Publications

Non-Hermitian (NH) lattice Hamiltonians display a unique kind of energy gap and ex- treme sensitivity to boundary conditions. Due to the NH skin effect, the separation between edge and bulk states is blurred and the (conventional) bulk-boundary corre- spondence is lost. Here, we restore the bulk-boundary correspondence for the most paradigmatic class of NH Hamiltonians, namely those with one complex band and with- out symmetries. We obtain the desired NH Hamiltonian from the mean-field evolution of driven-dissipative cavity arrays, in which NH terms—in the form of non-reciprocal hopping amplitudes, gain and loss—are explicitly modeled via coupling to (engineered and non-engineered) reservoirs. This approach removes the arbitrariness in the defini- tion of the topological invariant, as point-gapped spectra differing by a complex-energy shift are not treated as equivalent; the origin of the complex plane provides a common reference (base point) for the evaluation of the topological invariant. This implies that topologically non-trivial Hamiltonians are only a strict subset of those with a point gap and that the NH skin effect does not have a topological origin. We analyze the NH Hamil- tonians so obtained via the singular value decomposition, which allows to express the NH bulk-boundary correspondence in the following simple form: an integer value ν of the topological invariant defined in the bulk corresponds to |ν| singular vectors exponen- tially localized at the system edge under open boundary conditions, in which the sign of ν determines which edge. Non-trivial topology manifests as directional amplification of a coherent input with gain exponential in system size. Our work solves an outstanding problem in the theory of NH topological phases and opens up new avenues in topological photonics.

Nonreciprocity means that the transmission of a signal depends on its direction of propagation. Despite vastly different platforms and underlying working principles, the realizations of nonreciprocal transport in linear, time-independent systems rely on Aharonov–Bohm interference among several pathways and require breaking time-reversal symmetry. Here we extend the notion of nonreciprocity to unidirectional bosonic transport in systems with a time-reversal symmetric Hamiltonian by exploiting interference between beamsplitter (excitation-preserving) and two-mode-squeezing (excitation non-preserving) interactions. In contrast to standard nonreciprocity, this unidirectional transport manifests when the mode quadratures are resolved with respect to an external reference phase. Accordingly, we dub this phenomenon ‘quadrature nonreciprocity’. We experimentally demonstrate it in the minimal system of two coupled nanomechanical modes orchestrated by optomechanical interactions. Next, we develop a theoretical framework to characterize the class of networks exhibiting quadrature nonreciprocity based on features of their particle–hole graphs. In addition to unidirectionality, these networks can exhibit an even–odd pairing between collective quadratures, which we confirm experimentally in a four-mode system, and an exponential end-to-end gain in the case of arrays of cavities.