Influence of the polarization of radiation on the shape of resonances of coherent population trapping on fine-structure levels

The dependence of the shape of resonances of coherent population trapping (CPT) on magnetic sublevels of thallium atoms, forming a generalized Λ-system with the magnetic sublevels of the fine-structure levels as lower ones, on the polarization of the radiation fields has been numerically studied. The cases of linear, elliptical, and circular polarizations have been considered. The shape and the number of CPT resonances for different polarizations have been compared. It has been concluded that the electromagnetically induced transparency can be changed by changing the polarization properties of the laser radiation. The possibility to decrease the number of observed resonances may be useful in high-resolution spectroscopy.     

The influence of the orientation and strength of a magnetic field on the coherent population trapping in the Λ system

The influence of the orientation and strength of a magnetic field on the dynamics and dispersion of the populations of the multilevel Λ system upon spontaneous decay into thermostat levels is considered. The radiation field consists of two components and is specified by the vector-potential in the electric dipole approximation. From the solution of the Schödinger equation for a system consisting of an atom in a magnetic field + radiation field, the probability of populating a common level for the generalized Λ system is determined in the resonance approximation. The calculation of the dynamics and dispersion of the populations demonstrates their dependence on the orientation of the magnetic field vector with respect to the light field polarization vector and on the relationship between the magnetic field strength and radiation field intensities. The coherent population trapping occurs only in the case when Rabi frequencies either exceed or are comparable to the Zeeman splitting of magnetic sublevels. By varying the orientation of the magnetic field, it is possible to change the dynamics and dispersion of the populations, thus affecting the coherent population trapping.     

Coherent population trapping spectra in presence of ac magnetic fields

Experimental and theoretical investigations are reported on the effects induced by an alternating magnetic field on coherent population trapping resonances. We show that the ac magnetic field produces sidebands of these resonances in such a way that the spectrum observed is similar to those observed via the FM spectroscopic technique. Because of the very narrow linewidth of the resonances, sidebands are resolved even for ac field frequencies as low as a fraction of a kHz. The theoretical model developed, which takes into account a very simple atomic structure, fits the experimental data quite well.     

若干参数对多能级系统粒子数陷俘的影响

运用缀饰态理论研究在外场、真空模耦合作用下多能级系统基于量子干涉效应的粒子数陷俘现象,得到了在干涉条件下系统陷俘粒子数的解析表达式,揭示出系统寝布居、驱动场拉比频率以及能级间隔等诸因素对粒子数陷俘效应的影响。研究结果表明,在特定的寝布居条件下,系统总陷俘粒子数对驱动场拉比频率和上能级间隔的依赖关系不总是简单的单调递增（递减）下,系统总陷俘粒子地驱动场拉比频率和上能级间隔的依赖关系不总是简单的单调递     

Dispersion of populations of a multilevel system in a strong field of laser emission and a magnetic field

Using the theory and the calculation method developed previously, numerical experiments on the study of dispersion of populations of a multilevel atomic system in strong fields of laser radiation in resonance with adjacent transitions and in a constant magnetic field are conducted. The effect of the magnetic field strength on the character of coherent population trapping in a multilevel system is studied. It is shown that the effect, depending on the magnetic field strength, may be observed for both and for one of the magnetic sublevels of the level that is doubly degenerate in the magnetic quantum number, for which resonance fluorescence is studied. The possibility of obtaining population inversion for magnetic sublevels in the excited state of a multilevel atom under an appropriate choice of parameters is demonstrated.     

High contrast resonances of the coherent population trapping on sublevels of the ground atomic term

We have detected and analyzed narrow, high contrast coherent population trapping resonances, which appear in transmission of the probe monochromatic light beam under action of the counterpropagating two-frequency laser radiation, on example of the nonclosed three level ??-system formed by spectral components of the Doppler broadened D₂ line of cesium atoms (in the cell with the rarefied Cs vapor). These nontrivial resonances are determined directly by the trapped atomic population on the definite lower level of the ??-system and may be used in atomic frequency standards, sensitive magnetometers and in ultrahigh resolution laser spectroscopy of atoms and molecules.     

Two-color coherent population trapping in a single Cs hyperfine transition,with application in magnetometry

We investigate the coherent population trapping effect occurring between the Zeeman sublevels of a given hyperfine state of Cs when excited by a single-mode diode laser, which is frequency modulated in the kHz–MHz range. In the presence of a dc magnetic field, simultaneous excitation of pairs of ground-state magnetic sublevels to common excited magnetic sublevels is performed. As a result, coherent population trapping resonance is detected at only a given modulation frequency, whose value gives a measure of the magnetic field. The parameters of the resonances are measured in order to determine the ultimate accuracy of the magnetic field measurement. Received: 6 December 2002 / Revised version: 24 February 2003 / Published online: 2 June 2003 RID="*" ID="*"Corresponding author. Fax: +39-0577/23-4689, E-mail: biancalana@unisi.it     

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.     

COHERENT POPULATION TRAPPING IN MULTILEVEL LASER-INDUCED CONTINUUM STRUCTURE SYSTEM INCLUDING CASCADE TWO-PHOTON PROCESSES

We have investigated the atomic coherent population trapping in a mul tilevel laser-induced continuum structure system including cascade two-photon processes, in which two sets of quasicontinua of excited levels to be modeled as the Bixon-Jortner quasicontinuum are laser-embedded into a previously structu reless atomic continuum.The condition leading to the atomic coherent population trapping and the coherent population trapping state are given explicitly. And th e effects of the Fano factors, the laser intensities and the detunings on the am ount of population trapped in the atomic bound states and the populations distri buted in the two sets of quasicontinua are also examined.     

