Fig. 1. Simultaneous, precise tracking of spin angle and amplitude.
a) Bloch-sphere representation of the atomic state evolution. Ellipsoids show uncertainty volumes (not to scale) as the state evolves anti-clockwise from an initial, Fy-polarized state with isotropic uncertainty. An x-oriented magnetic field B drives a coherent spin precession in the Fy–Fz plane. Quasi-continuous measurement of Fz produces a reduction in Fz and Fy variances, with a corresponding increase in var(Fx). b) Observed Faraday rotation angle φ ∝ Fz versus time. Each circle shows the rotation angle from one V-polarized pulse. A magnetic field of 37.6 mG produces the observed oscillation, while dephasing due to residual magnetic gradients and off-resonant scattering of probe photons cause the decay of coherence. Blue circles show a single, representative trace, overlaid on 453 repetitions of the experiment shown as orange dots. The time zero corresponds to the first probe pulse; the end of optical pumping is 58 µs earlier. c) Experimental geometry: 1.9 × 106 cold 87Rb atoms are confined in a weakly-focused single beam optical dipole trap (ODT). Transverse optical pumping is used to produce Fy polarisation. On-axis, 0.6 µs pulses with mean photon number 2.74 × 106 experience Faraday rotation by an angle φ ∝ Fz. A polarimeter consisting of waveplates, a polarising beamsplitter, high-quantum-efficiency photodiodes, and charge-sensitive amplifiers measures the output Stokes component Sy. A reference detector before the atoms measures input Stokes component S0 = |Sx|. The rotation angle is computed as φ = arcsin(Sy/Sx).