Polarization spectroscopy of Rb and Cs

Theoretical calculation of ⁸⁵Rb and ¹³³Cs D₁ signals in polarization spectroscopy is presented by using the method of velocity-selective optical pumping in a four-level system. Since good agreement between theory and experiment has been found in Na D₁ polarized signals, the theoretical calculation can be also applied to Rb and Cs D₁ lines. Rb and Cs atoms have higher total angular momentum F in the hyperfine structures than Na atom and then the calculation is more complicated. The relative signal intensities in polarization spectroscopy are compared with those in saturation spectroscopy.     

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.     

Nuclear spins of76Rb and119Cs byβ radiation detected optical pumping

An optical pumping apparatus has been attached to the reconstructed ISOLDE on-line mass separator at CERN in order to obtain nuclear data of isotopes far fromβ stability. As first results the spins of⁷⁶Rb (T _1/2=36.8 s) and¹¹⁹Cs (T _1/2=37.7 s) have been determined byβ radiation detected optical pumping (β-RADOP) to beI=1 andI=9/2 respectively.     

Faraday effect on the Rb <Emphasis Type="Italic">D</Emphasis> <Subscript>1</Subscript> line in a cell with a thickness of half the wavelength of light

The rotation of the radiation polarization plane in a longitudinal magnetic field (Faraday effect) on the D₁ line in atomic Rb vapor has been studied with the use of a nanocell with the thickness L varying in the range of 100–900 nm. It has been shown that an important parameter is the ratio L/λ, where λ = 795 nm is the wavelength of laser radiation resonant with the D₁ line. The best parameters of the signal of rotation of the radiation polarization plane have been obtained at the thickness L = λ/2 = 397.5 nm. The fabricated nanocell had a large region with such a thickness. The spectral width of the signal reached at the thickness L = 397.5 nm is approximately 30 MHz, which is much smaller than the spectral width (≈ 500 MHz) reached with ordinary cells with a thickness in the range of 1–100 mm. The parameters of the Faraday rotation signal have been studied as functions of the temperature of the nanocell, the laser power, and the magnetic field strength. The signal has been reliably detected at the laser power P_L ≥ 1 μW, magnetic field strength B ≥ 0.5 G, and the temperature of the nanocell T ≥ 100°C. It has been shown that the maximum rotation angle of the polarization plane in the longitudinal magnetic field is reached on the F_g = 3 → F_e = 2 transition of the ⁸⁵Rb atom. The spectral profile of the Faraday rotation signal has a specific shape with a sharp peak, which promotes its applications. In particular, Rb atomic transitions in high magnetic fields about 1000 G are split into a large number of components, which are completely spectrally resolved and allow the study of the behavior of an individual transition.     

Atomic resonance behavior in laser-induced Rb atom desorption—the effect of ambient gas atoms and molecules

We report an observation that in a typical optical pumping cell containing Rb metal and 150 Torr N₂ gas, a cw laser beam of a few tens of mW and beam size 5.5 mm² can desorb Rb films on cell surfaces when the laser is tuned to the Rb D₁ line. The frequency dependence of the Rb desorption rate displays atomic resonance behavior. The desorption is suggested to be mediated by the ambient gas atoms (Rb) and molecules (N₂). The phenomenon was used to provide evidence for the existence of thin Rb films on seemingly clear cell surfaces.     

Optical pumping of short lived Β-radioactive isotopes and the magnetic moment of37K

²¹Na (T _1/2=23 sec) and³⁷K(T _1/2=1.25 sec) have been produced in gas targets by (d, n) reactions and polarized by means of optical pumping or spin exchange scattering with optically pumped⁸⁷Rb. An asymmetry up to 3% in theΒ-decay of the polarized nuclei was found, which served to detect rf transitions between hfs levels of the atomic ground states of²¹Na and³⁷K.δF=0 andδF=1 resonances have been recorded, yielding spin, hfs separation and magnetic moment, especiallyI(³⁷K)=3/2,δW(³⁷K)=240.266 (3) Mc/sec andΜ _I(³⁷K)=0.02033(6) nm (diamagnetically corrected). For²¹Na earlier rf-spectroscopic data have been confirmed.     

