Non-reciprocal and topological quantum dissipative phases with trapped ions

We theoretically simulate topological dissipative phases in a one-dimensional chain of trapped ions through

their vibrational degrees of freedom. The existence of topologically non-trivial phases reveals the presence

of edge states that produce amplification of external fields and provide robustness against disorder. Although

topological features are rigorously defined just for large chains, we observe the inheritance of topological phases

on a dimer. In particular, this is reflected in the non-reciprocal response under an external field with dissipation

and in the normalized phonon number imbalance between the two ions. Apart from that, we discovered the presence of

Exceptional Points (EPs) in a regime without dissipation. We characterize the presence of these non-Hermitian EPs

through the dynamics of the system, observing a power-law behaviour of the coherences.

Eventually, we analyze larger chains where the system can be topologically classified attending to the discrete symmetries and characterized through

the winding number as a topological invariant. We take care of the system stability and explore a fundamental

application related to quantum sensing, claiming that topological phases enhance the scalability of the signal-

to-noise ratio with the number of ions.