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The conventional implementation of parity-time symmetry relies on the interplay of gain and loss. Here, Bentzien et al. present a novel approach towards non-Hermiticity that leverages nonorthogonal modes in coupled waveguides explicitly avoiding the use of either gain or loss.

Bloch oscillations consist of periodic spreading and relocalization of particle wave functions, but have been so far observed only in separable states. Here the authors observe them for two-photon N00N states in integrated photonic circuits, revealing transitions from particle bunching to anitbunching.

Vanishing Chern numbers usually mean that a system is topologically trivial, but this rule may be violated for periodically driven systems. Here, Maczewskyet al.report topologically protected edge modes in a periodically driven photonic lattice with all bands of zero Chern number.

In its optical manifestation, supersymmetry can potentially establish close relationships between seemingly different dielectric structures. Here, the authors use the perfect global phase matching afforded by supersymmetry for mode conversion and mode division multiplexing in highly multimoded systems.

Single-photon W-states — coherent superpositions of all qubits with equal probability amplitudes — involving up to 16 spatial modes are generated by means of evanescently-coupled waveguide technology. A scheme capable of exploiting the maximal entanglement of W-states is proposed for the efficient generation of random numbers.

The efficiency of coherent transport can be enhanced through interaction between the system and a noisy environment. Here, Biggerstaff et al. report an experimental simulation of environment assisted coherent transport using laser-written waveguides, showing that controllable decoherence yields an increase in transport efficiency.

To date, experimental demonstrations of PT-symmetric systems have been restricted to one dimension. Here, the authors experimentally realize and characterize a two-dimensional PT-symmetric system using photonic lattice waveguides with judiciously designed refractive index landscape and an alternating loss distribution.

Topological insulators are characterized by quantized topological invariants. Here, the authors report an insulator state showing spectral bands without quantized indices, yet robust boundary states in a photonic setup.

The propagation of light in photonic crystals with a honeycomb structure mirrors the behaviour of charges in graphene, therefore allowing for the investigation of electronic properties that cannot otherwise be accessed in graphene itself. This approach is now used to predict unexpected edge states that localize in the bearded edges of hexagonal lattices.

Magnetic effects are fundamentally weak at optical frequencies. Now, by applying inhomogeneous strain in photonic band structures of a honeycomb lattice of waveguides, scientists show experimentally and theoretically that it is possible to induce a pseudomagnetic field at optical frequencies. The field yields 'photonic Landau levels', which suggests the possibility of achieving greater field enhancements and slow-light effects in aperiodic photonic crystal structures than those available in periodic structures.

The authors propose a non-Hermitian topological insulator with a real-valued energy spectrum based on a periodically driven Floquet model implemented in a photonic platform where generalized parity–time symmetry is protected against spontaneous symmetry breaking under a spatiotemporal gain and loss distribution.

Combining space topology and time topology, topological states that are localized simultaneously in space and time are theoretically and experimentally demonstrated, potentially enabling the space-time topological shaping of light waves with applications in spatiotemporal wave control for imaging, communications and topological lasers.

Transport of particles in the presence of disorder is of interest for applications in electronics as well as photonics. Here the authors show theoretically and experimentally that based on dissipation alone, transport of light undergoes a change from ballistic to diffusive transport even in the absence of disorder.

Counter-propagating chiral edge states are demonstrated in a photonic structure able to effectively incorporate fermionic time-reversal symmetry, thus providing the photonic implementation of an electronic topological insulator.

Parity–time symmetry in second quantization is demonstrated in an integrated non-Hermitian coupled waveguide structure. A counterintuitive shift of the position of the Hong–Ou–Mandel dip is observed in integrated lossy waveguide structures.

Disorder in arrays of evanescently coupled waveguides turns out to have unexpected consequences on the photon number statistics of coherent light.

A clever approach has been used to imprint a phase pattern on a laser beam. The pattern is not only random at each point, but also depends on information stored elsewhere in the pattern.

Topologically protected bound states in parity–time-symmetric non-Hermitian photonic lattices are theoretically predicted and experimentally demonstrated.

Fourier analysis has become a standard tool in contemporary science. Here, Weimann et al. report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform, with potential applications in integrated quantum computation.

