Single-Beam All-Optical Nonzero-Field Magnetometric Sensor for Magnetoencephalography Applications

We present a method for measuring the magnetic field that allows hyperfine and Zeeman optical pumping, excitation and detection of magnetic resonance by means of a single laser beam with time-modulated ellipticity. This improvement allows us to significantly simplify the Bell-Bloom magnetometric scheme, while retaining its sensitivity. The method does not require the use of radio-frequency fields, which is essential when creating arrays of sensors. The results of experimental studies demonstrate the efficiency of the proposed method and its potential applicability in most challenging magnetoencephalographic tasks.

Figure 1

(a) Scheme of hyperfine ($F=3,4$) and Zeeman ($m_F=-F..F$) levels of the $6^2{S}_{1/2}$ ground state of Cs in the presence of strong optical pumping. (b) Single-beam modulation period: ${\sigma }^{\pm }$, circular polarizations; $\pi$, linear polarization. (c) The phases of the precession of the collective magnetic moment $\mathbf{M}$ around the MF vector $\mathbf{B}$: at resonance, the precession of $\mathbf{M}$ is precisely synchronized with the optical pump modulation; at the moments when the beam is linearly polarized and is used as a probe, the projection of $\mathbf{M}$ onto the direction of the beam ($x$ axis) is zero; when the modulation frequency is detuned from magnetic resonance, a phase shift between $M$ and OP appears; as a consequence, so does the projection $M_X$ of the moment. (d) Simplified setup diagram: 1, cell with Cs vapor; 2, multilayer magnetic shield; 3, solenoid; 4, external cavity diode laser; 5, EOM; 6, balanced photodetector.

Figure 2

(a) Light at the EOM output, presented as the sum of two circular components, conventionally designated as ${\sigma }^{-}$ and ${\sigma }^{+}$. (b) The same light, represented as a sum of two linear components (${\pi }^{\parallel }$ and ${\pi }^{\perp }$) and one alternating circular (${\sigma }^{\pm }$) component. (c) Azimuth and ellipticity (or phase delay) of the EOM output light. Solid lines correspond to a ${45}^{\circ }$ angle of the EOM axis relative to the polarization azimuth of the incoming light: dashed lines, ${42}^{\circ }$; dash-dotted lines, ${38}^{\circ }$; dotted lines, ${30}^{\circ }$. Lines represent calculation, symbols experiment.

Figure 3

(a) One period of beam modulation: the intensities of ${\sigma }^{\pm }$ and $\pi$ polarizations, the projection of the magnetic moment $\mathbf{M}$ onto the beam, and the signal $S$ at nonzero resonance detuning. (b) The $S_X$ and $S_Y$ components of the signal, obtained using nonmodulated ($M_X$, $M_Y$) and modulated ($S_{1X}$, $S_{1Y}$, $S_{3X}$, $S_{3Y}$) OD beam (calculation on the basis of stationary solutions of the Bloch equations; the numbers in the indices correspond to the number of the signal harmonic). (c) Experimentally measured amplitudes of the first and third harmonics of $S_X$ and $S_Y$ components of the signal; smooth lines are the result of approximation and serve as a guideline to the eye.

Figure 4

Experimentally measured dependences of (a),(e),(i) signal amplitude, (b),(f),(k) resonance width, (c),(g),(l) ultimate, i.e., limited by shot noise of the detecting light sensitivity, (d),(h) the cell optical depth, and (m) the ellipticity of the beam from (a)–(d) the detuning of the beam frequency relative to the transition $F=3\leftrightarrow F^{\mathrm{\prime }}=3$ of the Cs $D_1$ line, (e)–(h) the beam intensity, and (i)–(m) the amplitude of the EOM control voltage. Also shown (d) are the calculated Cs absorption profiles in a vacuum cell and a cell filled with nitrogen at a pressure of 100 torr. The conditions under which the experiments are carried out are indicated in the upper cells of each column.

Figure 5

Signal and noise amplitudes in the vicinity of magnetic resonance (37.9 kHz).

Figure 6

Time dependences of free precession signals at different optical pumping intervals.