Localized and delocalized topological modes of heat

The topological physics has sparked intensive investigations into topological lattices in photonic, acoustic, and mechanical systems, powering counterintuitive effects otherwise inaccessible with usual settings. Following the success of these endeavors in classical wave dynamics, there has been a growing interest in establishing their topological counterparts in diffusion. Here, we propose an additional real-space dimension in diffusion, and the system eigenvalues are transformed from "imaginary" to "real." By judiciously tailoring the effective Hamiltonian with coupling networks, localized and delocalized topological modes are realized in heat transfer. Simulations and experiments in active thermal lattices validate the effectiveness of the proposed theoretical strategy. This approach can be applied to establish various topological lattices in diffusion systems, offering insights into engineering topologically protected edge states in dynamic diffusive scenarios.

Topological Anderson phases in heat transport

Topological Anderson phases (TAPs) offer intriguing transitions from ordered to disordered systems in photonics and acoustics. However, achieving these transitions often involves cumbersome structural modifications to introduce disorders in parameters, leading to limitations in flexible tuning of topological properties and real-space control of TAPs. Here, we exploit disordered convective perturbations in a fixed heat transport system. Continuously tunable disorder-topology interactions are enabled in thermal dissipation through irregular convective lattices. In the presence of a weak convective disorder, the trivial diffusive system undergos TAP transition, characterized by the emergence of topologically protected corner modes. Further increasing the strength of convective perturbations, a second phase transition occurs converting from TAP to Anderson phase. Our work elucidates the pivotal role of disorders in topological heat transport and provides a novel recipe for manipulating thermal behaviors in diverse topological platforms.

Ultrafast Unidirectional On-Chip Heat Transfer

Effective and rapid heat transfer is critical to improving electronic components' performance and operational stability, particularly for highly integrated and miniaturized devices in complex scenarios. However, current thermal manipulation approaches, including the recent advancement in thermal metamaterials, cannot realize fast and unidirectional heat flow control. In addition, any defects in thermal conductive materials cause a significant decrease in thermal conductivity, severely degrading heat transfer performance. Here, the utilization of silicon-based valley photonic crystals (VPCs) is proposed and numerically demonstrated to facilitate ultrafast, unidirectional heat transfer through thermal radiation on a microscale. Utilizing the infrared wavelength region, the approach achieves a significant thermal rectification effect, ensuring continuous heat flow along designed paths with high transmission efficiency. Remarkably, the process is unaffected by temperature gradients due to the unidirectional property, maintaining transmission directionality. Furthermore, the VPCs' inherent robustness affords defect-immune heat transfer, overcoming the limitations of traditional conduction methods that inevitably cause device heating, performance degradation, and energy waste. The design is fully CMOS compatible, thus will find broad applications, particularly for integrated optoelectronic devices.

Dynamical encircling of multiple exceptional points in anti-PT symmetry system

Exceptional points (EPs) in non-Hermitian systems have turned out to be at the origin of many intriguing effects with no counterparts in Hermitian cases. A typically interesting behavior is the chiral mode switching by dynamically winding the EP. Most encircling protocols focus on the two-state or parity-time (PT) symmetry systems. Here, we propose and investigate the dynamical encircling of multiple EPs in an anti-PT-symmetric system, which is constructed based on a one-dimensional lattice with staggered lossy modulation. We reveal that dynamically encircling the multiple EPs results in the chiral dynamics via multiple non-Hermiticity-induced nonadiabatic transitions, where the output state is always on the lowest-loss energy sheet. Compared with the PT-symmetric systems that require complicated variation of the gain/loss rate or on-site potentials, our system only requires modulations of the couplings which can be readily realized in various experimental platforms. Our scheme provides a route to study non-Hermitian physics by engineering the EPs and implement novel photonic devices with unconventional functions.

Chiral photon blockade in the spinning Kerr resonator

We propose how to achieve chiral photon blockade by spinning a nonlinear optical resonator. We show that by driving such a device at a fixed direction, completely different quantum effects can emerge for the counter-propagating optical modes, due to the spinning-induced breaking of time-reversal symmetry, which otherwise is unattainable for the same device in the static regime. Also, we find that in comparison with the static case, robust non-classical correlations against random backscattering losses can be achieved for such a quantum chiral system. Our work, extending previous works on the spontaneous breaking of optical chiral symmetry from the classical to purely quantum regimes, can stimulate more efforts towards making and utilizing various chiral quantum effects, including applications for chiral quantum networks or noise-tolerant quantum sensors.

Tunable spin splitting of reflected Laguerre-Gaussian beams on controllable metamaterials with anti-PT symmetry

The intriguing photonic spin Hall effect (PSHE) of reflected Laguerre-Gaussian (LG) beams can be exhibited on the systems with optical anti-parity-time (Anti-PT) symmetry. During the reflection, the left/right circularly polarized (LCP/RCP) components of reflected LG beams are considered. By controlling parameters of the Anti-PT systems, the PSHE of reflected LCP/RCP can be identical and symmetrical with respect to incident-reflected plane (IRP). Due to gain/non-Hermitian effects of designed Anti-PT systems, special PSHE near the strong gain points (SGP) and exceptional points (EPs) can be obtained simulatively. Through analyses in PSHE of reflected LCP on four similar Anti-PT systems, specific conclusions that can even be extended to more general cases. Moreover, simulations of PSHE by simultaneously varying the incident angles * and imaginary/real dielectric constants Im/Re[ε] of the Anti-PT systems, specal PSHE and other novel optical phenomena with real applications can be revealed. So Anti-PT systems not only provide novel ways to regulate the PSHE of reflected LG beams, but also offer possibilities for new optical characteristics of devices.