Bose-Einstein condensation of 87Rb in a levitated crossed dipole trap

We report an apparatus and method capable of producing Bose-Einstein condensates (BECs) of ～1 × 10^{6 87}Rb atoms, and ultimately designed for sympathetic cooling of ¹³³Cs and the creation of ultracold RbCs molecules. The method combines several elements: (i) the large recapture of a magnetic quadrupole trap from a magneto-optical trap; (ii) efficient forced RF evaporation in such a magnetic trap; (iii) the gain in phase-space density obtained when loading the magnetically trapped atoms into a far red-detuned optical dipole trap, and (iv) efficient evaporation to BEC within the dipole trap. We demonstrate that the system is capable of sympathetically cooling the |F = 1, m _F = ?1〉 and |1,0? sublevels with |1, +1〉 atoms. Finally we discuss the applicability of the method to sympathetic cooling of ¹³³Cs with ⁸⁷Rb.     

Influence of transverse magnetic fields and depletion of working levels on the nonlinear resonance Faraday effect

The nonlinear resonance Faraday effect is studied under the condition of coherent population trapping in ⁸⁷Rb vapor at the D₁-line F=2→F′=1 transition. The influence of transverse magnetic fields on the nonlinear optical Faraday rotation is studied. For the transverse fields perpendicular to the electromagnetic-wave polarization, a simple theoretical model is proposed, which is in good agreement with experimental data. The optimal intensity providing the maximum sensitivity is found based on the results obtained. The influence of working-level depletion on the parameters of Faraday rotation in open systems is studied experimentally and theoretically. The system was closed in the experiment by using an additional laser to increase the sensitivity and extend the dynamic range of measured fields. The importance of compensating for the depletion in the presence of spurious magnetic fields is shown; in particular, the sensitivity was enhanced by a factor of 50 in experiments with a buffer gas.     

A high phase-space density mixture of 87Rb and 133Cs: towards ultracold heteronuclear molecules

We report the production of a high phase-space density mixture of ⁸⁷Rb and ¹³³Cs atoms in a levitated crossed optical dipole trap as the first step towards the creation of ultracold RbCs molecules via magneto-association. We present a simple and robust experimental setup designed for the sympathetic cooling of ¹³³Cs via interspecies elastic collisions with ⁸⁷Rb. Working with the |F = 1,m _F = +1〉 and the |3, +3〉 states of ⁸⁷Rb and ¹³³Cs respectively, we measure a high interspecies three-body inelastic collision rate ～10^?25?10^?26 cm⁶ ? s^?1 which hinders the sympathetic cooling. Nevertheless by careful tailoring of the evaporation we can produce phase-space densities near quantum degeneracy for both species simultaneously. In addition we report the observation of an interspecies Feshbach resonance at 181.7(5) G and demonstrate the creation of Cs₂ molecules via magneto-association on the 4(g)4 resonance at 19.8 G. These results represent important steps towards the creation of ultracold RbCs molecules in our apparatus.     

Structure of magnetic resonance in <Superscript>87</Superscript>Rb atoms

Magnetic resonance at the F_g = 1 \( \rightleftarrows \)F_e = 1 transition of the D₁ line in ⁸⁷Rb has been studied with pumping and detection by linearly polarized radiation and detection at the double frequency of the radiofrequency field. The intervals of allowed values of the static and alternating magnetic fields in which magnetic resonance has a single maximum have been found. The structure appearing beyond these intervals has been explained. It has been shown that the quadratic Zeeman shift is responsible for the three-peak structure of resonance; the radiofrequency shift results in the appearance of additional extrema in resonance, which can be used to determine the relaxation constant Γ₂. The possibility of application in magnetometry has been discussed.     

Influence of atomic alignment on crossover signals in saturation spectroscopy

The crossover resonance between the atomic transitions² S _1/2(F=2)→² P _1/2(F′=1, 2), observed in the saturation spectrum of sodium, was found to be sensitive to the atomic orientation of the ground state, produced by velocity selective optical pumping. For zero magnetic field and the same linear polarization of saturating and probing beam, a negative signal was recorded for the crossover, corresponding to an increase in absorption of the probing beam. Application of a sufficiently strong magnetic field perpendicular to the polarization vector causes the destruction of the alignment, leading to a change in sign for the crossover intensity, i.e., to an enhanced transmission of the probing beam. It was shown experimentally that an increase in the atomic transit time has the same effect. Using optical pumping theory all qualitative features could be accounted for.     

