Light-Induced shifts in the frequency of a multiphoton radiooptical SHF resonance in alkali atoms

A computation is carried out for light-induced shifts in the frequency of a multiphoton radiooptical SHF resonance in alkali atoms on the basis of the quantum formalism of spherical tensors. The components of a light-induced shift in frequency at magneto-independent 0–0– and 1,–1-transitions in⁸⁷Rb atoms under the conditions of isotopic filtration of the resonance light of pumping are calculated. The difference between the temperatures of a filter cell is discovered at which the point of zero shift in the frequency of radiooptical resonance is attained. The components of the light-induced shift of frequency in optically oriented⁸⁷Rb and¹³³Cs atoms are compared in the absence of collisional reorientation in excited state. The prevailing role of the tensor component of light-induced shift in pumping by the D₁-line of a head doublet and the effect of the orientational dependence of the frequency of a multiphoton resonance on change in the sign of the pumping source radiation polarization are noted. St. Petersburg State Polytechnical University, 29 Politekhnicheskaya Str., St. Petersburg, 195251, Russia. Translated from Zburnal Prikladnoi Spektroskopii, Vol. 65, No. 6, pp. 832–838, November–December, 1998.     

Experimental investigation of evaporative cooling mixture of bosonic 87Rb and fermionic 40K atoms with microwave and radio frequency radiation

We investigate sympathetic cooling fermions ⁴⁰K by evaporatively cooling bosonic ⁸⁷Rb atoms in a magnetic trap with microwave and radio frequency induced evaporations in detail. The mixture of bosonic and fermionic atoms is prepared in their polarized spin states |F=9/2, m_F=9/2> for ⁴⁰K and |F=2, m_F=2> for ⁸⁷Rb, which is trapped in Quadrupole--Ioffe--Configuration trap. Comparing microwave with radio frequency evaporatively cooling bosonic ⁸⁷Rb atoms with sympathetically cooling Fermi gas ⁴⁰K, we find that the presence of rubidium atoms in the |2,1> Zeeman states, which are generated in the evaporative process, gives rise to a significant loss of ⁴⁰K due to inelastic collisions. Thus, the rubidium atoms populated in the |2, 1> Zeeman states should be removed in order to effectively perform sympathetically cooling ⁴⁰K with the evaporatively cooled ⁸⁷Rb atoms.     

85Rb灯对87Rb原子的光抽运

本文对用⁸⁵Rb灯不经滤光泡直接对⁸⁷Rb吸收泡的光抽运作了观测,得到了比传统的用⁸⁷Rb灯经⁸⁵Rb滤光泡对⁸⁷Rb吸收泡进行光抽运更强的基态0—0跃迁共振讯号。并在一定温度下观察到负的共振讯号。到目前为止,还不能对这种负的共振讯号作出解释。同时还测量了共振线宽和光频移。对在⁸⁷Rb原子频标中应用的可能性作了评述。 关键词：     

Collisions of alkali-metal atoms Cs and Rb in the ground state. Spin exchange cross sections

Collisions of alkali-metal atoms ¹³³Cs and ⁸⁵Rb in the ground state are considered in the energy interval of 10^–4–10^–2 au. Complex cross sections of the spin exchange, which allow one to calculate the processes of polarization transfer and the relaxation times, as well as the magnetic resonance frequency shifts caused by spin exchange Cs–Rb collisions, are obtained.     

Phase transition and relaxation processes by 87Rb and 39K nuclear magnetic measurements of RbKSO4 single crystals

⁸⁷Rb and ³⁹K nuclear magnetic resonance (NMR) spectra of RbKSO₄ single crystals were measured at room temperature. ⁸⁷Rb central line has the angular dependences of second-order quadrupolar shifts. From these results, the quadrupole coupling constant and the asymmetry parameter were determined at room temperature. In addition, the spin–lattice relaxation rate, 1/T₁, and the spin–spin relaxation rate, 1/T₂, were measured as a function of temperature. The values of 1/T₁ for the ⁸⁷Rb and ³⁹K nuclei were found to increase with increasing temperature, and 1/T₁ was determined to be proportional to Tⁿ. Therefore, for the ⁸⁷Rb and ³⁹K nuclei, Raman processes with n=2 are more significantly in nuclear quadrupole relaxation than direct processes.     

