All-Optical Vector Atomic Magnetometer

We demonstrate an all-optical magnetometer capable of measuring the magnitude and direction of a magnetic field using nonlinear magneto-optical rotation in cesium vapor. Vector capability is added by effective modulation of the field along orthogonal axes and subsequent demodulation of the magnetic-resonance frequency. This modulation is provided by the ac Stark shift induced by circularly polarized laser beams. The sensor exhibits a demonstrated rms noise floor of $\sim 65\mathrm{fT}/\sqrt{\mathrm{Hz}}$ in measurement of the field magnitude and $0.5\mathrm{mrad}/\sqrt{\mathrm{Hz}}$ in the field direction; elimination of technical noise would improve these sensitivities to $12\mathrm{fT}/\sqrt{\mathrm{Hz}}$ and $10\mu \mathrm{rad}/\sqrt{\mathrm{Hz}}$, respectively. Applications for this all-optical vector magnetometer would include magnetically sensitive fundamental physics experiments, such as the search for a permanent electric dipole moment of the neutron.

Figure 1

Experimental schematic. An amplitude-modulated, circularly polarized pump beam (not shown) propagates in the $\widehat{x}$ direction. The local oscillator (LO) controls the pump AOM and serves as a reference to the lock-in amplifier (LIA), whose analog output is recorded by a data acquisition card (DAQ) and read into a computer (PC). A linearly polarized probe beam passes through the cell and is split by the polarizing beam splitter (PBS) of a balanced polarimeter; the output of this polarimeter is demodulated by the lock-in. Two circularly polarized light-shift beams $L{S}_y$ and $L{S}_z$ are independently modulated and sent through the cell along $\widehat{y}$ and $\widehat{z}$. Coils allow the magnetic field ${\mathbf{B}}_0$ to be tilted in the $\widehat{y}\text{−}\widehat{z}$ plane.

Figure 2

The measured ratio of the Larmor frequency shift induced by the $L{S}_y$ and $L{S}_z$ beams, plotted as a function of field angle $\theta$ from the $\widehat{z}$ axis. The curve shows a fit to Eq. (3). Each data point resulted from 20 s of averaging; uncertainties in the data points are below ${10}^{-2}$.

Figure 3

Linear-spectral-density plot of the scalar field measurement with the $L{S}_z$ beams turned off (blue line) and turned on at a constant power of 1 mW (red line). For these data, $\theta =0$ and the light-shift beam power was not actively controlled. The black trace is the predicted noise floor of the scalar field measurement taken from a (separate) recording of the light-shift beam power, from which a magnetic LSD was derived by using the observed light-shift coefficients ${\alpha }_y$ and ${\alpha }_z$.

Figure 4

Measured field angle $\theta$ as a function of time while the applied $\widehat{y}$ field is being switched. The average rms noise for a constant field angle translates to a precision of $0.47\mathrm{mrad}/\sqrt{\mathrm{Hz}}$ in measurement of the field direction. The steps in the plotted ratio are slightly low-pass filtered due to the time constants of the lock-in amplifier and the secondary demodulation at ${\omega }_y$ and ${\omega }_z$.