Topological triple phase transition in non-Hermitian Floquet quasicrystals.

Phase transitions connect different states of matter and are often concomitant with the spontaneous breaking of symmetries. An important category of phase transitions is mobility transitions, among which is the well known Anderson localization1, where increasing the randomness induces a metal-insulator transition. The introduction of topology in condensed-matter physics2-4 lead to the discovery of topological phase transitions and materials as topological insulators5. Phase transitions in the symmetry of non-Hermitian systems describe the transition to on-average conserved energy6 and new topological phases7-9. Bulk conductivity, topology and non-Hermitian symmetry breaking seemingly emerge from different physics and, thus, may appear as separable phenomena. However, in non-Hermitian quasicrystals, such transitions can be mutually interlinked by forming a triple phase transition10. Here we report the experimental observation of a triple phase transition, where changing a single parameter simultaneously gives rise to a localization (metal-insulator), a topological and parity-time symmetry-breaking (energy) phase transition. The physics is manifested in a temporally driven (Floquet) dissipative quasicrystal. We implement our ideas via photonic quantum walks in coupled optical fibre loops11. Our study highlights the intertwinement of topology, symmetry breaking and mobility phase transitions in non-Hermitian quasicrystalline synthetic matter. Our results may be applied in phase-change devices, in which the bulk and edge transport and the energy or particle exchange with the environment can be predicted and controlled.

Spin-orbit microlaser emitting in a four-dimensional Hilbert space.

A step towards the next generation of high-capacity, noise-resilient communication and computing technologies is a substantial increase in the dimensionality of information space and the synthesis of superposition states on an N-dimensional (N > 2) Hilbert space featuring exotic group symmetries. Despite the rapid development of photonic devices and systems, on-chip information technologies are mostly limited to two-level systems owing to the lack of sufficient reconfigurability to satisfy the stringent requirement for 2(N - 1) degrees of freedom, intrinsically associated with the increase of synthetic dimensionalities. Even with extensive efforts dedicated to recently emerged vector lasers and microcavities for the expansion of dimensionalities1-10, it still remains a challenge to actively tune the diversified, high-dimensional superposition states of light on demand. Here we demonstrate a hyperdimensional, spin-orbit microlaser for chip-scale flexible generation and manipulation of arbitrary four-level states. Two microcavities coupled through a non-Hermitian synthetic gauge field are designed to emit spin-orbit-coupled states of light with six degrees of freedom. The vectorial state of the emitted laser beam in free space can be mapped on a Bloch hypersphere defining an SU(4) symmetry, demonstrating dynamical generation and reconfiguration of high-dimensional superposition states with high fidelity.

Reconfigurable refraction manipulation at synthetic temporal interfaces with scalar and vector gauge potentials.

Photonic gauge potentials, including scalar and vector ones, play fundamental roles in emulating photonic topological effects and for enabling intriguing light transport dynamics. While previous studies mainly focus on manipulating light propagation in uniformly distributed gauge potentials, here we create a series of gauge-potential interfaces with different orientations in a nonuniform discrete-time quantum walk and demonstrate various reconfigurable temporal-refraction effects. We show that for a lattice-site interface with the potential step along the lattice direction, the scalar potentials can yield total internal reflection (TIR) or Klein tunneling, while vector potentials manifest direction-invariant refractions. We also reveal the existence of penetration depth for the temporal TIR by demonstrating frustrated TIR with a double lattice-site interface structure. By contrast, for an interface emerging in the time-evolution direction, the scalar potentials have no effect on the packet propagation, while the vector potentials can enable birefringence, through which we further create a "temporal superlens" to achieve time-reversal operations. Finally, we experimentally demonstrate electric and magnetic Aharonov-Bohm effects using combined lattice-site and evolution-step interfaces of either scalar or vector potential. Our work initiates the creation of artificial heterointerfaces in synthetic time dimension by employing nonuniformly and reconfigurable distributed gauge potentials. This paradigm may find applications in optical pulse reshaping, fiber-optic communications, and quantum simulations.

Robust Anderson transition in non-Hermitian photonic quasicrystals.