Optimal transport of cold atoms by modulating the velocity of traps

This work experimentally demonstrates a new method of optimizing the transport of cold atoms via modulating the velocity profile imposed on a magnetic quadrupole trap.The trap velocity and corresponding modulation are controlled by varying the currents of two pairs of anti-Helmholtz coils.Cold 87Rb atoms are transported in a non-adiabatic regime over 22 mm in 200 ms.For the transported atoms their final-vibration amplitude dependences of modulation period number,depth,and initial phase are investigated.With modulation period n = 5,modulation depth K = 0.55,and initial phase φ = 0,cold atom clouds with more atom numbers,smaller final-vibration amplitude,and lower temperature are efficiently transported.Theoretical analysis and numerical simulation are also provided,which are in good agreement with experimental results.     

Observation of polarized atoms of rubidium isotopes in experiments on optical orientation in a He–Rb mixture under conditions of a pulsed gas discharge

We are the first to have observed magnetic resonance signals from atoms of ⁸⁵Rb and ⁸⁷Rb isotopes when using the indirect optical orientation in conditions of helium–rubidium gas discharge plasma. An anomalously small ratio of magnetic resonance signals from isotopes of rubidium and metastable helium upon optical orientation of ⁴Не atoms has been detected. The experimental results have been considered theoretically, and an explanation of the observed anomaly in the signals is presented.Z     

Repetition rate spectroscopy of the dark line resonance in rubidium

Spectroscopy of a Λ structure in ⁸⁷Rb is performed with a mode locked laser. A dark line, resulting from population trapping between the hyperfine levels, is observed when the repetition rate is 1/57th of the hyperfine splitting. Simulation of coherent interaction of Rb atoms with laser pulses shows darklines corresponding to different submultiple of the hyperfine splitting. It is demonstrated experimentally and theoretically that the resonance width is insensitive to fluctuations in optical frequency.     

Collisions of alkali K and Rb atoms in ground state: Modification of interaction potentials

The interaction of alkali K and Rb atoms that reside in the ground state is considered in the range of collision energies E = 10⁻⁴ to 10⁻² au. The singlet (X ¹Σ⁺) and triplet (a ³Σ⁺) interaction potentials available in the literature are analyzed and modified. For the KRb dimer in the range of interatomic distances 15–21a ₀, we chose analytical representations of the singlet and triplet potentials that more accurately describe the interaction of alkali Rb and K atoms in the ground state. Complex cross sections of the spin exchange are calculated for the first time that permit one to calculate the processes of polarization transfer and relaxation times, as well as shifts in the magnetic resonance frequencies caused by K-Rb spin exchange collisions.     

Frequency shift of the magnetic resonance in 5<Emphasis Type="Italic">s</Emphasis><Superscript>2</Superscript><Emphasis Type="Italic">S</Emphasis><Subscript>1/2</Subscript> rubidium atoms due to spin-exchange collisions with optically oriented cesium atoms

For the case of cesium atoms optically oriented in a mixture of cesium and rubidium vapors, the temperature dependence of the frequency shift of a magnetic resonance excited in a set of Zeeman sublevels for two hyperfine states of ⁸⁷Rb 5s ² S _1/2 atoms. It is shown that, in a weak magnetic field of about 2 × 10^?6 T, this shift is determined by the spin-exchange interaction of rubidium atoms with optically oriented ¹³³Cs atoms.     

