Alkali-metal-vapor magnetometers, using coherent precession of polarized atomic spins for magnetic field measurement, have become one of the most sensitive magnetic field detectors. Their application areas range from practical uses such as detections of NMR signals to fundamental physics research such as searches for permanent electric dipole moments. One of the main noise sources of atomic magnetometers comes from the light shift that depends on the frequency of the pump laser. In this work, we theoretically study the light shift, taking into account the relaxation due to the optical pumping and the collision between alkali atoms and between alkali atoms and the buffer gas. Starting from a full master equation containing both the ground and excited states, we adiabatically eliminate the excited states and obtain an effective master equation in the ground-state subspace that shows an intuitive picture and dramatically accelerates the numerical simulation. Solving this effective master equation, we find that in the light-narrowing regime, where the line width is reduced while the coherent precession signal is enhanced, the frequency-dependence of the light shift is largely reduced, which agrees with experimental observations in cesium magnetometers. Since this effective master equation is general and is easily solved, it can be applied to an extensive parameter regime, and also to study other physical problems in alkali-metal-vapor magnetometers, such as heading errors.
Narrowing of magnetic-resonance lines in a dense optically pumped alkali-metal vapor
(87Rb) has been observed. This observation is shown to be a result of optical pumping with a monochromatic light source tuned such that the real part of the vapor polarizability, which is responsible for light shifts, is essentially zero. A model based on the Bloch equations is used to describe the observed narrowing effect, and results of numerical calculations based on this model are presented. The results agree qualitatively with observations, and show correctly the disappearance of the effect at low light levels. This narrowing effect is of importance to the development of precision frequency standards and magnetometers utilizing monochromatic light sources (such as semiconductor lasers).
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.
A new and unusual phenomenon which we call light narrowing is reported and discussed in this paper. We discovered this effect in dense, spin-polarized cesium vapor optically pumped with a cw blue dye laser beam tuned to the second resonance
D1 line (4593 \AA{}). We observe a significant narrowing of the radio-frequency power-broadened magnetic resonance lines (linewidths narrow by as much as a factor of 2.5) when the intensity of the circularly polarized incident dye laser beam is increased by either focusing the beam or by the removal of attenuating filters from the focused beam. The magnetic resonance linewidths in spin-polarized cesium vapor were measured over a wide range of cesium number densities (5\ifmmode\times\else\texttimes\fi{}
1012 ${\mathrm{cm}}^{\ensuremath{-}3}$ \ensuremath{\le}[Cs]\ensuremath{\le}1\ifmmode\times\else\texttimes\fi{}
1016 ${\mathrm{cm}}^{\ensuremath{-}3}$). This corresponds to cesium spinexchange rates of 4.5\ifmmode\times\else\texttimes\fi{}
103 to 9\ifmmode\times\else\texttimes\fi{}
106 ${\mathrm{sec}}^{\ensuremath{-}1}$. For low cesium number densities (5\ifmmode\times\else\texttimes\fi{}
1012 [Cs]3\ifmmode\times\else\texttimes\fi{}
1014 ${\mathrm{cm}}^{\ensuremath{-}3}$) the light-narrowing effect is large (a factor of 2.5) and independent of [Cs]. In the region of 3\ifmmode\times\else\texttimes\fi{}
1014 to 1\ifmmode\times\else\texttimes\fi{}
1015 ${\mathrm{cm}}^{\ensuremath{-}3}$ in number densities, the light-narrowing effect decreases with increasing [Cs]. At high cesium number densities ([Cs]> 1\ifmmode\times\else\texttimes\fi{}
1015 ${\mathrm{cm}}^{\ensuremath{-}3}$) this light-narrowing effect almost completely disappears. In the limit of low-radio-frequency power the magnetic resonance linewidths for focused and unfocused dye laser beam are nearly the same. Experimental observations on this new effect are presented in detail. In the latter part of this paper a self-contained theoretical treatment of the light-narrowing effect is developed. Using Bloch equations in the presence of optical pumping, spin relaxation (diffusion, electron randomization), rapid spin exchange, and radio-frequency magnetic field, expressions for magnetic resonance line shapes are derived. In general, we find good agreement between our experimental results and the theory.
Alkali-metal-vapor magnetometers, using coherent precession of polarized atomic spins for magnetic-field measurement, have become one of the most sensitive magnetic-field detectors. Their application areas range from practical uses such as NMR signal detection to fundamental physics research such as searches for permanent electric dipole moments. One of the main noise sources of atomic magnetometers comes from the light shift that depends on the frequency of the pump laser. In this work, we theoretically study the light shift, taking into account the relaxation due to the optical pumping and the collision between alkali-metal atoms and between alkali-metal atoms and the buffer gas. Starting from a full master equation containing both the ground and excited states, we adiabatically eliminate the excited states and obtain an effective master equation in the ground-state subspace that shows an intuitive picture and dramatically accelerates the numerical simulation. Solving this effective master equation, we find that in the light-narrowing regime, where the linewidth is reduced while the coherent precession signal is enhanced, the frequency dependence of the light shift is largely reduced, which agrees with experimental observations in cesium magnetometers. Since this effective master equation is general and is easily solved, it can be applied to an extensive parameter regime, and also to study other physical problems in alkali-metal-vapor magnetometers, such as heading errors.
SummaryThe ground-state level-crossing resonance, or Hanle resonance, in atomic vapors are widely used for atomic magnetometry. In this paper, we report observations of anomalous level-crossing resonances for Rb vapor in a buffer-gas cell. By optically pumping alkali atoms with a ring-shaped laser beam and detecting the spin polarization in the hole of the pumping light with an off-resonance light, we observe a polarization reversion when scanning the transverse magnetic field around zero. Both experiments and simulations are demonstrated.