Frequency-modulation spectroscopy of coherent dark resonances in <Superscript>87</Superscript>Rb atoms

The results of frequency-modulation (FM) spectroscopy of coherent dark resonances from the Zeeman sublevels of the transition F=2↔ F=1 of D ₁ line in absorption of ⁸⁷Rb atoms are presented and discussed in detail. By contrast with the conventional spectroscopy of coherent dark resonances employing two laser beams, relative frequency of which can be varied, these data has been obtained with the help of a single frequency-modulated laser field. Variation of the modulation frequency plays then a similar role as the variation of the relative frequency in conventional spectroscopy. Experimental data are fit to the theoretical calculations, which are based on the theory of FM spectroscopy of coherent dark resonances recently developed by us. Feasibility of using such experimental technique for accurate measurements of magnetic fields is also discussed.     

Two strongly contrasting Λ-systems in the <Emphasis Type="Italic">D</Emphasis> <Subscript>1</Subscript> line of <Superscript>87</Superscript>Rb in a transverse magnetic field

Four different types of spectroscopic cells that cover all possible existing versions of sealed-off cells (containing alkali atomic vapor) characterized by drastically different relaxation rates γ_rel are used to study the electromagnetically induced transparency spectra of two Λ-systems in the D₁ line of ⁸⁷Rb in the presence of transverse magnetic field. Two cw narrowband diode-lasers are used to form the coupling laser radiation (with a fixed frequency) and the probe radiation with a tunable frequency. Two strongly contrasting Λ-systems are found: the first shows resonances that are transformed from dark resonances to bright resonances in all cases apart from nanocells, whereas the second shows four dark resonances in all four different types of cell. The theoretical simulations are in good agreement with the experimental results.     

Electromagnetically induced transparency resonances inverted in magnetic field

The phenomenon of electromagnetically induced transparency (EIT) is investigated in a Λ-system of the ⁸⁷Rb D ₁ line in an external transverse magnetic field. Two spectroscopic cells having strongly different values of the relaxation rates γ_rel are used: an Rb cell with antirelaxation coating (L ~ 1 cm) and an Rb nanometric- thin cell (nanocell) with a thickness of the atomic vapor column L = 795 nm. For the EIT in the nanocell, we have the usual EIT resonances characterized by a reduction in the absorption (dark resonance (DR)), whereas for the EIT in the Rb cell with an antirelaxation coating, the resonances demonstrate an increase in the absorption (bright resonances (BR)). We suppose that such an unusual behavior of the EIT resonances (i.e., the reversal of the sign from DR to BR) is caused by the influence of an alignment process. The influence of alignment strongly depends on the configuration of the coupling and probe frequencies as well as on the configuration of the magnetic field.     

Band-edge exciton fine structure of single CdSe/ZnS nanocrystals in external magnetic fields

We report a spectroscopic study of the two lowest-energy exciton levels of individual CdSe/ZnS nanocrystals under applied magnetic fields. Field-induced coupling between the bright and the dark excitonic states is directly observed in the low-temperature photoluminescence spectrum and decay and allows the determination of the angle between the nanocrystal c axis and the field. Orientation-dependent Zeeman splittings of the dark and bright exciton sublevels are measured and provide the corresponding exciton Landé factors, as well as spin-flip relaxation rates between Zeeman sublevels.     

Frequency modulation spectroscopy of coherent dark resonances of multi-level atoms in a magnetic field

The resonances of coherent population trapping (CPT) excited by a frequency-modulated (FM) field at the Zeeman sublevels during the transition F _g = 2 → F _e = 1 of the ⁸⁷Rb D ₁-absorption line were studied theoretically. The influence of the nonlinear Zeeman effect on the structure of the observed resonances was considered. The spectra of CPT resonances were calculated for different values of magnetic field induction and compared with the experimental data.     

