Direct Nondestructive Imaging of Magnetization in a Spin-1 Bose-Einstein Gas

Polarization-dependent phase-contrast imaging is used to resolve the spatial magnetization profile of an optically trapped ultracold gas. This probe is applied to Larmor precession of degenerate and nondegenerate spin-1 ${}^{87}\mathrm{Rb}$ gases. Transverse magnetization of the Bose-Einstein condensate persists for the condensate lifetime, with a spatial response to magnetic field inhomogeneities consistent with a mean-field model of interactions. In comparison, the magnetization of the noncondensed gas decoheres rapidly. Rotational symmetry implies that the Larmor frequency of a spinor condensate be density independent, and thus suitable for precise magnetometry with high spatial resolution.

Figure 1

Imaging system for direct detection of atomic magnetization. Left: Circularly polarized probe light illuminates the trapped gas. A first lens and phase plate form a primary phase-contrast image which is selectively masked and then reimaged by a second lens onto the camera as one of $\sim 40$ frames which form a single composite image. Top right: Clebsch-Gordan coefficients for the imaging transition. Bottom right: Sample images of a BEC (a) with the atomic spin along $-\widehat{y}$ and (b) with the spin along $+\widehat{y}$, demonstrating the magnetization sensitivity of our technique.

Figure 2

Direct imaging of Larmor precession of a spinor BEC through magnetization-sensitive phase-contrast imaging. Shown are 31 consecutive images each with $325\times 18\mu \mathrm{m}$ field of view. (a) Larmor precession is observed as a periodic modulation in the intensities of repeated images of a single condensate. (b) The peak signal strength oscillates at a rate which results from aliased sampling of a precisely measured 38.097(15) kHz Larmor precession at a sampling rate of 20 kHz. (c) In the presence of an $8\mathrm{mG}/\mathrm{cm}$ axial gradient, images indicate “winding” of the transverse magnetization along the condensate. Images begin (a) 24.5 ms or (c) 14.5 ms after the tipping rf pulse. In (a), the field gradient is cancelled to less than $0.2\mathrm{mG}/\mathrm{cm}$.

Figure 3

Decay of the Larmor-precession amplitude for (a) a BEC and (b) a thermal cloud. Data from the tip and hold (filled circles) or hold and tip (open circles) methods are compared (see text). The $1/e$ decay time of Larmor precession in a BEC was $670\pm 120\mathrm{ms}$, close to that of the hold and tip signal ($830\pm 120\mathrm{ms}$), indicating no decoherence source other than number loss. The $65\pm 10\mathrm{ms}$ decay time of Larmor precession in a thermal cloud was an order of magnitude shorter than that of the hold and tip signal ($1100\pm 500\mathrm{ms}$).

Figure 4

Dependence of Larmor-precession decay rate on applied gradient [27]. Decay rates for the condensate are represented by filled circles and for the thermal cloud by open circles. The solid curve is a theoretical prediction for the thermal-cloud precession decay rate, as discussed in the text.