Quantum theory for phonon lasing and non-classical state generation in mixed-species and single trapped ions

TL;DR

This paper provides a comprehensive quantum theoretical analysis of phonon lasing in trapped ions, proposing new single-ion schemes and exploring non-classical states for enhanced sensing.

Contribution

It introduces a novel single-ion phonon lasing approach and analyzes non-classical state generation with potential for improved quantum sensing.

Findings

Confirmed lasing behavior above threshold through second-order coherence

Proposed a single-ion phonon lasing scheme with experimental advantages

Demonstrated up to two orders of magnitude sensitivity enhancement in sensing

Abstract

In this article we present a comprehensive theoretical investigation of phonon lasing with mixed-species trapped ions, as demonstrated in [T. Behrle, Phys. Rev. Lett. 131 (2023)], employing both a semi-classical mean-field description and a full quantum theory. We derive an analytic expression for the second-order coherence function, confirming the experimental observation of the system's lasing behaviour above threshold. Building on the successful implementation of the two-ion lasing scheme, we propose a novel approach for achieving phonon lasing with a single trapped ion, offering significant experimental advantages and making the implementation of multiple phonon lasers within a single setup feasible. Furthermore, we explore lasing in a squeezed basis and in different regimes of the Lamb-Dicke approximation, highlighting the potential to produce non-classical states with promising applications in precision sensing. Our analysis of a sensing protocol based on squeezed states, using experimentally feasible parameters, shows a sensitivity enhancement of up to two orders of magnitude.