Observation of non-Hermitian skin effect in thermal diffusion

The paradigm shift of Hermitian systems into the non-Hermitian regime profoundly modifies inherent property of the topological systems, leading to various unprecedented effects such as the non-Hermitian skin effect (NHSE). In the past decade, the NHSE has been demonstrated in quantum, optical and acoustic systems. Beside those wave systems, the NHSE in diffusive systems has not yet been observed, despite recent abundant advances in the study of topological thermal diffusion. In this work, we design a thermal diffusion lattice based on a modified Su-Schrieffer-Heeger model and demonstrate the diffusive NHSE. In the proposed model, the asymmetric temperature field coupling inside each unit cell can be judiciously realized by appropriate configurations of structural parameters. We find that the temperature fields trend to concentrate toward the target boundary which is robust against initial excitation conditions. We thus experimentally demonstrated the NHSE in thermal diffusion and verified its robustness against various defects. Our work provides a platform for exploration of non-Hermitian physics in the diffusive systems, which has important applications in efficient heat collection, highly sensitive thermal sensing and others.

Observation of parity-time symmetry in diffusive systems

Phase modulation has scarcely been mentioned in diffusive physical systems because the diffusion process does not carry the momentum like waves. Recently, non-Hermitian physics provides a unique perspective for understanding diffusion and shows prospects in thermal phase regulation, exemplified by the discovery of anti-parity-time (APT) symmetry in diffusive systems. However, precise control of thermal phase remains elusive hitherto and can hardly be realized, due to the phase oscillations. Here we construct the PT-symmetric diffusive systems to achieve the complete suppression of thermal phase oscillation. The real coupling of diffusive fields is readily established through a strong convective background, and the decay-rate detuning is enabled by thermal metamaterial design. We observe the phase transition of PT symmetry breaking with the symmetry-determined amplitude and phase regulation of coupled temperature fields. Our work shows the existence of PT symmetry in dissipative energy exchanges and provides unique approaches for harnessing the mass transfer of particles, wave dynamics in strongly scattering systems, and thermal conduction.

Experimental Demonstration of Controllable PT and Anti-PT Coupling in a Non-Hermitian Metamaterial

Non-Hermiticity has recently emerged as a rapidly developing field due to its exotic characteristics related to open systems, where the dissipation plays a critical role. In the presence of balanced energy gain and loss with environment, the system exhibits parity-time (PT) symmetry, meanwhile as the conjugate counterpart, anti-PT symmetry can be achieved with dissipative coupling within the system. Here, we demonstrate the coherence of complex dissipative coupling can control the transition between PT and anti-PT symmetry in an electromagnetic metamaterial. Notably, the achievement of the anti-PT symmetric phase is independent of variations in dissipation. Furthermore, we observe phase transitions as the system crosses exceptional points in both anti-PT and PT symmetric metamaterial configurations, achieved by manipulating the frequency and dissipation of resonators. This work provides a promising metamaterial design for broader exploration of non-Hermitian physics and practical application with a controllable Hamiltonian.

Machine Learning Aided Design and Optimization of Thermal Metamaterials

Artificial Intelligence (AI) has advanced material research that were previously intractable, for example, the machine learning (ML) has been able to predict some unprecedented thermal properties. In this review, we first elucidate the methodologies underpinning discriminative and generative models, as well as the paradigm of optimization approaches. Then, we present a series of case studies showcasing the application of machine learning in thermal metamaterial design. Finally, we give a brief discussion on the challenges and opportunities in this fast developing field. In particular, this review provides: (1) Optimization of thermal metamaterials using optimization algorithms to achieve specific target properties. (2) Integration of discriminative models with optimization algorithms to enhance computational efficiency. (3) Generative models for the structural design and optimization of thermal metamaterials.

Twisted moiré conductive thermal metasurface

Extensive investigations on the moiré magic angle in twisted bilayer graphene have unlocked the emerging field-twistronics. Recently, its optics analogue, namely opto-twistronics, further expands the potential universal applicability of twistronics. However, since heat diffusion neither possesses the dispersion like photons nor carries the band structure as electrons, the real magic angle in electrons or photons is ill-defined for heat diffusion, making it elusive to understand or design any thermal analogue of magic angle. Here, we introduce and experimentally validate the twisted thermotics in a twisted diffusion system by judiciously tailoring thermal coupling, in which twisting an analog thermal magic angle would result in the function switching from cloaking to concentration. Our work provides insights for the tunable heat diffusion control, and opens up an unexpected branch for twistronics -- twisted thermotics, paving the way towards field manipulation in twisted configurations including but not limited to fluids.

Deep Learning-Assisted Active Metamaterials with Heat-Enhanced Thermal Transport

Heat management is crucial for state-of-the-art applications such as passive radiative cooling, thermally adjustable wearables, and camouflage systems. Their adaptive versions, to cater to varied requirements, lean on the potential of adaptive metamaterials. Existing efforts, however, feature with highly anisotropic parameters, narrow working-temperature ranges, and the need for manual intervention, which remain long-term and tricky obstacles for the most advanced self-adaptive metamaterials. To surmount these barriers, heat-enhanced thermal diffusion metamaterials powered by deep learning is introduced. Such active metamaterials can automatically sense ambient temperatures and swiftly, as well as continuously, adjust their thermal functions with a high degree of tunability. They maintain robust thermal performance even when external thermal fields change direction, and both simulations and experiments demonstrate exceptional results. Furthermore, two metadevices with on-demand adaptability, performing distinctive features with isotropic materials, wide working temperatures, and spontaneous response are designed. This work offers a framework for the design of intelligent thermal diffusion metamaterials and can be expanded to other diffusion fields, adapting to increasingly complex and dynamic environments.

Nonreciprocal Heat Circulation Metadevices

Thermal nonreciprocity typically stems from nonlinearity or spatiotemporal variation of parameters. However, constrained by the inherent temperature-dependent properties and the law of mass conservation, previous works have been compelled to treat dynamic and steady-state cases separately. Here, by establishing a unified thermal scattering theory, the creation of a convection-based thermal metadevice which supports both dynamic and steady-state nonreciprocal heat circulation is reported. The nontrivial dependence between the nonreciprocal resonance peaks and the dynamic parameters is observed and the unique nonreciprocal mechanism of multiple scattering is revealed at steady state. This mechanism enables thermal nonreciprocity in the initially quasi-symmetric scattering matrix of the three-port metadevice and has been experimentally validated with a significant isolation ratio of heat fluxes. The findings establish a framework for thermal nonreciprocity that can be smoothly modulated for dynamic and steady-state heat signals, it may also offer insight into other heat-transfer-related problems or even other fields such as acoustics and mechanics.