Anderson localization, i.e., the suppression of diffusion in lattices with a random or incommensurate disorder, is a fragile interference phenomenon that is spoiled out in the presence of dephasing effects or a fluctuating disorder. As a consequence, Anderson localization-delocalization phase transitions observed in Hermitian systems, such as in one-dimensional quasicrystals when the amplitude of the incommensurate potential is increased above a threshold, are washed out when dephasing effects are included. Here we consider localization-delocalization spectral phase transitions occurring in non-Hermitian (NH) quasicrystals with local incommensurate gain and loss and show that, contrary to the Hermitian case, the non-Hermitian phase transition is robust against dephasing effects. The results are illustrated by considering synthetic quasicrystals in photonic mesh lattices.

Photonic random walks with traps.

Random walks (RW) behave very differently for classical and quantum particles. Here we unveil a ubiquitous distinctive behavior of random walks of a photon in a one-dimensional lattice in the presence of a finite number of traps, at which the photon can be destroyed and the walk terminates. While for a classical random walk, the photon is unavoidably destroyed by the traps. For a quantum walk, the photon can remain alive, and the walk continues forever. Such an intriguing behavior is illustrated by considering photonic random walks in synthetic mesh lattices with controllable decoherence, which enables the switch from quantum to classical random walks.

Photonic Mpemba effect.

The Mpemba effect (ME) is the counterintuitive phenomenon in statistical physics for which a far-from-equilibrium state can relax toward equilibrium faster than a state closer to equilibrium. This effect has raised great curiosity for a long time and has been studied extensively in many classical and quantum systems. Here, it is shown that the Mpemba effect can be observed in optics as well. Specifically, the process of light diffusion in finite-sized photonic lattices under incoherent (dephasing) dynamics is considered. Rather surprisingly, it is shown that certain highly localized initial light distributions can diffuse faster than initial broadly delocalized distributions. The effect is illustrated by considering the random walk of optical pulses in fiber-based temporal mesh lattices, which should provide an experimentally accessible setup for the demonstration of the Mpemba effect in optics.

Non-Hermitian dynamical topological winding in photonic mesh lattices.

Topological winding in non-Hermitian systems is generally associated to the Bloch band properties of lattice Hamiltonians. However, in certain non-Hermitian models, topological winding naturally arises from the dynamical evolution of the system and is related to a new form of geometric phase. Here we investigate dynamical topological winding in non-Hermitian photonic mesh lattices, where the mean survival time of an optical pulse circulating in coupled fiber loops is quantized and robust against Hamiltonian deformations. The suggested photonic model could provide an experimentally accessible platform for the observation of non-Hermitian dynamical topological windings.

Dephasing-Induced Mobility Edges in Quasicrystals.

Mobility edges (ME), separating Anderson-localized states from extended states, are known to arise in the single-particle energy spectrum of certain one-dimensional lattices with aperiodic order. Dephasing and decoherence effects are widely acknowledged to spoil Anderson localization and to enhance transport, suggesting that ME and localization are unlikely to be observable in the presence of dephasing. Here it is shown that, contrary to such a wisdom, ME can be created by pure dephasing effects in quasicrystals in which all states are delocalized under coherent dynamics. Since the lifetimes of localized states induced by dephasing effects can be extremely long, rather counterintuitively decoherence can enhance localization of excitation in the lattice. The results are illustrated by considering photonic quantum walks in synthetic mesh lattices.

Temporal Goos-Hänchen Shift in Synthetic Discrete-Time Heterolattices.

Experimental demonstration of tunable temporal Goos-Hänchen shift (GHS) in synthetic discrete-time heterolattices with scalar and vector gauge potentials is reported. By using Heaviside-function modulation in two fiber loops, we create a sharp gauge-potential interface and observe temporal GHS for total internal reflection (TIR), which manifests as a time delay rather than a spatial shift. The TIR occurs as the incident mode falls into the band gap of transmitted region with band shifting by scalar and vector potential. We find that both scalar and vector potential codetermine GHS by controlling the decay (imaginary part) and oscillation (real part) of a penetrated evanescent wave, in stark contrast to traditional spatial GHS only determined by the decay factor. We also observe diverging characteristics of GHS at band-gap edges where evanescent-to-propagating wave transition occurs. GHS for frustrated total internal reflection (FTIR) by a finite-width evanescent barrier is also demonstrated, which shows saturation properties to the single-interface TIR case under infinite-width limit. Finally, we develop an accumulation measurement method using multiple TIRs to improve the precision for measuring even tinier GHS. The study initiates precise measurement of temporal GHS for discrete-time reflections, which may feature potential applications in precise time-delay control and measurement.