Coherent population trapping in a gas of excited atoms

Coherent population trapping in a gas discharge was studied for transitions between excited levels of neon atoms. Resonances corresponding to the arising of coherent population trapping in the Λ and V schemes for Zeeman sublevels of the lower and upper working states were observed in the presence of a longitudinal magnetic field. The effect of nonlinear polarization plane rotation under coherent population trapping conditions was studied. The possibility of using the results obtained in this work for diagnostics of local magnetic fields and other plasma parameters in gas discharges was considered.     

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.     

Optimization of stabilization regimes in atomic clocks,based on the effect of coherent population trapping

Using the atomic density matrix formalism, we investigate the dynamic regime of formation of the error signal for resonances of coherent population trapping excited in a three-level Λ-system by a bichromatic field. The optimal parameters of harmonic modulation used in the frequency locked loop are determined with allowance for low-frequency noise.     

High buffer gas pressure perturbation of coherent population trapping in sodium vapors

We report an experimental investigation of coherent population trapping in specially selected Zeeman levels of the sodium atom, performed under high buffer gas pressure in a polydimethylsiloxane coated cell at room temperature. The results show that coherent population trapping will not be completely destroyed when the buffer gas pressure reaches 1100 Torr for He and 1000, 800, and 500 Torr, for Ne, Ar and Kr, respectively. Buffer gases with heavier mass play a larger destructive role for the coherent population trapping. The line width of the dark resonance is reduced with buffer gas pressure. The behavior of the dark resonances on increasing buffer gas is discussed and possible applications are pointed out.     

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.     

High contrast atomic magnetometer based on coherent population trapping

We present an experimental and theoretical investigation of the coherent population trapping （CPT） resonance excited on the D1 line of 87Rb atoms by bichromatic linearly polarized laser light. The experimental results show that a lin｜｜lin tran- sition scheme is a promising alternative to the conventional circular-circular transition scheme for an atomic magnetometer. Compared with the circular light transition scheme, linear light accounts for high-contrast transmission resonances, which makes this excitation scheme promising for high-sensitivity magnetometers. We also use linear light and circular light to detect changes of a standard magnetic field, separately.     

Possibility of the use of the magnetic field for creating a quantum filter on the <Emphasis Type="Italic">D</Emphasis><Subscript>1</Subscript><Superscript>87</Superscript>Rb line

The possibility of the use of the F = 2?F = 1 transition of the D ₁ absorption line of the ⁸⁷Rb atom for creating of a single-photon quantum filter based on coherent population trapping (CPT) has been analyzed. It has been shown that the external magnetic field is necessary for ensuring the creation of the quantum filter on boson isotopes of alkali atoms. The field strength should be enough for the manifestation of the splitting of the Zeeman CPT resonances that is much larger than their spectral widths. The splittings of the CPT resonances, which characterize the nonlinearity of the Zeeman effect, have been measured for the ⁸⁷Rb atom and the possibility of the use of this system for the quantum filter is concluded.     

原子相干对里德伯原子稳定性的影响

研究了含级联双光子过程的多束缚态激光场诱导原子连续态结构系统中原子的相干捕获,给出了产生相干捕获的条件及暗态的表达式,讨论了原子初态和激光强度对原子相干捕获及粒子布居值在束缚态上分布的影响,揭示了原子相干对稳定里德伯原子的重要作用。     

Control of amplification without inversion in H2 and LiH molecules: Dependence on relative magnitude of probe and coherent field Rabi frequencies in three-level Λ system

Dependence of amplification without inversion (AWI) on the relative strength of probe and coherent field Rabi frequencies has been studied in H₂ and LiH molecules for three-level Λ configuration. We have derived exact analytical expressions for coherences and populations keeping all the orders of probe field Rabi frequency (G) and coherent field Rabi frequency. (Θ) in the steady state limit. Previously, first-order approximation (i.e. keeping only the first-order term in G) was used and hence AWI was studied for the condition Θ>>G. Here, by using the exact analytical expressions of coherences and populations, we have shown that AWI is maximum when Θ is within the same order of probe field Rabi frequency G irrespective of the choice of different ro-vibrational transitions in both the molecules. However, the shape of the gain profile and the maximum value of gain on the probe field and the absorption on coherent field depend on the choice of different ro-vibrational levels as the upper lasing levels. Effect of bidirectional pumping, homogeneous and inhomogeneous broadening on AWI process has been studied. By solving the density matrix equations numerically it has been shown that both the transient and the steady state AWI can be obtained and the numerical values of coherences and populations at large time are in very good agreement with exact analytical values in the steady state limit. It has been shown that in molecules AWI can be obtained on probe field of smaller wavelength than that of the coherent field which has not been observed in atoms so far.     

Ultracold RbSr molecules can be formed by magnetoassociation

We investigate the interactions between ultracold alkali-metal atoms and closed-shell atoms using electronic structure calculations on the prototype system Rb+Sr. There are molecular bound states that can be tuned across atomic thresholds with a magnetic field and previously neglected terms in the collision Hamiltonian that can produce zero-energy Feshbach resonances with significant widths. The largest effect comes from the interaction-induced variation of the Rb hyperfine coupling. The resonances may be used to form paramagnetic polar molecules if the magnetic field can be controlled precisely enough.     

Dark resonances in 87Rb atomic vapors interacting with the field of copropagated linearly polarized waves of various frequencies

The results of theoretical and numerical analysis of resonances of coherent population trapping in ⁸⁷Rb atomic vapors, obtained using copropagated linearly polarized waves, are presented. Various schemes for exciting dark resonance are compared with a view to obtaining a new-generation small-size quantum frequency standard.