Collective Dissipation and Parameter Sensitivity in Trapped Ions Coupled to a Common Thermal Reservoir

TL;DR

This paper explores how a common thermal reservoir causes collective dissipation and affects the dynamics, entanglement, and parameter estimation in two trapped ions, revealing conditions for decoherence-free modes and enhanced measurement sensitivity.

Contribution

It derives a microscopic model showing reservoir-induced correlations lead to collective decay channels and decoherence-free modes, with implications for entanglement and parameter estimation in trapped ions.

Findings

Reservoir-induced correlations generate collective decay channels.

Matching cross-damping and local damping creates a decoherence-free mode.

Cross-damping enhances the estimability of system and reservoir parameters.

Abstract

We investigate the dynamics of two trapped ions interacting with a common thermal reservoir, focusing on how cross-correlated dissipation influences heating, steady-state behavior, and parameter sensitivity. Starting from a microscopic system--reservoir model, we derive the corresponding Heisenberg--Langevin equations and show that reservoir-induced correlations generate collective decay channels and, when the cross-damping rate matches the local damping, a decoherence-free normal mode that preserves memory of the initial excitations. Using the Fisher information associated with motional population measurements, we identify the parameter regimes in which cross-damping enhances the estimability of both system and reservoir properties. For nonclassical initial states, we also show that reservoir-mediated correlations can generate or maintain entanglement, with the strongest effects occurring near the decoherence-free condition.