Heading-Error-Free Optical Atomic Magnetometry in the Earth-Field Range

We demonstrate an alignment-based ${}^{87}\mathrm{Rb}$ magnetometer that is immune to nonlinear Zeeman (NLZ) splitting, addressing an important problem in alkali-metal atomic magnetometry. In our scheme, there is a single magnetic resonance peak and well-separated hyperfine transition frequencies, making the magnetometer insensitive or even immune to NLZ-related heading errors. It is shown that the magnetometer can be implemented for practical measurements in geomagnetic environments, and the photon-shot-noise-limited sensitivity reaches $9\mathrm{fT}/\sqrt{\mathrm{Hz}}$ at $5\mathrm{\mu }\mathrm{T}$ and remains at tens of $\mathrm{fT}/\sqrt{\mathrm{Hz}}$ at $50\mathrm{\mu }\mathrm{T}$ at room temperature.

Figure 1

Schematic of NLZ-heading-error-free magnetometer. (a) Nonlinear Zeeman effect of the ${}^{87}\mathrm{Rb}$ ground state $5{}^2{\mathrm{S}}_{1/2}$ and corresponding magnetic resonance frequencies. In the $F=2$ ($F=1$) hyperfine state, there are four (two) different $\mathrm{\Delta }m=1$ magnetic resonance frequencies, labeled from ${\omega }_1$ to ${\omega }_4$ (${\omega }_5$ to ${\omega }_6$), respectively, and three (one) different $\mathrm{\Delta }m=2$ magnetic resonance frequencies, labeled from ${\omega }_1^{\prime }$ to ${\omega }_3^{\prime }$ (${\omega }_4^{\prime }$), respectively. (b) Energy levels of ${}^{87}\mathrm{Rb}$ atoms and its excitation scheme. The pump beam is a 795 nm laser beam exciting the $5{}^2{\mathrm{S}}_{1/2}F=2$ to $5^2{\mathrm{P}}_{1/2}{F}^{\prime }=2$ transition, which generates atomic spin polarization in the $5{}^2{\mathrm{S}}_{1/2}F=1$ state via repopulation pumping; the probe beam is a 780 nm laser tuned to the low-frequency side relative to the $5{}^2{\mathrm{S}}_{1/2}F=1$ to $5^2{\mathrm{P}}_{3/2}{F}^{\prime \prime }=0$ transition. (c) Alignment resonance setup. Pump: a linearly polarized 795 nm laser beam used to generate the atomic alignment polarization. Probe: a linearly polarized 780 nm laser beam used to detect the Larmor precession of the atomic alignment polarization via optical rotation. AOM: the acousto-optic modulator used to pulse the pump beam. PBS: polarizing beam splitter. BS: beam splitter. $\lambda /2$: half-wave plate. BPD: balanced photodiode. BPF: bandpass filter with central wavelength of 780 nm, which is used to prevent the pump beam from entering the BPD. BD: beam dump. LIA: lock-in amplifier. PC: personal computer. (d) Orientation resonance setup. Pump: a circularly polarized 795 nm laser beam used to generate the atomic orientation polarization. Probe: a linearly polarized 780 nm laser beam used to detect the Larmor precession of the atomic orientation polarization via optical rotation. $\lambda /4$: quarter-wave plate. Other labels are the same as those in (c).

Figure 2

Magnetic resonances of alignment and orientation polarization with background magnetic fields of different strengths. (a) Alignment resonance. (b) Orientation resonance. The background magnetic field is set along the $z$ direction, with strength ranging from $20\mathrm{\mu }\mathrm{T}$ to $50\mathrm{\mu }\mathrm{T}$. Different magnetic resonances are shifted vertically for clarity. Since the alignment-resonance frequency is about twice that of the orientation resonance, the scale of detuning in (a) is also twice that of (b). The amplitude of the alignment signal is smaller than that of the orientation signal for the reasons explained in Ref. [40].