Faraday spectroscopy of atoms confined in a dark optical trap

We demonstrate Faraday spectroscopy with a high duty cycle and sampling rate using atoms confined to a blue-detuned optical trap. Our trap consists of a crossed pair of high-charge-number hollow laser beams, which forms a dark, boxlike potential. We have used this to measure transient magnetic fields in a $500\text{−}\mu \text{m}$-diameter spot over a 400 ms time window with nearly unit duty cycle at a 500-Hz sampling rate. We use these measurements to quantify and compensate time-varying magnetic fields to $\approx 10$ nT per time sample.

Figure 1

(Color online) Layout of experiment. Crossed hollow beams confine atoms to a 0.48-mm-diameter spot. Relay lenses for the hollow beams are not shown. Faraday pump and probe beams propagate along the $x$ axis to a balanced polarimeter. WP: Wollaston prism. Osc: oscilloscope. Image of beam and cross sectional profile are shown.

Figure 2

(Color online) Faraday signals for (a) trapped sample and (b) untrapped sample. The untrapped atoms fall away from the probe region within 20 ms, while the trapped atoms remain with 150-ms time constant. Insets in (a) are expanded views of the raw data.

Figure 3

(Color online) (a) Polarimeter output for single-shot data (top) and averaged data (bottom). (b) Fast-Fourier transform (FFT) of data in (a). Fits to a Lorentzian profile are shown as solid lines. Single-shot (circles) and averaged (squares) data are shown.

Figure 4

(Color online) (a) Larmor precession frequency as a function of time with various levels of compensation. Dashed: no compensation; dotted: compensation of eddy currents, and solid: full compensation. Inset to (a) shows magnified view of compensation. Fluctuations in our Larmor precession are dominated by uncompensated harmonics of the ac line. (b) Magnetic field spectrum with no compensation (dotted), and 60 Hz compensation (solid).

Figure 5

2D image of data that exposes qualitative magnetic field features without FFT processing: (a) uncompensated, (b) 60-Hz compensation, (c) full compensation.

Figure 6

(Color online) Comparison of 64 data runs (dashed line) to a simulated signal with white noise added to have similar SNR as the experiment (black line). For clarity, the signals are offset from each other.

Figure 7

(Color online) Simulations of atom number remaining for different degrees of optical pumping. With no optical pumping or probe beams (longest-lived curve) the atoms still scattered $\approx 1\text{photon}/\text{ms}$ from the trap beams. A curve fit is shown for the case of scattering seven photons/ms. This time constant of 160 ms agrees well with our experimental value of 150 ms (Fig. 2).

Figure 8

(Color online) Larmor precession signals with and without the trap light at two different relative orientations of the laser polarization with respect to the magnetic field. These were done at (a) 0° (revivals maximized) and (b) 54° (revivals suppressed).