Level pinning of anti-PT-symmetric circuits for efficient wireless power transfer

Wireless power transfer (WPT) technology based on magnetic resonance (a basic physical phenomenon) can directly transfer energy from the source to the load without wires and other physical contacts, and has been successfully applied to implantable medical devices, electric vehicles, robotic arms and other fields. However, due to the frequency splitting of near-field coupling, the resonant WPT system has some unique limitations, such as poor transmission stability and low efficiency. Here, we propose anti-resonance with level pinning for high-performance WPT. By introducing the anti-resonance mode into the basic WPT platform, we uncover the competition between dissipative coupling and coherent coupling to achieve novel level pinning, and construct an effective anti-parity-time (anti-PT)-symmetric non-Hermitian system that is superior to previous PT-symmetric WPT schemes. On the one hand, the eigenvalue of the anti-PT-symmetric system at resonance frequency is always pure real in both strong and weak coupling regions, and can be used to overcome the transmission efficiency decrease caused by weak coupling, as brought about by, for example, a large size ratio of the transmitter to receiver, or a long transmission distance. On the other hand, due to the level pinning effect of the two kinds of coupling mechanisms, the working frequency of the system is guaranteed to be locked, so frequency tracking is not required when the position and size of the receiver change. Even if the system deviates from the matching condition, an efficient WPT can be realized, thereby demonstrating the robustness of the level pinning. The experimental results show that when the size ratio of the transmitter coil to the receiver coil is 4.29 (which is in the weak coupling region), the transfer efficiency of the anti-PT-symmetric system is nearly 4.3 (3.2) times higher than that of the PT-symmetric system when the matching conditions are satisfied (deviated). With the miniaturization and integration of devices in mind, a synthetic anti-PT-symmetric system is used to realize a robust WPT. Anti-PT-symmetric WPT technology based on the synthetic dimension not only provides a good research platform for the study of abundant non-Hermitian physics, but also provides a means of going beyond traditional near-field applications with resonance mechanisms, such as resonance imaging, wireless sensing and photonic routing.

Discrete dynamics of light in an anti-parity-time symmetric photonic lattice in atomic vapors

We demonstrate the realization of an anti-parity-time (PT)-symmetric photonic lattice in a coherent three-level Λ-type 85Rb atomic system both experimentally and theoretically. Such an instantaneously reconfigurable anti-PT-symmetric photonic lattice is "written" by two one-dimensional coupling fields, which are arranged alternately along the x direction and can modulate the refractive index of the atomic vapor in a spatially periodical manner via controllable atomic coherence. By properly adjusting the relevant atomic parameters, the phase shift between two adjacent lattice channels occurs in the constructed non-Hermitian photonic system. Such a readily reconfigurable anti-PT-symmetric photonic lattice may open the door for demonstrating the discrete characteristics of the optical waves in periodic anti-PT-symmetric photonic systems.

Enhanced Sensing Mechanism Based on Shifting an Exceptional Point

Non-Hermitian systems associated with exceptional points (EPs) are expected to demonstrate a giant response enhancement for various sensors. The widely investigated enhancement mechanism based on diverging from an EP should destroy the EP and further limits its applications for multiple sensing scenarios in a time sequence. To break the above limit, here, we proposed a new enhanced sensing mechanism based on shifting an EP. Different from the mechanism of diverging from an EP, our scheme is an EP nondemolition and the giant enhancement of response is acquired by a slight shift of the EP along the parameter axis induced by perturbation. The new sensing mechanism can promise the most effective response enhancement for all sensors in the case of multiple sensing in a time sequence. To verify our sensing mechanism, we construct a mass sensor and a gyroscope with concrete physical implementations. Our work will deepen the understanding of EP-based sensing and inspire designing various high-sensitivity sensors in different physical systems.

In situ Simulation of Thermal Reality

Simulated reality encompasses virtual, augmented, and mixed realities-each characterized by different degrees of truthfulness in the visual perception: "all false," "coexistence of true and false," and "difficult distinction between true and false," respectively. In all these technologies, however, the temperature rendering of virtual objects is still an unsolved problem. Undoubtedly, the lack of thermal tactile functions substantially reduces the quality of the user's real-experience perception. To address this challenge, we propose theoretically and realize experimentally a technological platform for the in situ simulation of thermal reality. To this purpose, we design a thermal metadevice consisting of a reconfigurable array of radiating units, capable of generating the thermal image of any virtual object, and thus rendering it in situ together with its thermal signature. This is a substantial technological advance, which opens up new possibilities for simulated reality and its applications to human activities.

Non-Hermitian Waveguide Cavity QED with Tunable Atomic Mirrors

Optical mirrors determine cavity properties by means of light reflection. Imperfect reflection gives rise to open cavities with photon loss. We study an open cavity made of atom-dimer mirrors with a tunable reflection spectrum. We find that the atomic cavity shows anti-PT symmetry. The anti-PT phase transition controlled by atomic couplings in mirrors indicates the emergence of two degenerate cavity supermodes. Interestingly, a threshold of mirror reflection is identified for realizing strong coherent cavity-atom coupling. This reflection threshold reveals the criterion of atomic mirrors to produce a good cavity. Moreover, cavity quantum electrodynamics with a probe atom shows mirror-tuned properties, including reflection-dependent polaritons formed by the cavity and probe atom. Our Letter presents a non-Hermitian theory of an anti-PT atomic cavity, which may have applications in quantum optics and quantum computation.

