Enhancing Sensitivity of an Atom Interferometer to the Heisenberg Limit using Increased Quantum Noise

TL;DR

This paper proposes a method to reach the Heisenberg limit in atom interferometry by using Schrödinger Cat states, achieving enhanced sensitivity despite increased quantum noise, with potential applications in atomic clocks.

Contribution

The authors introduce a protocol utilizing Schrödinger Cat states for phase amplification, enabling sensitivity at the Heisenberg limit while managing quantum noise, and discuss practical implementation constraints.

Findings

Achieves Heisenberg limit sensitivity with increased quantum noise.

Uses Schrödinger Cat states for N-fold phase magnification.

Potential for atomic clocks with N-fold frequency increase.

Abstract

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 protocol uses a Schr\"odinger Cat state representing a 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 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. We find that the maximum improvement in sensitivity can be close to the ideal limit, for as many as ten million atoms.