Feshbach resonances in an ultracold mixture of 87Rb and 40K

We report the experimental preparations of the absolute ground states of ⁸⁷Rb and ⁴⁰K atoms (| F=1, m_F=1,〉+ |F=9/2, m_F=-9/2,〉) by means of the radio-frequency and microwave adiabatic rapid passages, and the observation of magnetic Feshbach resonances in an ultracold mixture of bosonic ⁸⁷Rb and fermionic ⁴⁰K atoms between 0 T and 6.0 × 10^-2 T, including 7 homonuclear and 4 heteronuclear Feshbach resonances. The resonances are identified by the abrupt trap loss of atoms induced by the strong inelastic three-body collisions. These Feshbach resonances should enable the experimental control of interspecies interactions.     

Magnetically trapped atoms for compact atomic clocks

We investigate the hyperfine transition of magnetically trapped non-condensed atoms. The two principal frequency shifts, the second order Zeeman effect and the mean field interaction are considered. Analytic models of the mean frequency and its trap induced spread are developed. Comparisons with existing experiments evaluate the role of the atoms’ oscillatory motion. The analytic model proves to be equivalent to existing Monte Carlo simulations. The formulae provide a simple tool for optimising the design of a new experiment. Applied to the two-photon transition |F=1,m _F =−1〉→|F=2,m _F =1〉 in ⁸⁷Rb and the conditions of a typical atom chip experiment, a line spread as small as 11 mHz is predicted giving a quality factor of 10¹². The system is promising for application in precision instruments such as compact atomic clocks.     

Ab-initio relativistic density functional calculations for spectral line shifts of Rb atoms in liquid helium

Accurate laser spectroscopic studies of the principal resonance transitions in Rb and Cs atoms embedded in liquid helium have shown appreciable line shifts and change in line profiles. A pilot attempt has been made here to compute ab-initio the spectral line shift of the resonance excitation lines in Rb under such a confinement. Relativistic density functional theory (RDFT) within local density approximation (LDA) has been adopted. A model cluster of fourteen helium atoms surrounding the central Rb is assumed. With an optimized radius of the cluster of 5.15 Å the RLDA estimate of the blue shift of the lowest ²S → ²P excitation line of Rb comes out to be 15.4 nm which compares very well with the experimental value of 16.4 nm.     

Simple and efficient magnetic transport of cold atoms using moving coils for the production of Bose–Einstein condensation

We have developed a simple magnetic transport method for the efficient loading of cold atoms into a magnetic trap. Laser-cooled ⁸⁷Rb atoms in a magneto-optical trap (MOT) are transferred to a quadrupole magnetic trap and they are then transported as far as 50 cm by moving magnetic trap coils with a low excess heating of atoms. A light induced atom desorption technique helps to reduce the collision loss during the magnetic transport. Using this method, we can load cold ⁸⁷Rb atoms into a magnetic trap in an ultra high vacuum chamber with high efficiency, and we can produce ⁸⁷Rb condensate atoms. PACS 39.25.+k; 32.80.Pj; 03.75.Pp     

Use of sub-Doppler optical resonances for measurement of weak magnetic fields by means of extremely thin rubidium vapor cell

We study experimentally and theoretically D ₁ lines of ⁸⁵Rb and ⁸⁷Rb atoms and show that using atomic-velocity-selective optical resonances which are formed in the transmission spectrum of an atomic rubidium-filled submicron cell at single pass of linearly polarized laser radiation, it is possible to measure weak magnetic fields beginning with 5 G. Having in mind the results obtained earlier with use of also submicron cell with ⁸⁷Rb (D ₁ line) and circularly polarized laser radiation, the entire range of measurable magnetic fields (both homogeneous and inhomogeneous) becomes 5–5000 G.     