Higher-order topological heat conduction on a lattice for detection of corner states

A heat conduction equation on a lattice composed of nodes and bonds is formulated assuming the Fourier law and the energy conservation law. Based on this equation, we propose a higher-order topological heat conduction model on the breathing kagome lattice. We show that the temperature measurement at a corner node can detect the corner state which causes rapid heat conduction toward the heat bath, and that several-nodes measurement can determine the precise energy of the corner states.

Non-Hermitian topology in static mechanical metamaterials

The combination of broken Hermiticity and band topology in physical systems unveils a novel bound state dubbed as the non-Hermitian skin effect (NHSE). Active control that breaks reciprocity is usually used to achieve NHSE, and gain and loss in energy are inevitably involved. Here, we demonstrate non-Hermitian topology in a mechanical metamaterial system by exploring its static deformation. Nonreciprocity is introduced via passive modulation of the lattice configuration without resorting to active control and energy gain/loss. Intriguing physics such as the reciprocal and higher-order skin effects can be tailored in the passive system. Our study provides an easy-to-implement platform for the exploration of non-Hermitian and nonreciprocal phenomena beyond conventional wave dynamics.

Giant, magnet-free, and room-temperature Hall-like heat transfer

Thermal chirality, generically referring to the handedness of heat flux, provides a significant possibility for modern heat control. It may be realized with the thermal Hall effect yet at the high cost of strong magnetic fields and extremely low temperatures. Here, we reveal magnet-free and room-temperature Hall-like heat transfer in an active thermal lattice composed of a stationary solid matrix and rotating solid particles. Rotation breaks the Onsager reciprocity relation and generates giant thermal chirality about two orders of magnitude larger than ever reported at the optimal rotation velocity. We further achieve anisotropic thermal chirality by breaking the rotation invariance of the active lattice, bringing effective thermal conductivity to a region unreachable by the thermal Hall effect. These results could enlighten topological and non-Hermitian heat transfer and efficient heat utilization in ways distinct from phonons.

Two-Dimensional Reconfigurable Non-Hermitian Gauged Laser Array

Topological effects in photonic non-Hermitian systems have recently led to extraordinary discoveries including nonreciprocal lasing, topological insulator lasers, and topological metamaterials, to mention a few. These effects, although realized in non-Hermitian systems, are all stemming from their Hermitian components. Here we experimentally demonstrate the topological skin effect and boundary sensitivity, induced by the imaginary gauge field in a two-dimensional laser array, which are fundamentally different from any Hermitian topological effects and intrinsic to open systems. By selectively and asymmetrically injecting gain into the system, we have synthesized an imaginary gauge field on chip, which can be flexibly reconfigured on demand. We show not only that the non-Hermitian topological features remain intact in a nonlinear nonequilibrium system, but also that they can be harnessed to enable persistent phase locking with intensity morphing. Our work lays the foundation for a dynamically reconfigurable on-chip coherent system with robust scalability, attractive for building high-brightness sources with arbitrary intensity profiles.

Non-Hermitian Chiral Heat Transport

Exceptional point (EP) has been captivated as a concept of interpreting eigenvalue degeneracy and eigenstate exchange in non-Hermitian physics. The chirality in the vicinity of EP is intrinsically preserved and usually immune to external bias or perturbation, resulting in the robustness of asymmetric backscattering and directional emission in classical wave fields. Despite recent progress in non-Hermitian thermal diffusion, all state-of-the-art approaches fail to exhibit chiral states or directional robustness in heat transport. Here we report the first discovery of chiral heat transport, which is manifested only in the vicinity of EP but suppressed at the EP of a thermal system. The chiral heat transport demonstrates significant robustness against drastically varying advections and thermal perturbations imposed. Our results reveal the chirality in heat transport process and provide a novel strategy for manipulating mass, charge, and diffusive light.

Observation of bulk quadrupole in topological heat transport

The quantized bulk quadrupole moment has so far revealed a non-trivial boundary state with lower-dimensional topological edge states and in-gap zero-dimensional corner modes. In contrast to photonic implementations, state-of-the-art strategies for topological thermal metamaterials struggle to achieve such higher-order hierarchical features. This is due to the absence of quantized bulk quadrupole moments in thermal diffusion fundamentally prohibiting possible band topology expansions. Here, we report a recipe for generating quantized bulk quadrupole moments in fluid heat transport and observe the quadrupole topological phases in non-Hermitian thermal systems. Our experiments show that both the real- and imaginary-valued bands exhibit the hierarchical features of bulk, gapped edge and in-gap corner states-in stark contrast to the higher-order states observed only on real-valued bands in classical wave fields. Our findings open up unique possibilities for diffusive metamaterial engineering and establish a playground for multipolar topological physics.

Convective Thermal Metamaterials: Exploring High-Efficiency, Directional, and Wave-Like Heat Transfer

Convective thermal metamaterials are artificial structures where convection dominates in the thermal process. Due to the field coupling between velocity and temperature, convection provides a new knob for controlling heat transfer beyond pure conduction, thus allowing active and robust thermal modulations. With the introduced convective effects, the original parabolic Fourier heat equation for pure conduction can be transformed to hyperbolic. Therefore, the hybrid diffusive system can be interpreted in a wave-like fashion, reviving many wave phenomena in dissipative diffusion. Here, recent advancements in convective thermal metamaterials are reviewed and the state-of-the-art discoveries are classified into the following four aspects, enhancing heat transfer, porous-media-based thermal effects, nonreciprocal heat transfer, and non-Hermitian phenomena. Finally, a prospect is cast on convective thermal metamaterials from two aspects. One is to utilize the convective parameter space to explore topological thermal effects. The other is to further broaden the convective parameter space with spatiotemporal modulation and multi-physical effects.

