Interferometry below the Standard Quantum Limit with Bose-Einstein Condensates

We discuss a scheme for using entangled Bose-Einstein condensates to detect phase differences with a resolution better than the standard quantum limit. To date, schemes have shown that the enhancement in phase resolution gained by entangling condensates is lost when dissipation is present. Here we show how this can be overcome by using number correlated condensates, as have been produced recently in the laboratory. We also outline a scheme for measuring this phase that is not destroyed when the effects of finite detector efficiency are considered.

Figure 1

Variation of the relative phase resolution with $2\kappa t$ for (a) a binomial state (solid curve) and the approximation given by (14) (crossed curve), (b) a cat state, and (c) a number correlated state for $N=50$. The dotted line indicates the point at which the cat state has been destroyed and no longer contains any phase information. The dashed region is enlarged in Fig. 2.

Figure 2

An enlargement of the dashed region in Fig. 1.