We investigate the problem of finding eigenenergies of a spin-1/2 atom subjected to a strong oscillating magnetic field and a transverse static magnetic field which is large enough to the extent that the Larmor frequency of the atom becomes nearly equal to the frequency of the oscillating field. The analysis is made by using a perturbation method based on the theory of a dressed atom, and it is found that the calculated level shift of the atom is in good agreement with the experimental one measured as a shift of the nutation frequency of optically pumped Rb atoms.|強い振動磁場とこれに垂直な静磁場とにさらされたスピン1/2の原子の固有エネルギーを見出す問題を研究する。静磁場は原子のラーマー周波数がその振動磁場の振動数とほとんど等しくなる程充分大きい。解析は着衣原子の理論に基づいた摂動の方法を用いてなされ,計算された原子のエネルギー準位の変化は光学的に励起されたRb原子の章動周波数の変化として測定された実験値と良く一致することが見出される。
We investigate the problem of finding eigenenergies of a spin-1/2 atom subjected to a strong oscillating magnetic field and a transverse static magnetic field which is large enough to the extent that the Larmor frequency of the atom becomes nearly equal to the frequency of the oscillating field. The analysis is made by using a perturbation method based on the theory of a dressed atom, and it is found that the calculated level shift of the atom is in good agreement with the experimental one measured as a shift of the nutation frequency of optically pumped Rb atoms.|強い振動磁場とこれに垂直な静磁場とにさらされたスピン1/2の原子の固有エネルギーを見出す問題を研究する。静磁場は原子のラーマー周波数がその振動磁場の振動数とほとんど等しくなる程充分大きい。解析は着衣原子の理論に基づいた摂動の方法を用いてなされ,計算された原子のエネルギー準位の変化は光学的に励起されたRb原子の章動周波数の変化として測定された実験値と良く一致することが見出される。
Effects of a nonresonant oscillating magnetic field on transient precessions of ^<85> Rb atoms are studied in a rotating frame by using the optical pumping technique. The configuration of applied magnetic fields is such as the noresonant field is parallel to a static field along the light path (z axis) and perpendicular to another weak rf field. The shifts of nutation frequencies for particular values of the effective field were measured as a function of the amplitude of the nonresonant field, and new transient precessions were obtained just after the turning on and off of the nonresonant field pulse. These experimental results are compared with the solution of the Bloch equation for a spin-1/2 atom. The observed shifts of nutation frequencies are found to be well in agreement with theoretical curves, and discussions are given of the mechanism of appearance of the new transient precessions.|非共鳴な振動磁場の^<85>Rb原子の過渡的歳差運動に対する効果が回転系において光パンピングの技術を使って研究される。かけられた磁場の配置は非共鳴磁場が光の進行方向(z軸)にある静磁場に平行で他の弱いラジオ波に垂直になる様になっている。有効磁場の特別な値に対する章動周波数の変化が非共鳴磁場の振幅の関数として測定され、新しい過渡的歳差運動が非共鳴磁場パルスを加えた直後と切った直後に得られた。これらの実験結果はスピン1/2の原子に対するブロッホ方程式の解と比較され,観測された章動周波数の変化が理論曲線と良く一致するのが見出される。また,新しい過渡的歳差運動が生じるメカニズムが議論される。
Energies of the coupled system of a spin-1/2 atom in a static magnetic field and an oscillating rf field are analyzed with the resolvent formalism and numerically calculated by quantizing the rf field, for the general case that the strong rf field is oriented in an arbitrary direction to the static magnetic field. It is shown that, if the component of the static field along the direction of the rf field has particular values, level crossings take place and multiphoton transitions by even or odd numbers of rf photons become forbidden, even when the polarization of the rf field satisfies the parity condition for the multiphoton transitions. Particular attention is given to the direction and amount of the shifts of the level crossings by the rf field, together with the shifts of the anticrossings or of the multiphoton transitions. Theoretical results are verified by the optical-pumping experiments with cesium vapor.
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.
Calculations are made of the frequency, intensity, and polarization of the light emitted by an atom in a $^{2}P\ensuremath{-}^{2}S$ transition in a weak magnetic field having an oscillating component. Near resonance, or when the frequency of the oscillating component approaches the Larmor frequency of one of the two states involved in the radiation process, all of the quantities calculated are modified. Qualitatively similar results are to be expected for other transitions. Observations in very weak fields would be of particular interest because they would give information on nuclear spins as well as atomic g-factors. Under such conditions, the Zeemann components will in general not be resolvable. There will, however, be a change in the polarization of the edges of a spectral line at resonance. It is shown that very small changes in this polarization structure are theoretically detectable.
