Continuous real-time tracking of a quantum phase below the standard quantum limit

TL;DR

This paper introduces a real-time quantum phase tracking method using non-demolition measurements, enabling phase estimation below the standard quantum limit and naturally generating spin-squeezed states.

Contribution

It presents a novel continuous measurement scheme for real-time quantum phase tracking that surpasses the standard quantum limit without requiring population difference conversion.

Findings

Achieves phase estimation below the standard quantum limit.

Naturally generates spin-squeezed states during measurement.

Enables real-time tracking of time-varying quantum signals.

Abstract

We propose a scheme for continuously measuring the evolving quantum phase of a collective spin composed of $N$ pseudospins. Quantum non-demolition measurements of a lossy cavity mode interacting with an atomic ensemble are used to directly probe the phase of the collective atomic spin without converting it into a population difference. Unlike traditional Ramsey measurement sequences, our scheme allows for real-time tracking of time-varying signals. As a bonus, spin-squeezed states develop naturally, providing real-time phase estimation significantly more precise than the standard quantum limit of $\Delta \phi_\text{SQL} = 1/\sqrt{N}$ radians.