Quantum Nondemolition Measurement of Large-Spin Ensembles by Dynamical Decoupling

Quantum nondemolition (QND) measurement of collective variables by off-resonant optical probing has the ability to create entanglement and squeezing in atomic ensembles. Until now, this technique has been applied to real or effective spin one-half systems. We show theoretically that the buildup of Raman coherence prevents the naive application of this technique to larger spin atoms, but that dynamical decoupling can be used to recover the ideal QND behavior. We experimentally demonstrate dynamical decoupling by using a two-polarization probing technique. The decoupled QND measurement achieves a sensitivity 5.7(6) dB better than the spin projection noise.

Figure 1

Experimental sequence for projection-noise measurement. The CSS is prepared once and its magnitude $⟨{\widehat{J}}_{\mathbf{x}}⟩$ is measured. This serves as a measure of the spin polarization prior to the QND probing. We prepare the CSS a second time and assume it has the same spin polarization as in the first preparation. The state is probed with a train of pulses of alternating polarization. Measuring the spin polarization after the QND measurement tells us the amount of depolarization introduced in the QND probing. The QND probing scatters a non-negligible fraction of atoms into $F=2$, which are removed from the trap with resonant light in order to reduce the number of atoms in the trap. The whole cycle is repeated 10 times during one trap loading.

Figure 2

Variance of polarimeter signal as a function of atom number, comparing naive probing, i.e., a single input polarization, to “bang-bang” dynamically decoupled probing of different orders $p$. Gray curves indicate simulation results for: naive probing (solid), and decoupled probing with $p=1$ (widely dashed), $p=2$ (dashed), and $p=5$ (dotted). The black solid line shows the expected projection noise for $p\to \infty$, or the ideal QND interaction $G_2=0$. All curves are calculated using the independently measured interaction strength $G_1=1.27(5)\times {10}^{-7}$ and have no free parameters. Red squares are measured data using dynamical decoupling with $p=5$. Blue circles are measured data with naive probing, which show a quadratic scaling (dash-dotted line). Technical noise from laboratory fields dominates the naive probing results, and pushes them above the theoretical curve, while technical noise is suppressed in the two-polarization probing.