Detection of radio-frequency magnetic fields using nonlinear magneto-optical rotation

We describe a room-temperature alkali-metal atomic magnetometer for detection of small, high-frequency magnetic fields. The magnetometer operates by detecting optical rotation due to the precession of an aligned ground state in the presence of a small oscillating magnetic field. The resonance frequency of the magnetometer can be adjusted to any desired value by tuning the bias magnetic field. Based on experimentally measured signal-to-noise ratio, we demonstrate a sensitivity of $100\mathrm{pG}∕\sqrt{\mathrm{Hz}}$ (rms) in a $3.5\text{−}\mathrm{cm}$-diameter paraffin coated cell. Assuming detection at the photon shot-noise limit, we project a sensitivity as low as $25\mathrm{pG}∕\sqrt{\mathrm{Hz}}$ (rms).

Figure 1

(Color online) Linearly polarized light, resonant with the $D1$ $(F=2\to F^{\prime }=1)$ transition, with polarization vector along ${\mathbf{B}}_0$, produces an aligned ground state via optical pumping. Double headed vertical arrows indicate laser induced transitions between ground and excited states; dashed lines indicate transitions due to spontaneous decay. Ground-state populations, indicated by the solid black bars, are schematic only. A small rf magnetic field oscillating close to ${\Omega }_L$, transverse to ${\mathbf{B}}_0$, establishes coherences between neighboring $M_F$ states. Inset: surface whose radius represents the probability for finding maximal projection of ground-state angular momentum along a given direction (see, for example, Ref. 12).

Figure 2

Schematic of the experimental setup. An evacuated, paraffin coated cell is placed inside a double-wall oven. Temperature is controlled by flowing warm air through the space between the oven walls. A set of $\mu$-metal layers provides a magnetically shielded environment, and a set of coils maintains a stable, homogeneous magnetic field in the $z$ direction. An additional coil generates a small oscillating magnetic field in the $x$ direction. Linearly polarized light from an external-cavity diode laser passes through the cell and a balanced polarimeter monitors the polarization of the light as it exits the cell.

Figure 3

rf magnetic noise spectrum. The large peak is an applied field of $83\mathrm{nG}$ (rms) at ${\Omega }_L$. Light power into the cell was $40\mu \mathrm{W}$. Shown inset is the polarimeter noise (squares) as a function of total power collected by the polarimeter. The solid line is a fit based on Eq. (3) and the dashed line represents photon shot noise.

Figure 4

(a) Synchronously detected optical rotation and (b) transmission spectra as a function of light frequency for a light power of $60\mu \mathrm{W}$ and ${\omega }_{\mathit{rf}}={\Omega }_L$. The overall slope on the transmission curve is due to the change in incident laser power.

Figure 5

In-phase (stars) and quadrature (squares), synchronously detected optical-rotation signal as a function of the frequency of the applied oscillating magnetic field. Overlaying the data (solid lines) are fits to a single dispersive or absorptive Lorentzian. For these data, the light was tuned approximately to the center of the $F=2\to F^{\prime }=1$ transition and the power was $40\mu \mathrm{W}$. Inset: Optical-rotation signals for light detuned approximately one Doppler-broadened linewidth $(\approx 300\mathrm{MHz})$ towards lower frequencies from the $F=2\to F^{\prime }=1$ transition. Light power was $360\mu \mathrm{W}$, and the cell temperature was $20°\mathrm{C}$. ac Stark shifts result in a splitting of the resonance. Units are the same as in the main panel. The overall position of the resonance is different from that in the main panel because the bias field differed by a factor of 5.

Figure 6

(a) Half width at half maximum of the in-phase component of the rf NMOR resonance shown in Fig. 5 as a function of light power. The solid line overlaying the data is a linear fit. (b) The amplitude of the rf NMOR resonance ${\varphi }_{\mathit{max}}$, defined as the maximum value of the in-phase component.

Figure 7

Projected (stars) and experimentally measured (squares) sensitivity as a function of light power incident on the cell.