Effect of the surface integral in the torque equation of the electromagnetic angular momentum on the Faraday rotation

A circularly polarized plane wave of infinite transverse extent (δ = ∞) has no spin angular momentum, while a realistic light does carry it. This paradox originates from the presence (δ = ∞) and absence (δ ≈ 0) of the surface integral in the total angular momentum J. The same holds for the torque equation of dJ/dt, so that δ is also connected with the relative Faraday rotation angle Θ_F/θ_F when a radius (a) of a cylindrical medium with optical activity is only a little larger than that (b) of light beam, where Θ_F is the Faraday rotation angle and θ_F is the intrinsic Faraday rotation angle of a medium. It is shown here that it is possible to estimate δ for a realistic light from the drastic variation in Θ_F/θ_F near b/a = 1.     

Effect of optical pumping on the thulium absorption spectrum saturation and width

The numerical solution to optical Bloch equations for the transition F _g = 4 ? F _e = 5 with a wavelength of 410.6 nmin the thulium atom is presented. The absorption spectrum saturation and narrowing effects due to optical pumping are considered in detail.     

Cyclic interaction of Na atoms with circularly polarized laser radiation

Cyclic interaction of Na atoms with laser radiation is under consideration. In the experiment cyclic interaction was conducted through preliminary optical pumping of the atom into the ground state F = 2, M_F = 2 by a single-mode cw dye laser. The results of optical orientation of Na atom and cyclic interaction under different conditions of atomic excitation are presented. Possible applications of cyclic interaction of atom with radiation for detection and cooling of atoms is under discussion.     

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.     

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.     

Selective laser pumping of magnetic sublevels in the hyperfine structure of the cesium atom

The evolution of the populations of the magnetic sublevels of the cesium atom (¹³³Cs isotope) in resonant laser fields with linear polarization is analyzed using the equations for the density matrix. Analytic expressions are derived for stationary populations resulting from laser-induced optical transitions on the hyperfine structure components F _g = 3 ? F _e = 2, 3 and F _f = 4 ? F _e = 3, 4 of lines D ₁ (6² S _1/2 → 6² P _1/2) and D ₂ (6² S _1/2 → 6² P _3/2) depending on the initial values of the populations. The numerical solution of the evolution equations gives the characteristic times of stabilization of the steady regime as functions of laser field intensities and detuning from optical resonance. We determine the sequences of optical transitions increasing (by more than an order of magnitude) the population of the lower sublevel 6² S _1/2 F _g = 3 M = 0 of the “clock” microwave transition F _g = 3 M = 0 ? F _f = 4 M = 0 in the cesium frequency standard, which increases the signal intensity in the recording system by the same proportion.     

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.     

Tm and Tm-Tb-doped germanate glasses for S-band amplifiers

The mechanism involved in the Tm³⁺(³F₄)→Tb³⁺(⁷F_0,1,2) energy transfer as a function of the Tb concentration was investigated in Tm:Tb-doped germanate (GLKZ) glass. The experimental transfer rate was determined from the best fit of the ³F₄ luminescence decay due to the Tm→Tb energy transfer using the Burshtein model. The result showed that the 1700 nm emission from ³F₄ can be completely quenched by 0.8 mol% of Tb³⁺. As a consequence, the ⁷F₃ state of Tb³⁺ interacts with the ³H₄ upper excited state of Tm³⁺ slighting decreasing its population. The effective amplification coefficient β(cm⁻¹) that depends on the population density difference Δn=n(³H₄)-n(³F₄) involved in the optical transition of Tm³⁺ (S-band) was calculated by solving the rate equations of the system for continuous pumping with laser at 792 nm, using the Runge-Kutta numerical method including terms of fourth order. The population density inversion Δn as a function of Tb³⁺ concentration was calculated by computational simulation for three pumping intensities, 0.2, 2.2 and 4.4 kWcm⁻². These calculations were performed using the experimental Tm→Tb transfer rates and the optical constants of the Tm (0.1 mol%) system. It was demonstrated that 0.2 mol% of Tb³⁺ propitiates best population density inversion of Tm³⁺ maximizing the amplification coefficient of Tm-doped (0.1 mol%) GLKZ glass when operating as laser intensity amplification at 1.47 μm.     

Coherent spectroscopy of the 87RbFg=1→ Fe=0 closed transition

This paper has observed linewidth narrowing of dark states in rubidium cell by using the Hanle configuration. The reduction of the coherent resonance width under the transition of ^87Rb Fg = 1 → Fe = 0 is observed and the qualitative explanation about its mechanism is presented. Multiple subnatural width dips are obtained with a linearly polarized laser beam for the transitions of ^87Rb Fg = 1→Fe = 0, 1, 2. The feature of negative and positive slope, namely dispersionlike feature, is observed in the transmitted light.