Time-reversal Interferometry Using Cat States with Scalable Entangling Resources

TL;DR

Time-reversal Interferometry Using Cat States with Scalable Entangling Resources develops a practical route to generate Schrödinger-cat states using a finite sequence of OAT and rotations, achieving HL scaling in phase estimation. By introducing a time-reversal interferometric protocol, the method amplifies an accumulated phase without relying on variance reduction, and is compatible with optical lattice clock platforms. The authors analyze the quantum Fisher information of cat states, prove controllability in a symmetric Dicke subspace, and provide a gradient-based pulse design with demonstrative sequences; they also account for photon-scattering losses, showing HL scaling persists under realistic decoherence with a $1/\sqrt{N}$ time scaling. The work offers a scalable, robust path to ultra-high-precision sensing across quantum metrology and related fields.

Abstract

We propose a novel method for generating Schrödinger-cat states -- defined as equal superpositions of arbitrary coherent states -- using a concise sequence of rapid twist-and-turn pulses. We demonstrate that the required shearing strength for the protocol, which scales linearly with time, decreases with increasing number of atoms ($N$) in proportion to $1/\sqrt{N}$. The resulting states exhibit optimal quantum Fisher information, making them ideal for surpassing the classical limit of phase sensitivity in quantum metrology applications. Notably, our protocol is compatible with a time-reversal strategy for quantum metrology, ensuring its practical viability. Furthermore, we demonstrate that the Heisenberg limit scaling remains intact even when reducing the twisting employed in tandem with the number of atoms, thereby mitigating realistic losses such as photon scattering.

Figures (3)

• Figure 1: Sequence example where $n=6$ pulses are used to create a Schrödinger-cat state with $\theta = \pi/2$ in $N = 20$ atoms. The infidelity respect to the target is $\epsilon = 0.02$.
• Figure 2: (a) Schematic of the standard Ramsey interferometry scheme using a CSS. (b) Schematic of the modified Ramsey interferometry scheme using a Schrödinger-cat-sate.
• Figure 3: Schrödinger-cat states metrological gain with fixed normalized shearing strength. (a) Examples of Schrödinger-cat states generated by pulse sequence with $n=3$ OAT and $\hat{S}_x$ pulses, with fixed total shearing strength $\tilde{Q} = \sqrt{N} \chi t$, for $N = 50$. (b) Metrological gain when targeting Schrödinger-cat states with different angles $\Delta \phi$ with fixed shearing strength $\tilde{Q}$ using $n=3$ OAT and $\hat{S}_x$ pulses.