Delocalization of light in photonic lattices with unbounded potentials.

In classical mechanics, a particle cannot escape from an unbounded potential well. Naively, one would expect a similar result to hold in wave mechanics, since high barriers make tunneling difficult. However, this is not always the case, and it is known that wave delocalization can arise in certain models with incommensurate unbounded potentials sustaining critical states, i.e., states neither fully extended nor fully localized. Here we introduce a different and broader class of unbounded potentials, which are not quasiperiodic and do not require any specially tailored shape, where wave delocalization is observed. The results are illustrated by considering light dynamics in synthetic photonic lattices, which should provide a feasible platform for the experimental observation of wave delocalization in unbounded potentials.

Inhibition of non-Hermitian topological phase transitions in sliding photonic quasicrystals.

Non-Hermitian (NH) quasicrystals have been a topic of increasing interest in current research, particularly in the context of NH topological physics and materials science. Recently, it has been suggested and experimentally demonstrated using synthetic photonic lattices that a class of NH quasicrystals can feature topological spectral phase transitions. Here we consider a NH quasicrystal with a uniformly-drifting (sliding) incommensurate potential and show that, owing to violation of Galilean invariance, the topological phase transition is washed out and the quasicrystal is always in the delocalized phase with an entirely real-energy spectrum. The results are illustrated by considering quantum walks in synthetic photonic lattices.

Anderson localization without eigenstates in photonic quantum walks.

Anderson localization is ubiquitous in wavy systems with strong static and uncorrelated disorder. The delicate destructive interference underlying Anderson localization is usually washed out in the presence of temporal fluctuations or aperiodic drives in the Hamiltonian, leading to delocalization and restoring transport. However, in one-dimensional lattices with off diagonal disorder, Anderson localization can persist for arbitrary time-dependent drivings that do not break a hidden conservation law originating from the chiral symmetry, leading to the dubbed "localization without eigenstates." Here it is shown that such an intriguing phenomenon can be observed in discrete-time photonic quantum walks with static disorder applied to the coin operator and can be extended to non-Hermitian dynamics as well.

Accelerating Quantum Decay by Multiple Tunneling Barriers.

A quantum particle constrained between two high potential barriers provides a paradigmatic example of a system sustaining quasi-bound (or resonance) states. When the system is prepared in one of such quasi-bound states, the wave function approximately maintains its shape but decays in time in a nearly exponential manner radiating into the surrounding space, the lifetime being of the order of the reciprocal of the width of the resonance peak in the transmission spectrum. Naively, one could think that adding more lateral barriers would preferentially slow down or prevent the quantum decay since tunneling is expected to become less probable and due to quantum backflow induced by multiple scattering processes. However, this is not always the case and in the early stage of the dynamics quantum decay can be accelerated (rather than decelerated) by additional lateral barriers, even when the barrier heights are arbitrarily large. The decay acceleration originates from resonant tunneling effects and is associated to large deviations from an exponential decay law. We discuss such a counterintuitive phenomenon by considering the hopping dynamics of a quantum particle on a tight-binding lattice with on-site potential barriers.

Non-Hermitian laser arrays with tunable phase locking.

Inspired by the idea of non-Hermitian spectral engineering and non-Hermitian skin effect, a novel, to the best of our knowledge, design for stable emission of coupled laser arrays with tunable phase locking and strong supermode competition suppression is suggested. We consider a linear array of coupled resonators with asymmetric mode coupling displaying the non-Hermitian skin effect and show that, under suitable tailoring of complex frequencies of the two edge resonators, the laser array can stably emit in a single extended supermode with tunable phase locking and with strong suppression of all other skin supermodes. The proposed laser array design offers strong robustness against both structural imperfections of the system and dynamical instabilities typical of semiconductor laser arrays.

