Excerpts from thesis on “Atomic Magnetometers” by R. Jimenez Martinez, University of Colorado at Boulder (in collaboration with NIST)
[e-page 132] “Atomic magnetometers rely on the response of the spin of an ensemble of atoms to magnetic fields. As described in chapter 2, the dynamics of a spin coupled to a magnetic field Bo through the Zeeman interaction consists of the precession of the spin about the field. In the absence of a driving field, spin relaxation mechanisms restrict the synchronous precession of the spins about the magnetic field, which results in dephasing. In the presence of spin decoherence and optical pumping the response of the atomic spin ensemble to magnetic fields can be modeled phenomenologically through Bloch equations as described in chapter 2.”
“Thus, the end result of Larmor precession, optical pumping, and decoherence is that the spin of the ensemble is tilted with respect to the pumping light axis, and with the tilt being proportional to the magnetic field magnitude. Magnetometers working under these conditions are called zero-field atomic magnetometers. The dynamic range of these magnetometers is determined by the width of the zero-field resonance.”
“As discussed in chapter 2, at large alkali densities spin-exchange collisions can be a major source of spin relaxation.”
“However, as first observed by Happer et al. [19, 65], if the spin-exchange collision rate Rse is much faster than the Larmor precession, spin-exchange broadening can be suppressed.”
“This regime is often known as the spin-exchange relaxation-free (SERF) regime .”
Figure 2.2b below depicts the decay of polarization (shown also on e-page 189).
[e-page 32] Figure 2.2: (a) A single atom interacting with a magnetic field. All degrees of freedom are frozen, but its spin. The effect of the interaction is the precession of the spin about the magnetic field. In the real world the atom cannot be completely isolated from its environment. The spin will interact with this environment resulting in effects such as the sudden change in its precession phase. (b) An ensemble of atoms interacting with the same magnetic field as in (a). Here all degrees of freedom of the atoms are unfrozen. Thus in addition to interacting with the magnetic field B, the atoms move within the cell, collide and interact with each other and with the cell walls, which in turn causes the dephasing of the precession in the spin ensemble.
For 87Rb magnetometers (with respect to the measurement of Xe magnetization) refer to e-page 184:
6.7.4 Atomic magnetometers
“To detect and characterize the Xe polarization we use the ensemble of 87Rb atoms in each chamber as in situ magnetometers of the Xe magnetization.”
“These optically pumped 87Rb magnetometers are zero-field magnetometers which are sensitive to magnetic fields along the y axis. This type of magnetometer is described in chapter 5, and is very similar to the magnetometers discussed in references  and . The magnetic field along the y axis is modulated by introducing a radio-frequency field with 7 kHz modulation frequency and 1 µT amplitude along the y axis. The magnetometer signal is extracted by lock-in detection of the transmitted laser intensity at the modulation frequency. The measured sensitivities of the pump and probe magnetometers are 5 pT√ Hz and 16 pT√ Hz, respectively, while their bandwidth 40 Hz, which is limited by the response of the lock-in amplifiers. On resonance these magnetometers respond linearly to magnetic fields along their sensitivity axes, which is the y axis, that are smaller than the magnetometer resonance line-width. The estimated linewidth at zero-light levels is νHW HM ≈ 1µT. The broadening of the linewidth is dominated by collisions of 87Rb atoms with Xe atoms.”
A figure relevant to the above is found on e-page 187 (print page 170).
For an example of measuring the magnetic field due to the 129Xe magnetization (measuring 129Xe magnetization, measuring an ensemble of 129Xe) refer to section “6.8.1 Detection of 129Xe polarization” [e-page 185] and 6.8.2, 6.8.3
Measurement of the 129Xe free-induction decay (FID) - use of a group of Rb atoms
Fitting a FID signal
"Measurement of the 129Xe free-induction decay (FID) in each chamber (...) we estimate the corresponding 129Xe polarization."
A section which may eventually be interesting due to the mention of Fourier-transform:
[e-page 112] “The noise in the dispersive signal is measured with a fast-Fourier-transform spectrum analyzer when the static magnetic field is tuned on resonance (Figure 4.4).”
Chapter 2 [e-page 39] of this thesis:
Concepts: Nuclear spin, nuclear spin polarization, nuclear spin motion, measurement of nuclear spins
Image from e-page 45
Excerpt from e-page 38 of http://www-atoms.physics.wisc.edu/papers/2005Babcock.pdf - p.38
“In spin-exchange optical pumping, resonant circularly-polarized pump light is absorbed by alkali atoms, usually Rb, contained in a sealed glass cell. The transition of interest is 2S1/2 → 2P1/2 at 795nm. For most practical applications the hyperfine levels are not resolved due to the pressure broadening by the noble gas [Romalis 97]. Hence, all the hyperfine levels are pumped equally. The alkali atoms become spin polarized, then their polarization is transferred to the noble gas nuclei through collisions.”
The rate of polarization of the noble gas is given by,
[X dPHe dt = ∆Φ´ V (2.1)
where ∆Φ is the absorbed photon flux, ´ is the Rb-noble gas spin-exchange efficiency, V is the cell volume, and [X] is the noble gas density.
Here the ideal absorbed photon flux is given by
∆Φideal = ΓRP RP + Γ [A]V ; (2.2)
where Γ is the alkali relaxation rate, Rp is the pumping rate, and [A] is the alkali density.
From equations 2.1 and 2.2 it is apparent that in order to maximize ∆Φ and dPHe dt , one desires Rp À Γ.
The pumping rate is given by RP = Z ∞ 0 I (º)¾(º)dº ' P¼refc A∆º ; (2.3) where I (º) is the intensity of the pumping laser per unit frequency, ¾(º) = ¼refcg(º), which is the Rb absorption cross section. Here f is the oscillator strength, r e = 2:82 × 10−13 cm is the classical electron radius and g(º) is a normalized Lorenzian. A is the cross sectional area of the cell being pumped and P ¢ν is the power per unit frequency or spectral power which is the figure of merit for attaining high polarization in spin-exchange optical pumping (3)."