The Landé factors of hyperfine sublevels belonging to the same spectral term differ from each other. This leads to the appearance of an effective gyromagnetic ratio for an atomic ensemble, which can be defined as the ratio of the average magnetic moment to the average angular momentum. Characteristically, this quantity is not a constant, but rather depends on the populations of the hyperfine sublevels. States of an ensemble of atoms occupying their ground level in which the effective gyromagnetic ratio is zero are of much interest. Here, one of such states is considered by the example of alkali metal 87 Rb. The main idea is to suggest a method for preparing states with zero effective gyromagnetic ratio by means of two-frequency pumping of a saturated alkali-metal vapor in a cell containing a buffer gas. It is noteworthy that, according to calculations, correlation between the two fields is not required for attaining this goal.
The Landé factors of hyperfine sublevels belonging to the same spectral term differ from each other. This leads to the appearance of an effective gyromagnetic ratio for an atomic ensemble, which can be defined as the ratio of the average magnetic moment to the average angular momentum. Characteristically, this quantity is not a constant, but rather depends on the populations of the hyperfine sublevels. States of an ensemble of atoms occupying their ground level in which the effective gyromagnetic ratio is zero are of much interest. Here, one of such states is considered by the example of alkali metal 87 Rb. The main idea is to suggest a method for preparing states with zero effective gyromagnetic ratio by means of two-frequency pumping of a saturated alkali-metal vapor in a cell containing a buffer gas. It is noteworthy that, according to calculations, correlation between the two fields is not required for attaining this goal.
The optical orientation of the angular momenta of alkali atoms in the presence of a buffer gas (molecular nitrogen) has been studied experimentally. It has been shown that, even at a low concentration of molecular nitrogen in the cell, the excitation of 133 Cs atoms from the lower hyperfine level with F = 3, which belongs to the ground 2 S 1/2 state, results in a larger amplitude of the magnetic resonance than the excitation from the hyperfine level with F = 4. This result has been theoretically explained under the assumption that the spin state of the alkali atomic nucleus does not change at collision with a nitrogen molecule, which is accompanied by a nonradiative transition of the alkali atom from the excited 2 P 1/2 state to the ground 2 S 1/2 state.
A scheme for concentrating a large fraction (\ensuremath{\sim}100%) of the alkali-metal atoms in an atomic vapor in any single magnetic sublevel of the ground state is developed. This is experimentally demonstrated in the 87Rb vapor. The atomic vapor is optically pumped to a high degree of spin polarization after which two radio-frequency \ensuremath{\pi} pulses are applied to transfer the atomic population from the (2,2) or (2,-2) (F,MF) state to the (2,0) sublevel of the ground state. The resulting distribution is diagnosed using a microwave field tuned to the hyperfine transition (6834 MHz).
In the optical excitation of atoms with polarized light, producing excited atoms, only some of the Zeeman sublevels of the excited state are actually reached, so that large differences of population can be built up between Zeeman sublevels or between hyperfine structure (hfs) levels. This property can be used to detect radio-frequency resonance in optically excited atomic states. These resonances produce a characteristic change in intensity or in the degree of polarization of the light re-emitted. Zeeman intervals, Stark effects, and hfs intervals can be measured in this manner. (The Stark constant of the 63P1 level of Hg and the electric quadrupole moments of the alkali atoms have been obtained in this way.)The technique of “optical pumping” gives a way to concentrate atoms in some of the Zeeman sublevels of one of the hfs levels of the ground state.Atomic orientation has been obtained with the Na atom, in an atomic beam and in the vapor in equilibrium with the metal. The orientation effects have been studied by detection of radio-frequency resonance signals in the ground state. Orientation can be increased many times by adding a variable pressure of a foreign gas to the pure Na vapor. Because of the coupling between nuclear spin and electron spin, nuclear orientation is produced at the same time as atomic orientation.
The ground electronic state of even such simple atoms as those of alkali elements has the set of sublevels. These sublevels are hyperfine (HF) components and magnetic sublevels. The collisions with particles of nonmagnetic buffer gas or even with walls (when walls have proper coating) do not mix practically the populations of ground state HF sublevels, if the orbital moment of electrons in the ground state is equal to zero. Due to this reason these sublevels may be extremely long lived. Because of this, for instance, the so-called effects of optical orientation and optical pumping are apparent in atoms of alkali metals. The radiation can pump practically all the atoms (with which there is effective interaction) to a single HF component. In a situation in which optical pumping is a minor effect, the monochromatic absorption line consists of separate lines corresponding to intra-atomic transitions. The optical pumping is not significant, for example, if the radiation intensity is so low that now pumping between HF sublevels occurs in the time it takes the atom to traverse the light beam. Under the conditions of optical pumping and when other nonlinear effects are present, the absorption line profile can undergo considerable alteration. Many theoretical and experimental investigations have been done in the laser spectroscopy of resonant transitions of atoms (atoms of alkali metals) under the conditions of optical pumping within ground state HF structure. A characteristic feature of all such investigations is the velocity-selective excitation of absorbing atoms. Also, as a rule, the value of HF splitting is not very big in comparison to Doppler broadening in these experiments. Under such conditions, the absorption spectra consists of Doppler- broadened lines with nonlinear resonances, which emerge when two fields of different frequencies or different propagation directions are employed. When only one monochromatic traveling wave is employed, optical pumping leads to formation of a single smooth absorption line occupying a position between the resonant transitions frequencies associated with HF components. As HF splitting grows, the line profile remains smooth, its width is approximately equal to the size of the HF splitting. The strength of the optical pumping from one ground state HF component to another is greater for greater HF splitting in comparison to the Doppler width. In this regard, Cs and Rb are the most typical of the alkali atoms (the HF splitting exceeds the Doppler width by a factor close to 20). This is the qualitative picture of the absorption line profile (particularly for a monochromatic radiation) under the conditions of optical pumping between the HF sublevels of the electronic ground state, this qualitative picture had formed by now.
