延时变化的拍频调制结构.根据TDFWM-IL多能级理论,运用其非均匀加宽占主导时的公式拟合实验结果,从最佳拟合获得的退相时间T2=300 fs,这与由相干控制实验测得的...