Orientation of Cs 6p 2P3/2 atomic photofragments in a magnetic field: interference in the photodissociation of diatomic molecules

In a magnetic field, Cs₂ molecules were excited from the ground X¹Σ⁺_g(v_X=0,J_X=55) level to the D ¹Σ⁺_u(v=46,J=54) level by dissociation laser light linearly polarized parallel to the field, for which the magnetic sublevels were degenerated and thus all the transitions between them were simultaneously stimulated. Probe laser light excited the dissociated Cs 6p²P_3/2 atomic fragments to 6p²D_3/2 level and the resultant 6p²P_1/2 - 6d²D_3/2 emission was detected as the function of the wavelength of the probe light. The populations of the 6p²P_3/2,mj magnetic sublevels were determined from the relative strengths of the 6p²P_3/2,mj - 6d²D_3/2,m'j transitions induced by the probe light. Non-zero orientation O₀ was found in the ensemble of dissociated Cs 6p²P_3/2 atomic fragments. The orientation O₀ increased as the magnetic field strength increased. It was demonstrated both experimentally and theoretically that the orientation O₀ was induced through the interference in the excitation and dissociation paths in the presence of an external magnetic field, even when all degenerated transitions between the magnetic sublevels of the molecules are simultaneously excited by the light linearly polarized parallel to the field.     

Magneto-optical resonances in the field of counterpropagating waves

The resonance of the intersection of sublevels in a probe laser field resonant to the cyclic transition corresponding to the D ₂ ⁸⁷Rb line has been investigated in a zero magnetic field. The strong effect of an additional laser field acting on the adjacent transition has been revealed. In a cell without the buffer gas and antirelaxation coating, the amplitude of the probe-field absorption resonance can increase by more than an order of magnitude in the presence of a counterpropagating wave. The effect is observed at the laser frequency tuned to the cross resonance, when the counterpropagating waves simultaneously act on moving atoms at the cyclic and open transitions with the common lower level. The theoretical analysis of the effect of the additional field on the electromagnetically induced absorption resonance is in agreement with the experimental data.     

Inspection of a magneto-optical trap via electromagnetically induced absorption

Electromagnetically induced absorption (EIA) was observed for the first time on a sample of ⁸⁵Rb in a magneto-optical trap using low intensity cw copropagating pump and probe optical fields. Narrow resonances revealing the dependence of the ground-state Zeeman sublevels energy structure on the quadrupolar magnetic field and the trapping optical field intensity at different trap positions, were observed. Coherence resonances as narrow as 30 kHz were obtained under low trapping field intensities. The use of EIA spectroscopy for the magnetic field mapping of cold atomic samples is illustrated.     

Determination of the structure of hyperfine sublevels of Rb in strong magnetic fields by means of the coherent population trapping technique

The splitting of hyperfine sublevels of the ⁸⁵Rb atom in strong magnetic fields has been studied by means of the coherent population trapping technique. Narrow resonances with a high signal-to-noise ratio have been detected in a 30-μm-thick spectroscopic cell. The magnetic field in the direction transverse to the laser beams has been created by permanent magnets and has reached 1600 G. Owing to the exclusive narrowness of the cell, the field in it is almost uniform. The break of the coupling between the electronic and nuclear moments, as well as the transition to the Paschen-Back regime in magnetic fields above 600 G, has been observed. The derivatives of the frequency shifts of the observed resonances and their asymptotic values in strong magnetic fields have been determined in terms of the magnetic field strength. The experimental results have been interpreted within a theoretical model based on the known constants of the hyperfine structure of the Rb atom.     

射频场控制的磁子能级中单色激光吸收抑制

理论上研究了射频场作用下多塞曼能级系统中单色激光的吸收抑制现象.一束单色线偏振或者椭圆偏振的激光作用于铷原子两能级间,线或椭圆偏振矢量方向与磁场方向垂直.在磁场中冷铷原子能级发生分裂,通过一个射频场将这些磁子能级耦合起来.当扫描射频场频率时,计算表明原子对单色光的吸收谱中出现了透射峰,类似于电磁诱导透明现象,光吸收减弱,光场透射增强.对于线性偏振或者椭圆偏振的单色光均能得到透射增强的结果 .这种现象完全不同于通常光泵磁共振实验中射频场与磁子能级谐振时光被吸收最多的现象.这种扫描射频场频率时单色光的透射增强现象来自于磁子能级间的相干效应.计算表明在扫描射频场频率时单色光吸收谱中出现的透射峰与射频场的拉比频率和椭圆偏振光的左旋和右旋圆偏振成分相关.这种射频场控制的单色光透射增强效应在磁场测量,光信息处理等领域有潜在的应用价值.     