In spin-related fundamental researches, there have been considerable interests in the transfer of microscopic orders between magnetic sublevels of different kinds of atoms. As for gaseous atomic systems, collisional transfer of spin polarization from optically pumped atoms A to atoms B is attained through spin exchange collisions. So far many experiments have been reported on the transfer of longitudinal spin polarization created along a static magnetic field. Transfer of coherence, on the other hand,is possible only when the energy matching condition j!A !Bj < is satisfied, where !A and !B are the Larmor frequencies of atoms A and B, and the line width. This is the reason why transfer of spin polarization precessing around the static magnetic field has not been observed except for a few experiments; The coherence transfer has been observed in the experiments where the atoms are subjected to properly chosen rf magnetic fields. Recently, it has been reported that coherence transfer between different kinds of atoms is possible by using the light field which transversely pumps only one kind of atoms under properly chosen experimetal conditions. It has also been pointed out that, as for the system of Rb and K atoms, which happen to have the same gyro-magnetic ratio, the peculier distortion of the magnetic resonance signal line shapes observed in the collisionally pumped atoms can be explained by the spin exchange coupling between the resonant Rb and K atoms. It is suggested that the precessing spin polarization in Rb can be transferred to K atoms or vice versa, since their Zeeman splittings become equal in the hyperfine multiplets jF 1⁄4 1i and jF 1⁄4 2i of the ground state 2S1=2 with the same gyromagnetic ratio 1⁄4 2 700 kHz/G. The experimental apparatus of the present experiment is shematically shown in Fig. 1. In addition to a droplet of natural rubidium and potassium, the sample cell contains 50mbar Ar as a buffer gas. It is subjected to a static magnetic field of H0 1⁄4 0:786G along the z axis and irradiated transversely to the field by a light beam from a GaAlAs laser A (output power = 10mW, beam diameter = 1mm). It is left-handed circularly polarized and tuned to the Rb absorption lines (S1=2, F 1⁄4 1 ! P1=2, F 1⁄4 1 and 2) which are not resolved owing to the Doppler broadening. The intensity of the laser A is modulated by an AOM (acousto-optic-modulator) at the Larmor frequency !A 1⁄4 2 550 (1⁄4 700 0:786) kHz of Rb in a rectangular shape pulse. As mentioned above the precessing spin polarization in Rb can be transferred to K. The precessing spin polarization of Rb and that of K are detected from the Faraday rotations of the beams of probe lasers B ( 1⁄4 794 nm, output power = 3mW, beam diameter = 2mm) and C ( 1⁄4 769 nm, output power = 3mW, beam diameter = 2mm), respectively. The frequency of laser B is chosen to be a few GHz higher than the Rb absorption lines (S1=2, F 1⁄4 1 ! P1=2, F 1⁄4 1 and 2) to prevent the detection beam from destroying the polarization. Similarly, the frequency of laser C is chosen to be a few GHz higher than the K absorption lines (S1=2, F 1⁄4 1 and 2 ! P1=2, F 1⁄4 1 and 2) which are not resolved owing to the Doppler broadening. They are linearly polarized and counter-propagated against the pumping beam,making angles of about 1 to the pumping beam. In each case the transmitted light beam of probe laser passes through the analyzer which makes an angle 45 to the polarization of the incident beam,and then it is detected by a pin-photo diode. The signals are electronically averaged over a few hundred cycles. Figure 2(a) shows the typical examples of signals on the magnetizations M x and M B x of Rb and K, respectively, Fig. 1. Schematic diagram of the experimetal apparatus. AOM, acoustooptic modulator; PD, pin-photo diode; P, polarizer; A, analyzer.
The theory of how excited-state hyperfine structure can be determined using a magnetic field to decouple the nuclear and electronic angular momentum is presented. The initial excited state is assumed to have an anisotropic Zeeman sublevel population distribution, which can be conveniently created by a laser-induced multiphoton excitation of an unpolarized atom. The Zeeman sublevel populations are subsequently mixed by the hyperfine interaction. The degree of mixing is controlled by a magnetic field applied along the quantization axis. The relative Zeeman sublevel populations can be monitored by detecting the polarization of fluorescence emitted when the excited state radiatively decays. It is convenient to take the ratio of two time-integrated fluorescent signals measured for orthogonal linear polarizations, since this is independent of the excited-state number density. The plot of this ratio versus magnetic field is very well approximated by a Lorentzian curve whose half-width is proportional to the magnetic dipole hyperfine coupling constant. This method was used to determine the magnitude of the magnetic dipole constant of the cesium 8D3/2 state to be 3.92\ifmmode\pm\else\textpm\fi{}0.10 MHz, which is in excellent agreement with previous results.