SERF

Spin-exchange relaxation

Spin-exchange collisions preserve total angular momentum of a colliding pair of atoms but can scramble the hyperfine state of the atoms. Atoms in different hyperfine states do not precess coherently and thereby limit the coherence lifetime of the atoms. However, decoherence due to spin-exchange collisions can be nearly eliminated if the spin-exchange collisions occur much faster than the precession frequency of the atoms. In this regime of fast spin-exchange, all atoms in an ensemble rapidly change hyperfine states, spending the same amounts of time in each hyperfine state and causing the spin ensemble to precess more slowly but remain coherent. This so-called SERF regime can be reached by operating with sufficiently high alkali metal density (at higher temperature) and in sufficiently low magnetic field. | name-list-style=amp

The spin-exchange relaxation rate R_{se} for atoms with low polarization experiencing slow spin-exchange can be expressed as follows: : R_{se} = \frac{1}{2 \pi T_{se}} \left( \frac{2 I(2 I -1)}{3(2I+1)^2} \right) where T_{se} is the time between spin-exchange collisions, I is the nuclear spin, \nu is the magnetic resonance frequency, \gamma_e is the gyromagnetic ratio for an electron.

In the limit of fast spin-exchange and small magnetic field, the spin-exchange relaxation rate vanishes for sufficiently small magnetic field: : R_{se} = \frac{\gamma_e^2 B^2 T_{se} }{2 \pi} \frac{1}{2}\left( 1-\frac{(2I+1)^2}{Q^2} \right) where Q is the "slowing-down" constant to account for sharing of angular momentum between the electron and nuclear spins: | name-list-style=amp :Q(I=3/2)=4\left( 2 - \frac{4}{3+P^2} \right)^{-1} :Q(I=5/2)=6\left( 3 - \frac{48(1+P^2)}{19+26 P^2+3 P^4} \right)^{-1} :Q(I=7/2)=8\left( \frac{4(1+7P^2+7P^4+P^6)}{11+35P^2+17P^4+P^6} \right)^{-1} where P is the average polarization of the atoms. The atoms suffering fast spin-exchange precess more slowly when they are not fully polarized because they spend a fraction of the time in different hyperfine states precessing at different frequencies (or in the opposite direction).

Sensitivity

The sensitivity \delta B of atomic magnetometers are limited by the number of atoms N and their spin coherence lifetime T_2 according to :\delta B = \frac{1}{\gamma} \sqrt{\frac{2 R_{tot} Q}{F_z N} } where \gamma is the gyromagnetic ratio of the atom and F_z is the average polarization of total atomic spin F = I+S. | name-list-style=amp

In the absence of spin-exchange relaxation, a variety of other relaxation mechanisms contribute to the decoherence of atomic spin: :R_{tot} = R_D + R_{sd,self} + R_{sd,\mathrm{He}} + R_{sd,\mathrm{N_2}} where R_D is the relaxation rate due to collisions with the cell walls and R_{sd,X} are the spin destruction rates for collisions among the alkali metal atoms and collisions between alkali atoms and any other gasses that may be present.

In an optimal configuration, a density of 1014 cm−3 potassium atoms in a 1 cm3 vapor cell with ~3 atm helium buffer gas can achieve 10 aT Hz−1/2 (10−17 T Hz−1/2) sensitivity with relaxation rate R_{tot} ≈ 1 Hz.

Typical operation

Alkali metal vapor of sufficient density is obtained by simply heating solid alkali metal inside the vapor cell. A typical SERF atomic magnetometer can take advantage of low noise diode lasers to polarize and monitor spin precession. Circularly polarized pumping light tuned to the D_1 spectral resonance line polarizes the atoms. An orthogonal probe beam detects the precession using optical rotation of linearly polarized light. In a typical SERF magnetometer, the spins merely tip by a very small angle because the precession frequency is slow compared to the relaxation rates.

Advantages and disadvantages

SERF magnetometers compete with SQUID magnetometers for use in a variety of applications. The SERF magnetometer has the following advantages:

• Equal or better sensitivity per unit volume
• Cryogen-free operation
• All-optical measurement limits enables imaging and eliminates interference Potential disadvantages:
• Can only operate near zero field
• Sensor vapor cell must be heated

Applications

Applications utilizing high sensitivity of SERF magnetometers potentially include:

• High-performance magnetoencephalographic imaging | name-list-style=amp
• Sample magnetization measurement, especially rock samples

History

The SERF magnetometer was developed by Michael V. Romalis at Princeton University in the early 2000s. but the application to magnetic field measurement was not explored at that time. The name "SERF" was partially motivated by its relationship to SQUID detectors in a marine metaphor.

References

References

1. 王子隆. (2025). "Magnetic Field Regulation and Demodulation of Three-axis SERF Atomic Magnetometer". 电子科技大学.
2. (2025-02-25). "SERF态效应用零磁场环境实现技术研究进展". 激光与光电子学进展.