We study the performance of a single qubit-laser as a quantum sensor to measure the amplitude and phase of a driving field. By using parameter estimation theory we show that certain suitable field quadratures are optimal observables in the lasing phase. The quantum Fisher information scales linearly with the number of bosons and thus the precision can be enhanced by increasing the incoherent pumping acting on the qubit. If we restrict ourselves to measurements of the boson number observable, then the optimal operating point is the critical point of the lasing phase transition. Our results point out to an intimate connection between symmetry breaking, dissipative phase transitions and efficient parameter estimation.

We characterize topological phases in photonic lattices by unveiling a formal equivalence between the singular value decomposition of the non-Hermitian coupling matrix and the diagonalization of an effective Hamiltonian. Our theory reveals a relation between topological insulators and directional amplifiers. We exemplify our ideas with an array of photonic cavities which can be mapped into an AIII topological insulator. We investigate stability properties and prove the existence of stable topologically non-trivial steady-state phases. Finally, we show numerically that the topological amplification process is robust against disorder in the lattice parameters.

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Topological insulating phases are primarily associated with condensed-matter systems, which typically feature short-range interactions. Nevertheless, many realizations of quantum matter can exhibit long-range interactions, and it is still largely unknown the effect that these latter may exert upon the topological phases. In this Letter, we investigate the Su-Schrieffer-Heeger topological insulator in the presence of long-range interactions. We show that this model can be readily realized in quantum simulators with trapped ions by means of a periodic driving. Our results indicate that the localization of the associated edge states is enhanced by the long-range interactions, and that the localized components survive within the ground state of the model. These effects could be easily confirmed in current state-of-the-art experimental implementations.Introduction.-Topological phases are one of the most exotic forms of quantum matter. Among their many intriguing traits, we find that they are robust against local decoherence processes, or feature fractional particle excitations with prospective applications in quantum information processing [1, 2]. Some of the simplest systems showcasing non-trivial topological order are the topological insulators [3][4][5][6], gapped phases of non-interacting fermions which present gapless edge states. Despite of several experimental realizations [7, 8], the preparation and measurement of topological insulators is typically difficult in the solid state. Analog quantum simulators [5, 9-12, 14, 15], on the other hand, offer the possibility of exploring and exploiting the topological insulating phases, because of their inherent high degree of controllability. Furthermore, interactions in a quantum simulator can be tuned at will, opening up the possibility of investigating new regimes of the underlying models.Topological edge states usually occur in the insulating phase as long as an associated bulk invariant attains a nontrivial value, and the generic symmetries of the underlying Hamiltonian are preserved [16]. This property -known as the bulk-edge correspondence-is a generic feature of topological insulators. However, if interactions are taken into account, the presence of edge states is no longer guaranteed. For instance, it has been shown that one of the edge states present in the Mott insulating phase of the Bose-Hubbard model on a 1D superlattice is not stable against tunneling [17]. In this work, we extend these considerations to the case of interactions which are explicitly long ranged. Since topological phases are characteristically robust against local perturbations, but longrange interactions may not qualify as such, there is an ongoing effort to elucidate their effect upon the topological states [18][19][20]. This question is not of exclusive theoretical interest, since many experimental systems implementing topological phases of matter feature long-range interactions. In particular, we will show that trapped-ion quantum simulators can realize a long-range interacting version...

The Heisenberg scaling is typically associated with nonclassicality and entanglement. In this work, however, we discuss how classical long-range correlations between lattice sites in many-body systems may lead to a 1/N scaling in precision with the number of probes in the context of quantum optical dissipative systems. In particular, we show that networks of coupled single qubit lasers can be mapped onto a classical XY model, and a Heisenberg scaling with the number of sites appears when estimating the amplitude and phase of a weak periodic driving field. arXiv:1708.09361v2 [quant-ph]