  Zeros of partition functions, in particular Lee-Yang zeros, in a complex
plane provide important information for understanding phase transitions. A
recent discovery on the equivalence between the coherence of a central quantum
system and the partition function of the environment in the complex plane
enabled the experimental study of Lee-Yang zeros, with several pioneering
experiments on spin systems. Lee-Yang zeros have not been observed in Bosonic
systems. Here we propose an experimental scheme to demonstrate Lee-Yang zeros
in Bosonic systems associated with a single trapped ion by introducing strong
coupling between the spin and motion degrees of freedom, i.e. beyond the weak
coupling Lamb-Dicke regime. Our scheme provides new possibilities for quantum
simulation of the thermodynamics of Bosonic systems in the complex plane.
