Publications of Miguel Clavero-Rubio

Driven-dissipative quantum systems can exhibit robust transport and amplification in topological regimes, yet the connection between topology and the extent of correlations remains largely unexplored. In this work, we develop a general framework that links topological phases in driven-dissipative systems to bosonic correlations via the singular value decomposition (SVD). In essence, we claim that non-Hermitian topology in quadratic Liouvillians is directly encoded in steady-state correlations, providing an intrinsic characterization of topology without external probes. We show that topological amplification induces disorder-robust long-range order (LRO) in steady-state correlations at fixed frequency, establishing frequency-resolved correlations as direct signatures of non-Hermitian topological phases. We introduce a vector-valued topological invariant that captures the total number of singular-value gap closings across the frequency axis, extending the concept of adiabatic deformation from topological insulators to the case of topological phases of quadratic Liouvillians. Within this framework, we further demonstrate that the spatial structure of equal-time correlations encodes global topological information, manifested as a Gaussian spatial decay with distance in the topological phase, in contrast to the exponential decay characteristic of trivial phases. These findings open new avenues for quantum sensing and correlation engineering in non-Hermitian systems, with feasible implementations in platforms such as trapped ions and superconducting circuits.

We consider a linear array of trapped ions subjected to local parametric modulation of the trapping potential and continuous laser cooling. In our model, the phase of the parametric modulation varies linearly along the array, breaking time-reversal symmetry and inducing non-trivial topological effects. The linear response to an external force is investigated with the Green’s function formalism. We predict the appearance of topological amplification regimes in which the trapped ion array behaves as a directional amplifier of vibrational excitations. The emergence of topological phases is determined by a winding number related to non-Hermitian point-gap topology. Beyond its fundamental interests as a topological driven-dissipative system, our setup can be used for quantum sensing of ultra-weak forces and electric fields. We consider a scheme in which a trapped ion at one edge of the array acts as a sensor of an ultra-weak force, and the vibrational signal gets amplified towards the last trapped ion, which acts as a detector. We consider arrays of 2-30 $^{25}$Mg$^+$ ions, assuming that the detector ion’s displacement is measured via fluorescence with a spatial resolution of 200-500 nm, and predict sensitivities as small as 1 yN $\cdot$ Hz$^{-1/2}$. Our system has the advantage that the detected force frequency can be tuned by adjusting the frequency of the periodic drive.