Theoretical investigation of dynamics and concurrence of entangled [Formula: see text] and anti-[Formula: see text] symmetric polarized photons

Non-Hermitian systems with parity-time [Formula: see text] symmetry and anti-parity-time [Formula: see text] symmetry have exceptional points (EPs) resulting from eigenvector co-coalescence with exceptional properties. In the quantum and classical domains, higher-order EPs for [Formula: see text] symmetry and [Formula: see text]-symmetry systems have been proposed and realized. Both two-qubits [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] symmetric systems have seen an increase in recent years, especially in the dynamics of quantum entanglement. However, to our knowledge, neither theoretical nor experimental investigations have been conducted for the dynamics of two-qubits entanglement in the [Formula: see text]-[Formula: see text] symmetric system. We investigate the [Formula: see text]-[Formula: see text] dynamics for the first time. Moreover, we examine the impact of different initial Bell-state conditions on entanglement dynamics in [Formula: see text]-[Formula: see text], [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] symmetric systems. Additionally, we conduct a comparative study of entanglement dynamics in the [Formula: see text]-[Formula: see text] symmetrical system, [Formula: see text]-[Formula: see text] symmetrical system, and [Formula: see text]-[Formula: see text] symmetrical systems in order to learn more about non-Hermitian quantum systems and their environments. Entangled qubits evolve in a [Formula: see text]-[Formula: see text] symmetric unbroken regime, the entanglement oscillates with two different oscillation frequencies, and the entanglement is well preserved for a long period of time for the case when non-Hermitian parts of both qubits are taken quite away from the exceptional points.

Topological Atomic Spin Wave Lattices by Dissipative Couplings

Recent experimental advances in creating dissipative couplings provide a new route for engineering exotic lattice systems and exploring topological dissipation. Using the spatial lattice of atomic spin waves in a vacuum vapor cell, where purely dissipative couplings arise from diffusion of atoms, we experimentally realize a dissipative version of the Su-Schrieffer-Heeger (SSH) model. We construct the dissipation spectrum of the topological or trivial lattices via electromagnetically induced-transparency spectroscopy. The topological dissipation spectrum is found to exhibit edge modes within a dissipative gap. We validate chiral symmetry of the dissipative SSH couplings and also probe topological features of the generalized dissipative SSH model. This work paves the way for realizing non-Hermitian topological quantum optics via dissipative couplings.

Higher-Order Topological States in Thermal Diffusion

Unlike conventional topological materials that carry topological states at their boundaries, higher-order topological materials are able to support topological states at boundaries of boundaries, such as corners and hinges. While band topology has been recently extended into thermal diffusion for thermal metamaterials, its realization is limited to a 1D thermal lattice, lacking access to the higher-order topology. In this work, the experimental realization is reported of a higher-order thermal topological insulator in a generalized 2D diffusion lattice. The topological corner states for thermal diffusion are observed in the bandgap of diffusion rate of the bulk, as a consequence of the anti-Hermitian nature of the diffusion Hamiltonian. The topological protection of these thermal corner states is demonstrated with the stability of their diffusion profile in the presence of amorphous deformation. This work constitutes the first realization of higher-order topology in purely diffusive systems and opens the door for future thermal management with topological protection beyond 1D geometries.

Hyperparametric Oscillation via Bound States in the Continuum

Optical hyperparametric oscillation based on the third-order nonlinearity is one of the most significant mechanisms to generate coherent electromagnetic radiation and produce quantum states of light. Advances in dispersion-engineered high-Q microresonators allow for generating signal waves far from the pump and decrease the oscillation power threshold to submilliwatt levels. However, the pump-to-signal conversion efficiency and absolute signal power are low, fundamentally limited by parasitic mode competition and attainable cavity intrinsic Q to coupling Q ratio, i.e., Q_{i}/Q_{c}. Here, we use Friedrich-Wintgen bound states in the continuum (BICs) to overcome the physical challenges in an integrated microresonator-waveguide system. As a result, on-chip coherent hyperparametric oscillation is generated in BICs with unprecedented conversion efficiency and absolute signal power. This work not only opens a path to generate high-power and efficient continuous-wave electromagnetic radiation in Kerr nonlinear media but also enhances the understanding of a microresonator-waveguide system-an elementary unit of modern photonics.

Black-hole-inspired thermal trapping with graded heat-conduction metadevices

The curved space-time produced by black holes leads to the intriguing trapping effect. So far, metadevices have enabled analogous black holes to trap light or sound in laboratory spacetime. However, trapping heat in a conductive environment is still challenging because diffusive behaviors are directionless. Inspired by black holes, we construct graded heat-conduction metadevices to achieve thermal trapping, resorting to the imitated advection produced by graded thermal conductivities rather than the trivial solution of using insulation materials to confine thermal diffusion. We experimentally demonstrate thermal trapping for guiding hot spots to diffuse towards the center. Graded heat-conduction metadevices have advantages in energy-efficient thermal regulation because the imitated advection has a similar temperature field effect to the realistic advection that is usually driven by external energy sources. These results also provide an insight into correlating transformation thermotics with other disciplines, such as cosmology, for emerging heat control schemes.

On-chip mechanical exceptional points based on an optomechanical zipper cavity

Exceptional points (EPs) represent a distinct type of spectral singularity in non-Hermitian systems, and intriguing physics concepts have been studied with optical EPs recently. As a system beyond photonics, the mechanical oscillators coupling with many physical systems are expected to be further exploited EPs for mechanical sensing, topology energy transfer, nonreciprocal dynamics, etc. In this study, we demonstrated on-chip mechanical EPs with a silicon optomechanical zipper cavity, wherein two near-degenerate mechanical breathing modes are coupled via a single colocalized optical mode. By tailoring the dissipative and coherent couplings between two mechanical oscillators, the spectral splitting with 1/2 order response, a distinctive feature of EP, was observed successfully. Our work provides an integrated platform for investigating the physics related to mechanical EPs on silicon chips and suggests their possible applications for ultrasensitive measurements.

