Qubit-parity interference despite unknown interaction phases

TL;DR

This study demonstrates that qubit-parity interference can be observed in a trapped ion system even when the interaction phases are unknown and stable, using a minimal interferometric sequence that is insensitive to phase uncertainties.

Contribution

The paper introduces a method to observe qubit-parity interference without precise phase control, enabling scalable coherence measurement in complex quantum states.

Findings

Achieved 20% and 40% visibilities in interference fringes

Demonstrated robustness of interference to unknown stable phases

Provided a scalable coherence witness without full state tomography

Abstract

Quantum interference between interacting systems is fundamental to basic science and quantum technology, but it typically requires precise control of the interaction phases of lasers or microwave generators. Can interference be observed if those interaction phases are stable but unknown, usually prohibitive for complex state without active control? Here, we answer this question by experimentally preparing a Schr\"odinger-cat-like state of an internal qubit and a motional oscillator of a trapped $^{40}$Ca$^{+}$ ion, and its robustness to such uncontrolled phase. By applying alternating red and blue sideband pulses, we enforce a strict qubit-parity correlation and interference inherently insensitive to stable but unknown phases of the driving laser. For this qubit-parity interference, we use a minimal two-pulse interferometric sequence to demonstrate characteristic visibilities of $20\%$ and $40\%$, which approach the theoretical visibility limit, providing a scalable coherence witness without full state tomography for high-dimensional states.