Level-degeneracy effects in resonant nonlinear phenomena: Three-level atomic model

The role of level degeneracy in resonant nonlinear phenomena is examined by considering theJ=1 →J=0 atomic transition. The atomic medium is modelled as a homogeneously broadened three-level system and a closed-form expression for the medium susceptibility is obtained. It is used to discuss several nonlinear phenomena such as saturated absorption, optical bistability, and phase conjugation. The two-photon-induced coupling of the ground-state Zeeman sublevels leads to interesting polarization effects.     

Zeeman effect in the luminescence spectra of terbium-yttrium-aluminum garnet

The Zeeman effect is investigated in the green luminescence band corresponding to the 4f→4f radiative transition ⁵D₄ → ⁷F₅ of Tb ³⁺ ions in Tb _0.2 Y _2.8 A _l5 O ₁₂ terbium-yttrium-aluminum garnet at the temperature T = 85 K. It is demonstrated that an external field causes not only the Zeeman shifts of the resonant frequencies of radiative transitions in the luminescence spectra but also changes in the emission line intensities caused by modification of the optical transition probabilities in the σ₋ and σ₊ opposite circular polarization states. Special features of field dependences of the Zeeman effect for the emission lines are qualitatively explained based on the results of numerical energy spectrum calculations for the ⁵D₄ and ⁷F₅ multiplets of the Tb ³⁺ ion in yttrium-aluminum garnet in the geometry of the longitudinal and transverse Zeeman effects. The possibility of nonequilibrium population of sublevels of the (Γ₁, Γ₄) quasi-doublet state of the ⁵D₄ multiplet with energy of ∼20585 cm⁻¹ is demonstrated in an external magnetic field. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 38–45, June, 2008.     

Sublevel spectroscopy of alkali atoms in superfluid helium

We report the results of optical pumping and optical detection of magnetic resonance of alkali atoms (Cs and Rb) in superfluid helium. The magnetic resonances between the ground-state Zeeman sublevels and hyperfine levels are observed through monitoring theD ₁ fluorescence by means of the optical-rf double resonance technique. Although the ground stateg values in superfluid helium are the same as in vacuum within the experimental error, the hyperfine constant of the ground state of the Cs atom in superfluid helium is found to be slightly larger than in vacuum. Coherent transient spectroscopy is also performed.     

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.     

Creation and manipulation of coherences in molecules with a pulsed magnetic field

We demonstrate the application of a pulsed magnetic field for the creation and manipulation of coherences in molecular systems, using quantum beat spectroscopy for the detection of the dynamics of the molecular superposition states. In all cases, the experiments are performed on energy levels in electronically excited states of the (jet-cooled) CS₂ molecule populated by a short laser pulse. In the basic experiment, following excitation of initially degenerate Zeeman sublevels under zero field conditions with suitable laser polarization, quantum beats are generated at the moment the magnetic field is switched on, even when the field is delayed by several excited state lifetimes. By quenching of the field, it is shown that the molecule may be “frozen” in any superposition state of the participating sublevels. Using a combination of static and pulsed fields with different orientations, the molecule can be prepared in a more general state, described by coherences among all Zeeman substrates. This is achieved by choosing an appropriate time delay for the switched field, without any change to the geometrical parameters of the experiment such as laser polarization or detection direction. Numerical simulations of these dynamical coherence phenomena have been performed to support assignment and interpretation of the experimental results. Received: 8 April 1998 / Accepted: 3 June 1998     

Effect of the polarization of counterpropagating light waves on nonlinear resonances of the electromagnetically induced transparency and absorption in the Hanle configuration

A polarization method has been proposed for transforming the nonlinear electromagnetically induced transparency resonance into the electromagnetically induced absorption resonance (and vice versa) in the Hanle configuration in the field of counterpropagating waves. Numerical calculations have been performed for the F _g = 2 → F _e = 1 and F _g = 2 → F _e = 3 transitions in the ⁸⁷Rb atom. The qualitative analysis of the effect has been performed for the three-level Λ scheme of the atomic energy levels. The main theoretical conclusions are in qualitative agreement with our experimental data for ⁸⁷Rb. The results can be applied in magnetometry and nonlinear optics.     