Stable Atomic Magnetometer in Parity-Time Symmetry Broken Phase

Random motion of spins is usually detrimental in magnetic resonance experiments. The spin diffusion in nonuniform magnetic fields causes broadening of the resonance and limits the sensitivity and the spectral resolution in applications like magnetic resonance spectroscopy. Here, by observation of the parity-time (PT) phase transition of diffusive spins in gradient magnetic fields, we show that the spatial degrees of freedom of atoms could become a resource, rather than harmful, for high-precision measurement of weak signals. In the normal phase with zero or low gradient fields, the diffusion results in dissipation of spin precession. However, by increasing the field gradient, the spin system undergoes a PT transition, and enters the PT symmetry broken phase. In this novel phase, the spin precession frequency splits due to spatial localization of the eigenmodes. We demonstrate that, using these spatial-motion-induced split frequencies, the spin system can serve as a stable magnetometer, whose output is insensitive to the inevitable long-term drift of control parameters. This opens a door to detect extremely weak signals in imperfectly controlled environments.

Harnessing Dynamical Encircling of an Exceptional Point in Anti-PT-Symmetric Integrated Photonic Systems

Dynamically encircling an exceptional point in a non-Hermitian system can lead to chiral behaviors, but this process is difficult for on-chip PT-symmetric devices which require accurate control of gain and loss rates. Here, we experimentally demonstrated encircling an exceptional point with a fixed loss rate in a compact anti-PT-symmetric integrated photonic system, where chiral mode switching was achieved within a length that is an order of magnitude shorter than that of a PT-symmetric system. Based on the experimental demonstration, we proposed a topologically protected mode (de)multiplexer that is robust against fabrication errors with a wide operating wavelength range. With the advantages of simplified fabrication and characterization processes, the demonstrated system can be used for studying higher-order exceptional points and for exotic light manipulation.

Radiative anti-parity-time plasmonics

Space and guided electromagnetic waves, as widely known, are two crucial cornerstones in extensive wireless and integrated applications respectively. To harness the two cornerstones, radiative and integrated devices are usually developed in parallel based on the same physical principles. An emerging mechanism, i.e., anti-parity-time (APT) symmetry originated from non-Hermitian quantum mechanics, has led to fruitful phenomena in harnessing guided waves. However, it is still absent in harnessing space waves. Here, we propose a radiative plasmonic APT design to harness space waves, and experimentally demonstrate it with subwavelength designer-plasmonic structures. We observe two exotic phenomena unrealized previously. Rotating polarizations of incident space waves, we realize polarization-controlled APT phase transition. Tuning incidence angles, we observe multi-stage APT phase transition in higher-order APT systems, constructed by using the scalability of leaky-wave couplings. Our scheme shows promise in demonstrating novel APT physics, and constructing APT-symmetry-empowered radiative devices.

Anomalous spontaneous emission dynamics at chiral exceptional points

An open quantum system operated at the spectral singularities where dimensionality reduces, known as exceptional points (EPs), demonstrates distinguishing behavior from the Hermitian counterpart. Here, we present an analytical description of local density of states (LDOS) for microcavity featuring chiral EPs, and unveil the anomalous spontaneous emission dynamics from a quantum emitter (QE) due to the non-Lorentzian response of EPs. Specifically, we reveal that a squared Lorentzian term of LDOS contributed by chiral EPs can destructively interfere with the linear Lorentzian profile, resulting in the null Purcell enhancement to a QE with special transition frequency, which we call EP induced transparency. While for the case of constructive interference, the squared Lorentzian term can narrow the linewidth of Rabi splitting even below that of bare components, and thus significantly suppresses the decay of Rabi oscillation. Interestingly, we further find that an open microcavity with chiral EPs supports atom-photon bound states for population trapping and decay suppression in long-time dynamics. As applications, we demonstrate the advantages of microcavity operated at chiral EPs in achieving high-fidelity entanglement generation and high-efficiency single-photon generation. Our work unveils the exotic cavity quantum electrodynamics unique to chiral EPs, which opens the door for controlling light-matter interaction at the quantum level through non-Hermiticity, and holds great potential in building high-performance quantum-optics devices.

Thermal Willis Coupling in Spatiotemporal Diffusive Metamaterials

Willis coupling generically stems from bianisotropy or chirality in wave systems. Nevertheless, those schemes are naturally unavailable in diffusion systems described by a single constitutive relation governed by the Fourier law. Here, we report spatiotemporal diffusive metamaterials by modulating thermal conductivity and mass density in heat transfer. The Fourier law should be modified after homogenizing spatiotemporal parameters, featuring thermal Willis coupling between heat flux and temperature change rate. Thermal Willis coupling drives asymmetric heat diffusion, and the diffusion direction is reversible at a critical point determined by the degree of spatiotemporal modulation. Moreover, thermal Willis coupling stands robustly even when only thermal conductivity is modulated. These results may have potential applications for directional diffusion and offer insights into asymmetric manipulation of nonequilibrium mass and energy transfer.

Riemann-Encircling Exceptional Points for Efficient Asymmetric Polarization-Locked Devices

Dynamically encircling exceptional points (EPs) have unveiled intriguing chiral dynamics in photonics. However, the traditional approach based on an open manifold of Hamiltonian parameter space fails to explore trajectories that pass through an infinite boundary. Here, by mapping the full parameter space onto a closed manifold of the Riemann sphere, we introduce a framework to describe encircling-EP loops. We demonstrate that an encircling trajectory crossing the north vertex can realize near-unity asymmetric transmission. An efficient gain-free, broadband asymmetric polarization-locked device is realized by mapping the encircling path onto L-shaped silicon waveguides.