By means of the dressed atom concept examined theoretically by Cohen-Tannoudji and Haroche, the misalignment effects of an oscillating rf-field in optical-rf double resonances are investigated. We present a fully quantum mechanical calculation of higher-order effects in the frequency shifts of new coherence resonance for the general case that a spin-1/2 atom interacts with the oscillating rf-field in optical-pumping. It is analytically shown that the new type resonances can occur even by taking account of higher-order effects in the perturbation theory for the oscillating rf-field whose direction makes a special angle from that of a static field, and that the direction of the shift of the resonance field is not along that of the static field but perpendicular to that of the oscillating field. Theoretical results are compared with optical-pumping experiments of cesium vapor.
An atomic electron, in the vacuum of photons, can emit and reabsorb photons of any frequency. Such processes give rise to well known radiative corrections (Lamb—shift, g — 2, natural width of excited states...). We review in this paper similar effects which can be induced by the interaction of an atomic electron with an incident electromagnetic wave, and we try to get some physical insight in radiative processes by comparing these two types of « spontaneous » and « induced » effects. Optical pumping methods have been very useful for studying how atoms are perturbed by optical or RF photons. The Zeeman sublevels of an atomic ground state are broadened and shifted by a resonant or quasiresonant optical irradiation. The corresponding light-shifts (or « Lamp-shifts » as A. Kastler called them) are due to virtual absorptions and reemissions of incident photons. Another example of an induced effect is the modification of the magnetic properties of an atomic level due to a high frequency non resonant RF irradiation. The Larmor precession is slowed down and becomes anisotropic. The two previous examples correspond to two situations leading to simple calculations. For a resonant or quasiresonant excitation, a single atomic transition needs to be considered. Non perturbative treatments can be given which include the effect of the atom field coupling to all orders. For example, the « dressed atom » approach allows a unified treatment of various effects such as light shifts, Autler-Townes doublets resonance fluorescence triplets... On the other hand, for a high frequency irradiation, all atomic transitions must be included. It is possible in this case to derive an effective hamiltonian describing, to lowest order in the fine structure constant α, how electronic energy levels are perturbed in the presence of N photons ω. The remaining part of the paper is devoted to the analysis of such a situation. The terms of the effective hamiltonian proportional to the number N of incident photons correspond to the induced effects. They can be fully interpreted in semiclassical terms and they describe how the slow motion of the electron in the external static fields is modified by the high frequency vibration in the incident monochromatic wave. For example, the vibrating electron averages the static potential over a finite length, the angular oscillation of the spin reduces the effective magnetic moment. The remaining terms, which are independent of N, exist even in the vacuum of photons (N = 0) and describe the contribution of the mode ω to spontaneous radiative corrections. It is possible to split them into two parts. The first one has the same structure as the N-dependent terms, with N replaced by 1/2. It describes the corrections due to the vibration of the electron in vacuum fluctuations which have a spectral power density ħω/2 per mode. The second part represents the effect of radiation reaction, i.e. the interaction of the electron with its self field. Such an interpretation is confirmed by a Heisenberg equations approach where the total force acting upon the electron is split into two physical (i.e. hermitian) parts representing respectively the effect of the vacuum « free » field and the effect of the « source » field produced by the electron itself. These considerations are finally applied to the problem of the positive sign of g - 2. The g-factor can be written as 2 ωL/ωc, where ω L is the Larmor frequency of the spin and ωc the cyclotron frequency of the charge for an electron in a weak static field B 0. In the absence of radiative corrections, g = 2, and ω L = ωc. To lowest order in 1/c (order zero), radiation reaction slows down ωc but not ωL (a charge is more coupled to its self field than a magnetic moment). The effect of vacuum fluctuations appears only at order 2 in 1/c and corresponds to relativistic and magnetic effects which slow down both ωL and ωc. Therefore, it appears that, in the non relativistic domain, the main effect is a reduction of ωc by radiation reaction and this explains why 2 ωL/ωc becomes larger than 2. A complete relativistic calculation (to all orders in 1/ c, but to lowest order in α) does not change this conclusion since the contribution of non relativistic modes (ħω < mc2) is predominant in the integral giving g — 2.