Figure 1

Field sensitivity for repeated measurements using the spinor BEC magnetometer. Curves marked ASN (PSN) represent atom (photon) shot-noise limited sensitivities, assuming $\tau =250\mathrm{ms}$, $D=1$, and the atomic column density and probe light levels for our experiment. Diffusion of magnetization limits the sensitivity for a given length scale by imposing a limit on $\tau$ (short dashed line, assuming $D=1$). The gray line indicates the measured spatial root Allan variance; the sensitivity demonstrated in measurements of an optically induced magnetic field (see text), assuming duty cycles of $D=0.003$ (●) or $D=1$ (○), is also shown. Results are compared both to the ideal sensitivity of a quantum-limited SQUID magnetometer (dot-dashed line) and to demonstrated low-frequency sensitivities [5, 16] (△).Reuse & Permissions

Figure 2

(a) A sequence of phase contrast images, taken at a strobe rate of 14 kHz, reveal Larmor precession as an aliased frame-to-frame oscillation of the signal. (b) The resulting 2D map of the magnetic field, obtained by a pixel-by-pixel estimation of the Larmor precession phase, reveals the optically induced local magnetic field near the condensate center. (c) The 1D phase profile precisely maps the applied field inhomogeneity with peak strength of $166.2\pm 1.2\mathrm{pT}$.Reuse & Permissions

Figure 3

Single-shot measurements of the localized magnetic field imposed by a laser beam focused to $\sigma =24\mu \mathrm{m}$ rms width. Residuals are shown from a linear calibration fit of the field magnitude versus laser power. Error bars indicate standard deviations for 10 measurements per setting.Reuse & Permissions

Figure 4

Quantum evolution of an imprinted phase. (a) Cross sections of the phase imprint after free evolution times of $t=0$, 40, and 90 ms. Traces are offset for clarity. (b) The $1/e$ width and (c) peak value of the imprinted phase are compared to (b) numerical simulations based on a noninteracting spinor gas and to (c) the expected scaling imposed by normalization of magnetization.Reuse & Permissions