Geometric heat pump and no-go restrictions of nonreciprocity in modulated thermal diffusion

Thermodynamics strongly restricts the direction of heat flow in static macroscopic thermal diffusive systems. To overcome this constraint, spatiotemporal modulated systems are used instead. Here, we unveil the underlying geometric heat pump effect in macroscopic driven thermal diffusion, which is crucial for achieving thermal nonreciprocity. We obtain a geometric expression to formulate the nontrivial current in a driven system, manifesting as an extra pumped heat ably diffusing from cold to hot that has no analogy in static setups. Moreover, we analyze the underlying geometric curvature of driven diffusive systems and derive no-pumping restriction theorems that constrain the thermal action under modulations and guide the optimization of driving protocols. Following the restrictions from geometry, we finally implement a minimum experiment and observe the predicted pumped heat in the absence of thermal bias at every instant, which is independent of the driving speed in the adiabatic limit, clearly validating the geometric theory. An extension of the geometric pump effect and no-pumping restrictions to macroscopic mass diffusion governed by Fick's law is also discussed. These results pave the way for designing and implementing nonreciprocal and topological diffusive systems under spatiotemporal modulations.

Geometric Phase and Localized Heat Diffusion

Many unusual wave phenomena in artificial structures are governed by their topological properties. However, the topology of diffusion remains almost unexplored. One reason is that diffusion is fundamentally different from wave propagation because of its purely dissipative nature. The other is that the diffusion field is mostly composed of modes that extend over wide ranges, making it difficult to be rendered within the tight-binding theory as commonly employed in wave physics. Here, the above challenges are overcome and systematic studies are performed on the topology of heat diffusion. Based on a continuum model, the band structure and geometric phase are analytically obtained without using the tight-binding approximation. A deterministic parameter is found to link the geometric phase with the edge state, thereby proving the bulk-boundary correspondence for heat diffusion. The topological edge state is experimentally demonstrated as localized heat diffusion and its dependence on the boundary conditions is verified. This approach is general, rigorous, and able to reveal rich knowledge about the system with great accuracy. The findings set up a solid foundation to explore the topology in novel thermal management applications.

Observation of Topological Edge States in Thermal Diffusion

Topological band theory predicts that bulk materials with nontrivial topological phases support topological edge states. This phenomenon is universal for various wave systems and is widely observed for electromagnetic and acoustic waves. Here, the notion of band topology is extended from wave to diffusion dynamics. Unlike wave systems that are usually Hermitian, diffusion systems are anti-Hermitian with purely imaginary eigenvalues corresponding to decay rates. By direct probe of the temperature diffusion, the Hamiltonian of a thermal lattice is experimentally retrieved, and the emergence of topological edge decays is observed within the gap of bulk decays. The results of this work show that such edge states exhibit robust decay rates, which are topologically protected against disorder. This work constitutes a thermal analogue of topological insulators and paves the way to exploring defect-immune heat dissipation.

Quantum Simulation of Pseudo-Hermitian-φ-Symmetric Two-Level Systems

Non-Hermitian (NH) quantum theory has been attracting increased research interest due to its featured properties, novel phenomena, and links to open and dissipative systems. Typical NH systems include PT-symmetric systems, pseudo-Hermitian systems, and their anti-symmetric counterparts. In this work, we generalize the pseudo-Hermitian systems to their complex counterparts, which we call pseudo-Hermitian-φ-symmetric systems. This complex extension adds an extra degree of freedom to the original symmetry. On the one hand, it enlarges the non-Hermitian class relevant to pseudo-Hermiticity. On the other hand, the conventional pseudo-Hermitian systems can be understood better as a subgroup of this wider class. The well-defined inner product and pseudo-inner product are still valid. Since quantum simulation provides a strong method to investigate NH systems, we mainly investigate how to simulate this novel system in a Hermitian system using the linear combination of unitaries in the scheme of duality quantum computing. We illustrate in detail how to simulate a general P-pseudo-Hermitian-φ-symmetric two-level system. Duality quantum algorithms have been recently successfully applied to similar types of simulations, so we look forward to the implementation of available quantum devices.

Anyonic-parity-time symmetry in complex-coupled lasers

Non-Hermitian Hamiltonians, and particularly parity-time (PT) and anti-PT symmetric Hamiltonians, play an important role in many branches of physics, from quantum mechanics to optical systems and acoustics. Both the PT and anti-PT symmetries are specific instances of a broader class known as anyonic-PT symmetry, where the Hamiltonian and the PT operator satisfy a generalized commutation relation. Here, we study theoretically these novel symmetries and demonstrate them experimentally in coupled lasers systems. We resort to complex coupling of mixed dispersive and dissipative nature, which allows unprecedented control on the location in parameter space where the symmetry and symmetry breaking occur. Moreover, tuning the coupling in the same physical system allows us to realize the special cases of PT and anti-PT symmetries. In a more general perspective, we present and experimentally validate a new relation between laser synchronization and the symmetry of the underlying non-Hermitian Hamiltonian.

Heat transfer control using a thermal analogue of coherent perfect absorption

Recent investigations on non-Hermitian physics have unlocked new possibilities to manipulate wave scattering on lossy materials. Coherent perfect absorption is such an effect that enables all-light control by incorporating a suitable amount of loss. On the other hand, controlling heat transfer with heat may empower a distinct paradigm other than using thermal metamaterials. However, since heat neither propagates nor carries any momentum, almost all concepts in wave scattering are ill-defined for steady-state heat diffusion, making it formidable to understand or utilize any coherent effect. Here, we establish a scattering theory for heat diffusion by introducing an imitated momentum for thermal fields. The thermal analogue of coherent perfect absorption is thus predicted and demonstrated as the perfect absorption of exergy fluxes and undisturbed temperature fields. Unlike its photonic counterpart, thermal coherent perfect absorption can be realized for regular thermal materials, and be generalized for various objects.

A thermal analogue of coherent perfect absorption would allow to control heat transfer using heat, but the lack of momentum propagation in a thermal field seems to prevent any role for coherence. Here, the authors allow this by introducing an imitated momentum for steady-state heat diffusion.

