Spin-exchange relaxation-free magnetometry using elliptically polarized light

Spin-exchange relaxation free alkali-metal magnetometers typically operate in the regime of high optical density, presenting challenges for simple and efficient optical pumping and detection. We describe a high-sensitivity Rb magnetometer using a single elliptically polarized off-resonant laser beam. Circular component of the light creates relatively uniform spin polarization while the linear component is used to measure optical rotation generated by the atoms. Modulation of the atomic spin direction with an oscillating magnetic field shifts the detected signal to high frequencies. Using a fiber-coupled distributed feedback laser, we achieve magnetic field sensitivity of $7\text{fT}/\sqrt{\text{Hz}}$ with a miniature $5\times 5\times 5\text{mm}\text{Rb}$ vapor cell.

Figure 1

(Color online) (a) Assembled magnetometer sensor (side view). (b) A schematic of magnetometer arrangement (top view). a is a fiber holder and a collimator, b is a linear polarizer, c is a quarter waveplate, d is a focusing lens and a half-wave plate combination, e is polarizing beam splitter, and f is a prism. The angle between the polarizer axis and the fast axis of the quarter wave is equal to $\pi /8$ and the angle between the polarizer axis and the half-wave plate axis is equal to $\pi /4$.

Figure 2

(Dots) Experimental data showing amplitude of the zero-field resonance as a function of the angle between the polarizer and the quarter waveplate $\theta$. The measurements were made using low light intensities such that the rotation angle $\varphi ⪡\pi /4$. (Dash) Numerical fit to the data using a functional form of $\left|\text{sin}\left(4\theta \right)\right|$ expected for the resonance amplitude in the low-polarization limit.

Figure 3

(Dots) Experimentally observed light shift as a function $\theta$ under typical operating conditions. The light shift was measured by monitoring the strength of magnetic field in the $z$ direction required to minimize the zero-field resonance linewidth. (Dash) A fit to the experimental data using the functional form of the photon spin $s=\text{sin}\left(2\theta \right)$. The absolute value of the light shift is consistent with Eq. (9) within a factor of 2 due to uncertainty in the incident light intensity.

Figure 4

(a) A typical zero-field resonance seen as a function of transverse magnetic field $B_x$ when $B_y$ and effective $B_z$ magnetic fields are zeroed. The resonance has multiple peaks due to optical rotation angles greater than $\pi /4$. We estimate that roughly 40% contribution to the linewidth comes from residual light shifts. (b) Lock-in amplifier dispersion signal. The $x$ axis spans from –200 to 200 nT. The $y$ axis is in arbitrary units. A 2 kHz sinusoidal magnetic modulation of $200{\text{nT}}_{peak}$ amplitude was applied to $B_x$ to generate the signal.

Figure 5

(Dots) Normalized lock-in amplifier signal slope around $B_x=0$ as a function of the modulation amplitude for a fixed ratio of modulation amplitude to frequency equal to 0.17 nT/Hz which corresponds to modulation index $m=0.8$. (Dash) Predictions for the slope based on Eq. (10).

Figure 6

(Color online) (Solid line) Spectral density of the magnetic field noise. The 3 dB bandwidth of the magnetometer was 150 Hz. (Dashed line) Polarimetry technical noise observed by switching off the modulation field used for lockin detection. (Thick dashed line) Calculated photon shot-noise-limited sensitivity of the magnetometer.