The recent realization of topological phases in insulators and superconductors has advanced the search for robust quantum technologies. The prospect to implement the underlying topological features controllably has given incentive to explore optical platforms for analogous realizations. Here we realize a topologically induced defect state in a chain of dielectric microwave resonators and show that the functionality of the system can be enhanced by supplementing topological protection with non-hermitian symmetries that do not have an electronic counterpart. We draw on a characteristic topological feature of the defect state, namely, that it breaks a sublattice symmetry. This isolates the state from losses that respect parity-time symmetry, which enhances its visibility relative to all other states both in the frequency and in the time domain. This mode selection mechanism naturally carries over to a wide range of topological and parity-time symmetric optical platforms, including couplers, rectifiers and lasers.

Topological physics provides a robust framework for strategically controlling wave confinement and propagation dynamics. However, current implementations have been restricted to the limited design parameter space defined by passive topological structures. Active systems provide a more general framework where different fundamental symmetry paradigms, such as those arising from non-Hermiticity and nonlinear interaction, can generate a new landscape for topological physics and its applications. Here, we bridge this gap and present an experimental investigation of an active topological photonic system, demonstrating a topological hybrid silicon microlaser array respecting the charge-conjugation symmetry. The created new symmetry features favour the lasing of a protected zero mode, where robust single-mode laser action in the desired state prevails even with intentionally introduced perturbations. The demonstrated microlaser is hybrid implemented on a silicon-on-insulator substrate, and is thereby readily suitable for integrated silicon photonics with applications in optical communication and computing.

We show that topologically protected defect states can exist in open (leaky or lossy) systems even when these systems are topologically trivial in the closed limit. The states appear from within the continuum, thus in the absence of a band gap, and are generated via exceptional points (a spectral transition that occurs in open wave and quantum systems with a generalized time-reversal symmetry), or via a degeneracy induced by charge-conjugation symmetry (which is related to the pole transition of Majorana zero modes). We demonstrate these findings for a leaking passive coupled-resonator optical waveguide with asymmmetric internal scattering, where the required symmetries (non-Hermitian versions of time-reversal symmetry, chirality, and charge conjugation) emerge dynamically.

One of the principal goals in the design of photonic crystals is the engineering of band gaps and defect states. Here I describe the formation of topologically protected localized midgap states in systems with spatially distributed gain and loss. These states can be selectively amplified, which finds applications in the beam dynamics along a photonic lattice and in the lasing of quasi-one-dimensional photonic crystals.

We show that the one-particle density matrix $\rho$ can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of $\rho$) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues of $\rho$) reveals the distinctive Fock-space structure of the many-body eigenstates, exhibiting a steplike discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition. We analyze the inverse participation ratio of the natural orbitals and find that it is independent of system size in the localized phase.

We show that weak antilocalization by disorder competes with resonant Andreev reflection from a Majorana zero mode to produce a zerovoltage conductance peak of order e 2 / h in a superconducting nanowire. The phase conjugation needed for quantum interference to survive a disorder average is provided by particle-hole symmetry-in the absence of timereversal symmetry and without requiring a topologically nontrivial phase. We identify methods of distinguishing the Majorana resonance from the weak antilocalization effect.