光抽运实验中的微波-射频多量子跃迁

在⁸⁷Rb气泡光抽运实验中,我们同时用微波场和射频场作用在⁸⁷Rb原子上,观察到了⁸⁷Rb原子基态微波-射频多量子跃迁的光检测共振谱线。 关键词：     

Optical magnetometer with submicron spatial resolution based on Rb vapors

It is shown experimentally that use of fluorescence and transmission spectra obtained from nanocells with the thickness of column of rubidium atomic vapor L = λ/2 and L = λ, respectively (λ = 794 nm is the wavelength of laser radiation close to resonance with D ₁-line transition of Rb atoms), by means of a narrowband diode laser allows spectral separation and study of variations of probabilities of atomic transitions between ground and excited states of hfs of D ₁ lines of ⁸⁵Rb and ⁸⁷Rb atoms in the range of magnetic fields from 10 to 5000 G. Small thickness of atomic vapor column (∼390 nm and ∼794 nm) allows applying permanent magnets simplifying essentially creation of strong magnetic fields. Advantages of this technique are discussed as compared with the technique of saturated absorption. The obtained results show that a nanocell with submicrom thickness of vapor column may serve as a basis for designing a magnetometer with submicron local spatial resolution which is important in case of measuring strongly inhomogeneous magnetic fields. Experimental data are in good agreement with the theoretical results.     

Magnetic resonance investigations of phase transitions and modulation wave motions in incommensurate solids

We measured⁸⁷Rb nuclear magnetic resonance (NMR) and³⁵Cl nuclear quadrupole resonance (NQR) Hahn spin-echo magnetization decays in the incommensurate (I) phase of Rb₂ZnCl₄ and, in each case, obtained a Hahn echo decay that was shorter than the Carr-Purcell-Meiboom-Gill decay and one which decayed with a time constant proportional to the cube of the echo time. From these measurements we obtained from both the⁸⁷Rb NMR and³⁵Cl NQR measurements values for the diffusion coefficients that are comparable in magnitude, a fact that strongly supports the existence of slow modulation wave diffusionlike motions in the I phase, since such motions should affect both Rb and Cl ions similarly. In addition, we used⁸⁷Rb two-dimensional exchange-difference NMR to study atomic motions in the incommensurate (I) and paraelectric (P) phases to elucidate the nature of the I-P transition. We measured as a function of the mixing time the frequency shifts of the cross peaks from the main diagonal and observed a gradual increase towards an asymptotic value in the I phase but a sudden jump to the final value in the P phase. We interpreted the motions observed in the P phase as normal modes arising from simultaneous reorientations of ZnCl₄ tetrahedra and corresponding Rb ions displacements between two sites. These normal modes freeze out in the I phase and change to the diffusionlike motion of the modulation wave. We also performed³⁵Cl NQR lineshape andT ₁ measurements in K₂ZnCl₄ and obtained conclusive evidence for the presence of a narrow 1q (singly modulated) I phase between 146 and 149 K.     

Complex cross sections of spin exchange in collisions of sodium and potassium atoms in the ground state

Complex cross sections of the spin exchange are calculated for the first time for interacting Na and K atoms based on the data on the singlet (X ¹Σ⁺) and triplet (a ³Σ⁺) potentials that describe the interaction of these alkali-metal atoms in the ground state. The obtained cross sections allow one to theoretically consider the polarization transfer processes and calculate the relaxation times and the magnetic resonance frequency shifts caused by Na-K spin-exchange collisions.     

Characterization of an optical frequency comb using modified direct frequency comb spectroscopy

We introduce a method for determination of the absolute frequencies of comb lines within an optical frequency comb spectrum. The method utilizes the experimental and theoretical approach of the velocity-selective optical pumping of the atomic ground state hyperfine levels induced by resonant pulse-train excitation. The information on the laser pulse repetition frequency and carrier–envelope offset are physically mapped onto the ⁸⁷Rb ground state hyperfine level population velocity distributions. Theoretical spectra are calculated using an iterative analytic solution of the optical Bloch equations describing the resonant pulse-train excitation of four-level ⁸⁷Rb atoms. They are employed to fit the measured spectra and obtain the parameters of the frequency comb, thus providing a practical algorithm which can be used in real-time measurements.