# Enhancing Sensitivity of an Atom Interferometer to the Heisenberg Limit using Increased Quantum Noise. (arXiv:1707.08260v9 [quant-ph] UPDATED)

In a conventional atomic interferometer employing $N$ atoms, the phase
sensitivity is at the standard quantum limit: $1/\sqrt{N}$. Using
spin-squeezing, the sensitivity can be increased, either by lowering the
quantum noise or via phase amplification, or a combination thereof. Here, we
show how to increase the sensitivity, to the Heisenberg limit of $1/N$, while
increasing the quantum noise by $\sqrt{N}$, thereby suppressing by the same
factor the effect of excess noise. The proposed protocol makes use of a
Schr\"odinger Cat state representing a mesoscopic superposition of two
collective states of $N$ atoms, behaving as a single entity with an $N$-fold
increase in Compton frequency. The resulting $N$-fold phase magnification is
revealed by using atomic state detection instead of collective state detection.
We also show how to realize an atomic clock based on such a Schr\"odinger Cat
state, with an $N$-fold increase in the effective transition frequency. We also
discuss potential experimental constraints for implementing this scheme, using
one axis twist squeezing employing the cavity feedback scheme, and show that
the effects of cavity decay and spontaneous emission are highly suppressed due
to the $N$-fold phase magnification. We find that even for a modest value of
the cavity cooperativity parameter that should be readily accessible
experimentally, the maximum improvement in sensitivity is very close to the
ideal limit, for as many as ten million atoms.