Synchronous optical pumping of quantum revival beats for atomic magnetometry

We observe quantum beats with periodic revivals due to nonlinear spacing of Zeeman levels in the ground state of potassium atoms, and demonstrate their synchronous optical pumping by double modulation of the pumping light at the Larmor frequency and the revival frequency. We show that synchronous pumping increases the degree of spin polarization by a factor of 4. As a practical example, we explore the application of this double-modulation technique to atomic magnetometers operating in the geomagnetic field range, and find that it can increase the sensitivity and reduce magnetic-field-orientation-dependent measurement errors endemic to alkali-metal magnetometers.

Figure 1

Measurement of $⟨S_x⟩$ showing multiple quantum revivals. Synchronous pumping of quantum revivals is started $150\mathrm{ms}$ before $t=0$ and stopped at $t=60\mathrm{ms}$, allowing free decay of spin coherence. Inset (a) shows a comparison of the revival envelope with a density matrix simulation (dashed lines slightly offset vertically for visibility), while inset (b) shows double modulation of the pump laser frequency, so the optical pumping occurs only during instances of maximum expectation value of $⟨S_z⟩$.

Figure 2

Magnetic resonance spectra in a $0.5\mathrm{G}$ field with (dashed lines) and without (solid lines) secondary modulation at twice the revival frequency. Numerical simulation (a) and experimental measurements with magnetic field in $\widehat{y}$ direction (b) and tilted by 60° into the $\widehat{z}$ direction (c) with optical excitation of spin precession. (d) “$M_x$” magnetometer signal with rf excitation and magnetic field in $\widehat{z}$ direction. The signals are offset in the vertical direction by an arbitrary amount. Small random variations in the height of the peaks with secondary modulation and small sidebands are due to $60\mathrm{Hz}$ noise.

Figure 3

Calculated gain in magnetometer sensitivity due to higher spin polarization for secondary modulation with 1% (solid line) and 30% (dashed line) duty cycle relative to the case with no secondary modulation. The average optical pumping rate is set equal to the relaxation rate. The inset shows experimental magnetic resonance spectrum in a $0.21\mathrm{G}$ field with increased magnetic field gradients. Secondary modulation (solid line) shows individual resonances which are poorly resolved without it (dashed line).

Figure 4

Heading error determined from numerical simulation as a function of the magnetic field tilt angle $\theta$ away from the $y$ axis into the direction of the pump beam. With no secondary modulation the heading error depends on the resonance linewidth (solid line, $\Gamma =13\mathrm{Hz}$; dash-dotted line, $\Gamma =26\mathrm{Hz}$), while with secondary modulation the heading error is approximately quadratic in $\theta$ and is independent of the resonance linewdith (dashed line, $\Gamma =13\mathrm{Hz}$; dotted line, $\Gamma =26\mathrm{Hz}$). Inset (a) shows that without secondary modulation the slope of the heading error near $\theta =0$ scales as ${\Gamma }^2$. Inset (b) shows that with secondary modulation the curvature of the heading error near $\theta =0$ scales as $B^3$, indicating that it is due to third-order splitting of the energy levels.