射频场控制的磁子能级中单色激光吸收抑制

理论上研究了射频场作用下多塞曼能级系统中单色激光的吸收抑制现象.一束单色线偏振或者椭圆偏振的激光作用于铷原子两能级间,线或椭圆偏振矢量方向与磁场方向垂直.在磁场中冷铷原子能级发生分裂,通过一个射频场将这些磁子能级耦合起来.当扫描射频场频率时,计算表明原子对单色光的吸收谱中出现了透射峰,类似于电磁诱导透明现象,光吸收减弱,光场透射增强.对于线性偏振或者椭圆偏振的单色光均能得到透射增强的结果.这种现象完全不同于通常光泵磁共振实验中射频场与磁子能级谐振时光被吸收最多的现象.这种扫描射频场频率时单色光的透射增强现象来自于磁子能级间的相干效应.计算表明在扫描射频场频率时单色光吸收谱中出现的透射峰与射频场的拉比频率和椭圆偏振光的左旋和右旋圆偏振成分相关.这种射频场控制的单色光透射增强效应在磁场测量,光信息处理等领域有潜在的应用价值.     

Calculation of fine structure parameters by semiempirical method from energy intervals between magnetic sublevels

A method is developed for the semiempirical calculation of fine structure parameters from the experimental energy intervals between magnetic sublevels. The calculations are performed using the configuration of neutral carbon as an example. The calculated parameters are used to calculate the 2p ² configuration energy spectrum and the gyromagnetic ratios of the ³ P ₂ and ¹ D ₂ levels, as well as the magnetic splitting of triplet levels. The results are compared with available experimental and theoretical data. It is confirmed that the dependence of the energy of magnetic sublevels of np ² configurations on the magnetic induction is parabolic for sublevels with the projections M = 0, ±1 and is linear for sublevels with M = ±2.     

A study of dark resonance splitting for the D 1 line of 87Rb in strong magnetic fields

The process of electromagnetically induced transparency (EIT) is studied using an extremely thin cell with thickness of a vapor column of rubidium atoms L = 794 nm. Wavelengths of resonant laser beams ?? ?? 794 nm. Results of the study of behavior of the EIT resonance (which is also called the ??dark?? resonance) formed in the ?? system of the D ₁ line of ⁸⁷Rb atoms in strong magnetic fields up to 1700 G (0.17 T) are reported for the first time. Three dark resonances are recorded in magnetic fields with induction B < 300 G, two resonances are recorded at B > 650 G, and only one dark resonance is retained at B > 1200 G. A method of the formation of a dark resonance at a given frequency is demonstrated that will allow, under the corresponding conditions, the formation of a dark resonance also at B > 0.2 T. The experimental results are well described by the known theoretical models. Practical applications of these results are indicated.     

顺磁物质CeF3磁光Faraday效应及其温度特性的量子理论

本文计算了顺磁物质CeF₃因Ce³⁺离子从基态能级4f至5d的电偶极跃迁产生的Fara-day旋转。讨论晶场对Ce⁺³离子4f和5d能级的影响,通过唯象地引入一个与磁化强度M成正比的“附加磁场”H_m=λM,由此获得4f离子在外加磁场和“附加磁场”的共同作用下的一级Zeeman分裂。经劈裂后的两个子能级上各自产生左、右圆偏振光激发的电偶极跃迁,导致磁光Faraday效应。对于波长为0.6328μm的入射光,在60—300 关键词：     

外电场作用下Si_2O分子的激发特性

主要对2种Si2O分子异构体的激发特性进行研究,由计算结果可知,外电场对Si2O分子的激发能,振子强度,跃迁偶极矩及吸收光谱有着显著的影响.无外电场时三角型Si2O(C2v,1A1)分子在可见光区无吸收谱,外电场作用下其在可见光区(407.18—526.93nm)有比较弱的吸收谱.直线型Si-Si-O(C∞v,3Σ-)分子在有无外电场作用时在蓝光和紫光区均有一定的吸收谱,其中比较难得的是在蓝色光区(478.88—488.59nm)呈现较强的吸收谱.     