Non-Hermitian topological mobility edges and transport in photonic quantum walks.

In non-Hermitian quasicrystals, mobility edges (ME) separating localized and extended states in the complex energy plane can arise as a result of non-Hermitian terms in the Hamiltonian. Such ME are of topological nature, i.e., the energies of localized and extended states exhibit distinct topological structures in the complex energy plane. However, depending on the origin of non-Hermiticity, i.e., asymmetry of hopping amplitudes or complexification of the incommensurate potential phase, different winding numbers are introduced, corresponding to different transport features in the bulk of the lattice: while ballistic transport is allowed in the former case, pseudo-dynamical localization is observed in the latter case. The results are illustrated by considering non-Hermitian photonic quantum walks in synthetic mesh lattices.

Non-Hermitian Bloch-Zener phase transition.

Bloch-Zener oscillations (BZO), i.e., the interplay between Bloch oscillations and Zener tunneling in two-band lattices under an external direct current (DC) force, are ubiquitous in different areas of wave physics, including photonics. While in Hermitian systems such oscillations are rather generally aperiodic and only accidentally periodic, in non-Hermitian (NH) lattices BZO can show a transition from aperiodic to periodic as a NH parameter in the system is varied. Remarkably, the phase transition can be either smooth or sharp, contrary to other types of NH phase transitions which are universally sharp. A discrete-time photonic quantum walk on a synthetic lattice is suggested for an experimental observation of smooth BZO phase transitions.

Self-Healing of Non-Hermitian Topological Skin Modes.

A unique feature of non-Hermitian (NH) systems is the NH skin effect, i.e., the edge localization of an extensive number of bulk-band eigenstates in a lattice with open or semi-infinite boundaries. Unlike extended Bloch waves in Hermitian systems, the skin modes are normalizable eigenstates of the Hamiltonian that originate from the intrinsic non-Hermitian point-gap topology of the Bloch band energy spectra. Here, we unravel a fascinating property of NH skin modes, namely self-healing, i.e., the ability to self-reconstruct their shape after being scattered off by a space-time potential.

Aharonov-Bohm Caging and Inverse Anderson Transition in Ultracold Atoms.

Aharonov-Bohm (AB) caging, a special flat-band localization mechanism, has spurred great interest in different areas of physics. AB caging can be harnessed to explore the rich and exotic physics of quantum transport in flatband systems, where geometric frustration, disorder, and correlations act in a synergetic and distinct way than that in ordinary dispersive band systems. In contrast to the ordinary Anderson localization, where disorder induces localization and prevents transport, in flat band systems disorder can induce mobility, a phenomenon dubbed inverse Anderson transition. Here, we report on the experimental realization of the AB cage using a synthetic lattice in the momentum space of ultracold atoms with tailored gauge fields, and demonstrate the geometric localization due to the flat band and the inverse Anderson transition when correlated binary disorder is added to the system. Our experimental platform in a many-body environment provides a fascinating quantum simulator where the interplay between engineered gauge fields, localization, and topological properties of flat band systems can be finely explored.

Bulk-edge correspondence and trapping at a non-Hermitian topological interface.

In Hermitian systems, according to the bulk-edge correspondence, interfacing two topological optical media with different bulk topological numbers implies the existence of edge states, which can trap light at the interface. However, such a general scenario can be violated when dealing with non-Hermitian systems. Here we show that interfacing two semi-infinite Hatano-Nelson chains with different bulk topological numbers can result in the existence of infinitely many edge (interface) states; however, light waves cannot be rather generally trapped at the interface.

Rabi oscillations of bound states in the continuum.

Photonic bound states in the continuum (BICs) are special localized and non-decaying states of a photonic system with a frequency embedded into the spectrum of scattered states. The simplest photonic structure displaying a single BIC is provided by two waveguides side-coupled to a common waveguide lattice, where the BIC is protected by symmetry. Here we consider such a simple photonic structure and show that by breaking mirror symmetry and allowing for non-nearest neighbor couplings, a doublet of quasi-BIC states can be sustained, enabling weakly damped embedded Rabi oscillations of photons between the waveguides.