Selective laser spectroscopy of localized excitons in GaSe-GaTe solid solutions in a magnetic field

The Zeeman effect in the emission spectra of localized excitons in semiconductor solid solutions has been studied by selective laser spectroscopy. It was shown that the fine structure appearing in the emission spectra of GaSe_1−x Te_x crystals under resonant monochromatic excitation in a magnetic field originates from spin relaxation of the light-induced localized excitons between their Zeeman sublevels. The localized-exciton g factor and its dependence on the energy of localized-exciton formation and solid-solution composition has been measured. Fiz. Tverd. Tela (St. Petersburg) 41, 1389–1393 (August 1999)     

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.     

Anisotropy of absorption spectra of the rare-earth orthoaluminate TbAlO<Subscript>3</Subscript> in polarized light

Polarized spectra of the optical absorption of the 4f → 4f transition ⁷ F ₆ → ⁵ D ₄ in rare-earth orthoaluminate TbAlO₃ were experimentally studied at temperature T = 78 K. It was shown that the nontrivial character of the absorption anisotropy of TbAlO₃ at low temperatures could be related either to the symmetry of wave functions of the Stark sublevels of ⁷ F ₆ and ⁵ D ₄ multiplets combining in the optical transitions under study or to optical experiment geometry that takes into account the orientation of incident light polarization relative to the crystal axes and the axes of local coordinate systems of a rare-earth ion in orthoaluminate.     

Nonlinear Hanle effect in Cs vapor under strong laser excitation

We report results of a theoretical and experimental study of the ground state nonlinear Hanle effect under strong laser excitation. It is shown that besides the well-known zero-magnetic field suppression of absorption on F _g = F→F _e = F - 1 transitions caused by population trapping, an optical pumping induced enhanced absorption occurs on F _g = F→F _e = F + 1 transitions for small B-fields. The latter effect becomes more pronounced for high F values. The experiment with atomic vapor of Cs (D₂ line, F _g = 4) confirms an increase of the spectrally unresolved fluorescence yield at zero magnetic field and 600 mW/cm² laser intensity by 9% or 42%, when excitation occurs with linearly or circularly polarized light, respectively. The results of the experiment agree with numerical simulation studies using equations of motion for a density matrix. Received 24 November 2001 / Received in final form 25 March 2002 Published online 24 September 2002     

Collision-assisted Zeeman cooling of neutral atoms

We propose a new method to cool gaseous samples of neutral atoms. The gas is confined in a non dissipative optical trap in the presence of an homogeneous magnetic field. The method accumulates atoms in the m _F =0 Zeeman sub-level. Cooling occurs via collisions that produce atoms in states. Thanks to the second order Zeeman effect kinetic energy is transformed into internal energy and recycling of atoms is ensured by optical pumping. This method may allow quantum degeneracy to be reached by purely optical means. Received 10 May 2000     

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.     

Magnetooptics of the 1D2 → 3F4 radiative transition in thulium:yttrium-aluminum garnet Tm3+:YAG

The spectra of luminescence and magnetic circular polarization of luminescence in the ¹ D ₂ → ³ F ₄ emission band in thulium:yttrium-aluminum garnet Tm³⁺:YAG (Tm³⁺:Y₃Al₅O₁₂) have been investigated at temperatures T = 78 and 293 K, respectively. Based on the analysis of the magnetooptical and optical spectra, the optical transitions between the Stark sublevels of the ³ F ₄ and ¹ D ₂ multiplets in Tm³⁺:YAG were identified. It is shown that the symmetry and energies of the Stark sublevels of the ³ F ₄, ¹ D ₂, and ³ H ₆ multiplets, found experimentally from magnetic and magnetooptical studies, confirm the results of theoretical calculations of the energy spectrum of the rare earth Tm³⁺ ion in YAG. Original Russian Text ? U.V. Valiev, J.B. Gruber, I.R. Gapdulkhakov, N.I. Juraeva, A.K. Mukhammadiev, Sh.A. Rakhimov, I.S. édel’man, 2009, published in Optika i Spektroskopiya, 2009, Vol. 106, No. 6, pp. 937–944.     

Effect of Zeeman Depopulation Pumping on Cycling Atomic Transitions

The results of an investigation of fluorescence signal at 6S_1/2 (F_g = 4) → 6P_3/2 (F_e = 5) transition of D₂ line of atomic Cs vapor versus the magnetic field (up to B = 90 G), directed along the linear polarization of exciting light are presented. The recorded reduction of fluorescence in the magnetic field, which is especially strong at high intensity of laser radiation, is explained by conversion of the Zeeman optical pumping (the alignment) into the depopulation pumping under conditions, when the Zeeman frequency shift of individual transitions between magnetic sublevels exceeds the homogeneous width of transition. In consequence, the cycling hyperfine transition F_g = 4 → F_e = 5 is transformed into an open one.     

