# Phase protection of Fano-Feshbach resonances

## TL;DR

This paper demonstrates that bound states coupled to scattering states can be protected from decay when their relative phase is a multiple of pi, revealing a phase-based method to identify long-lived quantum states.

## Contribution

It introduces the concept of phase protection for Fano-Feshbach resonances, showing how phase conditions can significantly extend state lifetimes.

## Key findings

- Lifetimes vary over four orders of magnitude due to phase effects.
- Phase protection occurs when the relative phase is a multiple of pi.
- Experimental validation with molecular ions confirms the phase protection phenomenon.

## Abstract

Decay of bound states due to coupling with free particle states is a general phenomenon occurring at energy scales from MeV in nuclear physics to peV in ultracold atomic gases. Such a coupling gives rise to Fano-Feshbach resonances (FFR) that have become key to understanding and controlling interactions - in ultracold atomic gases, but also between quasiparticles such as microcavity polaritons. The energy positions of FFR were shown to follow quantum chaotic statistics. In contrast, lifetimes which are the fundamental property of a decaying state, have so far escaped a similarly comprehensive understanding. Here we show that a bound state, despite being resonantly coupled to a scattering state, becomes protected from decay whenever the relative phase is a multiple of $\pi$. We observe this phenomenon by measuring lifetimes spanning four orders of magnitude for FFR of spin-orbit excited molecular ions with merged beam and electrostatic trap experiments. Our results provide a blueprint for identifying naturally long-lived states in a decaying quantum system.