Preparation of cat states in many-body eigenbasis via non-local measurement

TL;DR

This paper introduces a protocol using non-local measurements and engineered dissipation to prepare and stabilize superpositions of many-body eigenstates, including GHZ states, in quantum spin chains, demonstrating robustness and tunability.

Contribution

It proposes a novel measurement-based method to generate and maintain superpositions of many-body eigenstates, advancing quantum state engineering techniques.

Findings

Protocol successfully generates superpositions like GHZ states.

Engineered superpositions exhibit long-lived metastability.

Method is compatible with current quantum simulators.

Abstract

Engineered dissipation offers a promising route to prepare correlated quantum many-body states that are otherwise difficult to access using purely unitary protocols. However, creating superpositions of multiple many-body eigenstates with tunable properties remains a major challenge. We propose to periodically interrupt the many-body evolution by precisely removing a given many-body Fock state through a non-local post-selected measurement protocol. Upon tuning the measurement period, we show that a dark state manifold survives the removal, allowing us to filter the system and generate a coherent superposition within this manifold at long times. As a testbed, we study a non-integrable spin-1 XY chain featuring a solvable family of eigenstates that can differ macroscopically in quasi-particle excitations. Our protocol generates tunable superpositions of these eigenstates, including the spin-1 Greenberger-Horne-Zeilinger state and a generalized variant with tunable spatiotemporal order. Under perturbations, the system exhibits an exceptionally long-lived metastable regime where the engineered superpositions remain robust. Our work provides new insight into quantum state preparation via non-local measurements using tools available in current quantum simulators.