The nonlinear properties of photonic topological insulators remain largely unexplored, as band topology is linked to linear systems. But nonlinear topological corner states and solitons can form in a second-order topological insulator, as shown by experiments.

A triple phase transition, where changing a single parameter simultaneously gives rise to metal–insulator, topological and a parity–time symmetry-breaking phase transitions, is observed in non-Hermitian Floquet quasicrystals.

Non-Abelian braiding, an essential process for realizing topological quantum computation, is implemented using an array of photonic integrated waveguides.

The behaviour of multi-dimensional excitation dynamics and localization transition is synthesized in one-dimensional lattices formed by planar photonic structures.

Photonic waveguides with appropriately engineered interactions allow the experimental realization of non-Abelian quantum holonomies of the symmetry group U(3), which is known from the strong nuclear force.

Polarization-dependent losses shape Hong–Ou–Mandel interference of photon pairs in birefringent waveguides. Seamless tunability of indistinguishable photon coincidences, all the way from enhancement to full suppression, is enabled by an appropriate choice of the observation basis.

An optical thermodynamic framework can describe the complex dynamics in highly multimodal systems. Now, the observation of all-optical Joule–Thompson expansion in an optical gas further validates this thermodynamic approach.

Departing from common approaches to designing Floquet topological insulators, here the authors present a photonic realization of Floquet topological insulators revealing topological phases that simultaneously support Chern and anomalous topological states.

The broadening of a wave-packet can be suppressed as it propagates through a periodic potential. The first-order effect of this so-called dynamic localization has been seen in many different systems. Higher-order effects are now seen for the first time in an optical pulse guided along curved photonic lattices.

An experimental realization of a photonic topological insulator is reported that consists of helical waveguides arranged in a honeycomb lattice; the helicity provides a symmetry-breaking effect, leading to optical states that are topologically protected against scattering by disorder.

The boson-sampling problem is experimentally solved by implementing Aaronson and Arkhipov's model of computation with photons in integrated optical circuits. These results set a benchmark for a type of quantum computer that can potentially outperform a conventional computer by using only a few photons and linear optical elements.

By introducing a further modal dimension to transform a two-dimensional photonic waveguide array, a photonic topological insulator with protected topological surface states in three dimensions, enabled by a screw dislocation, is demonstrated.

The electrons in 2D materials like graphene are described by the relativistic Dirac equation. Here the authors present a lattice of evanescently coupled waveguides that emulates a wide range of Dirac excitations and study the type-II edge states that emerge in this photonic system.

Photonic lattices provide a useful platform for simulating quantum dynamics and systems. Keil et al.fabricate coupled waveguides on-chip and use them to simulate the one-dimensional random mass Dirac model, a test-bed for both Dirac fermions and antiferromagnetic spin systems.

Experimental and theoretical results of wave propagation in a disordered system with non-Hermitian disorder are presented, showing that wave spreading occurs in the parameter regime where all eigenstates are expected to be localized.

A counter-intuitive state—known as a topological Anderson insulator—in which strong disorder leads to the formation of topologically protected rather than trivial states is realized in a photonic system.

Optical guiding by a synthetic gauge field is experimentally demonstrated through an array of evanescently coupled identical waveguides, opening the door to applications of artificial gauge fields in optical, microwave and acoustic systems and in cold atoms.

Although topological photonics has been an active field of research for some time, most studies still focus on the linear optical regime. This Perspective summarizes recent investigations into the nonlinear properties of discrete topological photonic systems.

A spatially oscillating two-dimensional waveguide array is used to realize a photonic topological insulator in synthetic dimensions with modal-space edge states, unidirectionality and robust topological protection.

Established to explain high-energy particle physics, supersymmetry has since been invoked to describe the interplay between symmetry and topology in numerous fields. Here, supersymmetric transformations are shown theoretically and experimentally to destroy and restore topology in a photonic crystal.

Synthetic optical materials have been recently employed as a powerful platform for the emulation of topological phenomena in wave physics. Topological phases offer exciting opportunities, not only for fundamental physics demonstrations, but also for practical technologies. Yet, their impact has so far been primarily limited to their claimed enhanced robustness. Here, we clarify the role of robustness in topological photonic systems, and we discuss how topological photonics may offer a wider range of important opportunities in science and for practical technologies, discussing emergent and exciting research directions.