Optical absorption zeeman spectroscopy of rare earth orthochromites

The optical absorption spectrum of Er³⁺ in ErCrO₃ in the phasesΓ ₁,Γ ₂ andΓ ₄ has been studied as a function of temperature and applied magnetic field. The experimental data for the Er³⁺ ground doublet splitting are analyzed using a single ion molecular field approach. The analysis shows that the Cr — Er interaction is predominantly antisymmetric exchange, the magnetic dipole-dipole interaction being an order of magnitude smaller. The Er — Er interaction is of exchange as well as of dipolar origin.     

外加磁场对简并二能级原子系统相干特性的影响

在铯原子简并二能级系统中6S_1/2F=4—6P_3/2 F'=5 的循环跃迁上获得了电磁感应吸收(EIA)峰，并研究了轴向均匀磁场对二能级系统相干效应的影响，即存在轴向均匀磁场时，观测到在铯原子6S_1/2F=4—6P_3/2F'=5 跃迁频率处EIA和电磁诱导透明(EIT)的混合结构，在合适的实验条件下，其结果与Ye等(2002)的理论分析相一致. 关键词： 电磁感应吸收(EIA) 铯原子 简并二能级系统     

铯饱和吸收光谱随抽运光强度的变化

研究了铯饱和吸收光谱随抽运光强度变化的情况，特别是６^２Ｓ_１／２Ｆ＝４→６^２Ｐ_３／２Ｆ′＝５的谱线的变化行为．在线偏振光抽运、线偏振光检测的情况下，计入所有相关的Ｚｅｅｍａｎ子能级之间的跃迁，考虑光抽运与饱和效应的共同作用，运用Ｒｕｎｇｅ-Ｋｕｔａ法则求解粒子数方程，计算得出的饱和吸收谱与实验结果符合得较好．还给出了较直观的物理解释 关键词：     

Saturated absorption spectroscopy: Elimination of crossover resonances with the use of a nanocell

It is demonstrated that the velocity-selective optical pumping/saturation resonances of the reduced absorption in a Rb vapor nanocell with thickness L = λ, 2λ, and 3λ (resonant wavelength λ = 780 nm) allow for the complete elimination of crossover (CO) resonances. We observe well-pronounced resonances corresponding to the F _g = 3 → F _e = 2, 3, and 4 hyperfine transitions of the ⁸⁵Rb D₂ line with line widths close to the natural width. A small CO resonance located midway between F _g = 3 → F _e = 3 and F _g = 3 → F _e = 4 transitions appears only for L ≥ 4λ. The D₂ line (λ = 852 nm) in a Cs nanocell exhibits a similar behavior. From the amplitude ratio of the CO and VSOP resonances, it is possible to determine the thickness of the column of alkali vapor in the range of 1–1000 μm. The absence of the CO resonances for nanocells with L ～ λ is attractive for the frequency reference application and for studying the transitions between the Zeeman sublevels in external magnetic fields.     

Study of atomic spectral lines in a magnetic field with use of a nanocell with the thickness <Emphasis Type="Italic">L</Emphasis> = λ

We propose a technique which we call “L = λ Zeeman technique” (LZT) for investigation of the transitions between the Zeeman sublevels of the hfs structure of alkali metal atoms in external magnetic fields. The technique is based on the employment of a nanocell with the thickness of the Rb atom vapor column equal to the wavelength of the laser radiation, 780 nm, resonant with the atomic rubidium D₂ transition. At the laser intensities of about 1 mW/cm² in the transmission spectrum of the nanocell narrow (～ 30 MHz) resonant peaks of reduced absorption appear localized exactly on the atomic transitions. In magnetic fields these peaks are split and their amplitudes and frequency positions depend on the magnetic field strength. The theoretical model well describes the experimental results.