Nonlinear Magnetooptical Resonance in 87Rb Vapor: The Influence of Stray Magnetic Fields and Excitation Radiation Intensity on the Basic Characteristics of the Effect in Cells with Antirelaxation Coating

Optics and Spectroscopy - The nonlinear Hanle effect is generally considered in the modern literature as a particular case of coherent population trapping (CPT) at degenerate Zeeman sublevels of...     

Testing of QED-Theory and Precise Measurements of the Rydberg Series for the He-Like Multicharged Ions

The wavelengths of the 1snp ¹ P ₁−1s ^{2 1} S ₀ transitions in He-like Mg XI, F VIII (n= 4–8) and Al XII (n=6,9) have been calculated in the framework of the 1/Z expansion method including relativistic effects and QED contributions. It is found that QED corrections to the ground-state ionization energy are significant at the present level of experimental accuracy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Amplification of radiation in atomic vapor induced by a linearly polarized laser radiation

We present the results of spectroscopic and polarization studies of dilute rubidium vapor exposed to a single-frequency linearly polarized diode laser radiation in a spectral range of atomic D₂ line. We report the origin of a circularly polarized radiation on V-type transitions of ⁸⁷Rb F _g = 2 → F _e = 3 and ⁸⁵Rb F _g = 3 → F _e = 4, and amplification of this radiation in backward direction caused by a partial population inversion among magnetic sublevels of the ground and excited levels. This is confirmed experimentally by high directivity of backward radiation, absence in its spectrum of ⁸⁵Rb F _g = 2 → F _e = 1 (Λ-type) radiation, as well as by different nature of intensity dependences of backward and fluorescence radiations.     

Flory radius of polymers in a periodic field: An exact analytic theory

We found an exact expression for the Flory radius R _F of Gaussian polymers placed in an external periodic field. This solution is expressed in terms of the two parameters η and a that describe the reduced strength of an external field and the period of the field to the polymer gyration radius ratio, respectively. R _F is found to be a decaying function of η for any values of a . Provided that the gyration radius is of the order of the period of an external field or less, the ground-state (GS) approximation of the exact result for R _F is shown to give qualitatively incorrect results. In addition to the “ground-state” contribution, the exact solution for R _F contains an additional term that is overlooked by the GS approximation. This term gives rise to the fact that R _F as a function of η exhibits power law behavior (rather than exponential decay obtained from the GS result) once η exceeds the threshold value η_con .     

Hyperfine interaction in the presence of a strong nonmonochromatic laser field

We analyse in a simple and qualitative way how the properties of electromagnetic field jointly with hyperfine interaction affect the possible coherences between Zeeman sublevels of an atomic structure. We show that in the limit of a strong and/or broadband light hyperfine structure plays no role in creation of the Zeeman coherences.     

Stern Gerlach interferometry with metastable argon atoms: an immaterial mask modulating the profile of a supersonic beam

A new Stern Gerlach interferometer operating with a nozzle beam of metastable argon atoms Ar^* (3p⁵ 4s, ³ P ₂) is described. The selection of incoming (polarisation) and outgoing (analysis) Zeeman sublevels is achieved by use of laser induced transitions at two wavelengths, 811.5 nm (closed J = 2 → J = 3 transition) and 801.5 nm (open J = 2 → J = 2 transition). Linear superpositions of Zeeman sublevels, just beyond the polariser and just before the analyser, are prepared by means of two zones where Majorana transitions take place. In between, a controlled magnetic field configuration (the phase object) is produced within a triple μ-metal shielding. Standard interference patterns are obtained by scanning the field and detecting the atoms by secondary electron emission from a Faraday cup. When a static radial magnetic gradient is used, the beam profile is modulated by interference. The transverse pattern, which can be translated at will by adding a homogeneous field, is observed for the first time using a multi-channel electron multiplier followed by a phosphor screen and a CCD camera. The results satisfactorily agree with all theoretical predictions. Received 27 June 2002 / Received in final form 20 September 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: perales@lpl.univ-paris13.fr RID="b" ID="b"UMR 7538 du CNRS