Robust Quantum Enhanced Phase Estimation in a Multimode Interferometer

By exploiting the correlation properties of ultracold atoms in a multimode interferometer, we show how quantum enhanced measurement precision can be achieved with strong robustness to particle loss. While the potential for enhanced measurement precision is limited for even moderate loss in two-mode schemes, multimode schemes can be more robust. A ring interferometer for sensing rotational motion with noninteracting fermionic atoms can realize an uncertainty scaling of $1/(N\sqrt{\eta })$ for $N$ particles with a fraction $\eta$ remaining after loss, which undercuts the shot-noise limit of two-mode interferometers. A second scheme with strongly interacting bosons achieves a comparable measurement precision and improved readout.

Figure 1

Top: A schematic showing the implementation of the scheme in time. For a description of each step see the main text. Bottom: A visual representation of the system. Ultracold atoms are confined to a 1D optical ring potential with a rotating barrier. The measurement precision is determined in the presence of particle loss.

Figure 2

The uncertainty of $\varphi =\Delta \omega t_m$ for different fractions of particles remaining, $\eta$, and $N=5$. The lines show $\delta \varphi$ for noninteracting fermions and TG ($M=18$) superpositions compared with the optimal two-mode (as given in 10), NOON and unentangled states. The noninteracting fermions and TG ($M=18$) superpositions afford better precision than the unentangled particles and the optimum two-mode initial state for all loss rates.