Quantum Squeezing and Sensing with Pseudo-Anti-Parity-Time Symmetry

The emergence of parity-time (PT) symmetry has greatly enriched our study of symmetry-enabled non-Hermitian physics, but the realization of quantum PT symmetry faces an intrinsic issue of unavoidable symmetry-breaking Langevin noises. Here we construct a quantum pseudo-anti-PT (pseudo-APT) symmetry in a two-mode bosonic system without involving Langevin noises. We show that the spontaneous pseudo-APT symmetry breaking leads to an exceptional point, across which there is a transition between different types of quantum squeezing dynamics; i.e., the squeezing factor increases exponentially (oscillates periodically) with time in the pseudo-APT-symmetric (broken) region. Such dramatic changes of squeezing factors and quantum dynamics near the exceptional point are utilized for ultraprecision quantum sensing. These exotic quantum phenomena and sensing applications can be experimentally observed in two physical systems: spontaneous wave mixing nonlinear optics and atomic Bose-Einstein condensates. Our Letter offers a physical platform for investigating exciting APT symmetry physics in the quantum realm, paving the way for exploring fundamental quantum non-Hermitian effects and their quantum technological applications.

Observation of Weyl exceptional rings in thermal diffusion

Thermal diffusion is dissipative and strongly related to non-Hermitian physics. At the same time, non-Hermitian Weyl systems have spurred tremendous interest across photonics and acoustics. This correlation has been long ignored and hence shed little light upon the question of whether the Weyl exceptional ring (WER) in thermal diffusion could exist. Intuitively, thermal diffusion provides no real parameter dimensions, thus prohibiting a topological nature and WER. This work breaks this perception by imitating synthetic dimensions via two spatiotemporal advection pairs. The WER is achieved in thermal diffusive systems. Both surface-like and bulk states are demonstrated by coupling two WERs with opposite topological charges. These findings extend topological notions to diffusions and motivate investigation of non-Hermitian diffusive and dissipative control.

A non-Hermitian Weyl equation indispensably requires a three-dimensional (3D) real/synthetic space, and it is thereby perceived that a Weyl exceptional ring (WER) will not be present in thermal diffusion given its purely dissipative nature. Here, we report a recipe for establishing a 3D parameter space to imitate thermal spinor field. Two orthogonal pairs of spatiotemporally modulated advections are employed to serve as two synthetic parameter dimensions, in addition to the inherent dimension corresponding to heat exchanges. We first predict the existence of WER in our hybrid conduction–advection system and experimentally observe the WER thermal signatures verifying our theoretical prediction. When coupling two WERs of opposite topological charges, the system further exhibits surface-like and bulk topological states, manifested as stationary and continuously changing thermal processes, respectively, with good robustness. Our findings reveal the long-ignored topological nature in thermal diffusion and may empower distinct paradigms for general diffusion and dissipation controls.

Diffusive Fizeau Drag in Spatiotemporal Thermal Metamaterials

Fizeau drag means that the speed of light can be regulated by the flow of water, owing to the momentum interaction between photons and moving media. However, the dragging of heat is intrinsically elusive, due to the absence of momentum in thermal diffusion. Here, we design a spatiotemporal thermal metamaterial based on heat transfer in porous media to demonstrate the diffusive analog to Fizeau drag. The space-related inhomogeneity and time-related advection enable the diffusive Fizeau drag effect. Thanks to the spatiotemporal coupling, different propagating speeds of temperature fields can be observed in two opposite directions, thus facilitating nonreciprocal thermal profiles. The phenomenon of diffusive Fizeau drag stands robustly even when the direction of advection is perpendicular to the propagation of temperature fields. These results could pave an unexpected way toward realizing the nonreciprocal and directional transport of mass and energy.

Topological engineering of terahertz light using electrically tunable exceptional point singularities

The topological structure associated with the branch point singularity around an exceptional point (EP) can provide tools for controlling the propagation of light. Through use of graphene-based devices, we demonstrate the emergence of EPs in an electrically controlled interaction between light and a collection of organic molecules in the terahertz regime at room temperature. We show that the intensity and phase of terahertz pulses can be controlled by a gate voltage, which drives the device across the EP. Our electrically tunable system allows reconstruction of the Riemann surface associated with the complex energy landscape and provides topological control of light by tuning the loss imbalance and frequency detuning of interacting modes. Our approach provides a platform for developing topological optoelectronics and studying the manifestations of EP physics in light-matter interactions.

Distinguish between typical non-Hermitian quantum systems by entropy dynamics

Non-Hermitian (NH) quantum systems attract research interest increasingly in recent years, among which the PT-symmetric, P-pseudo-Hermitian and their anti-symmetric counterpart systems are focused much more. In this work, we extend the usage of entropy to distinguish time-evolutions of different classes and phases of typical NH-systems. In detail, we investigate the entropy dynamics of two-level NH-systems after quantum decoherence induced by single-qubit projective measurements, finding that it depends on both the initial states and the selection of the computational bases of the measurements. In a general case, we show how to distinguish all the eight phases of the above NH-systems step by step, in which process three different initial states are necessary if the basis of measurement is fixed. We propose how the distinguishing process is realized in quantum simulation, in which quantum tomography is not needed. Our investigations can be applied to judge phase transitions of non-Hermitian systems.

Reciprocity of thermal diffusion in time-modulated systems

The reciprocity principle governs the symmetry in transmission of electromagnetic and acoustic waves, as well as the diffusion of heat between two points in space, with important consequences for thermal management and energy harvesting. There has been significant recent interest in materials with time-modulated properties, which have been shown to efficiently break reciprocity for light, sound, and even charge diffusion. However, time modulation may not be a plausible approach to break thermal reciprocity, in contrast to the usual perception. We establish a theoretical framework to accurately describe the behavior of diffusive processes under time modulation, and prove that thermal reciprocity in dynamic materials is generally preserved by the continuity equation, unless some external bias or special material is considered. We then experimentally demonstrate reciprocal heat transfer in a time-modulated device. Our findings correct previous misconceptions regarding reciprocity breaking for thermal diffusion, revealing the generality of symmetry constraints in heat transfer, and clarifying its differences from other transport processes in what concerns the principles of reciprocity and microscopic reversibility.