The emergence of multiple superradiant phases in Dicke lattice models has attracted considerable attention in the quantum optics community. However, a unified understanding of the origin of multistability and its relation to different superradiant phases is still lacking. Here, we develop a configuration-based understanding to classify the superradiant phases in Dicke lattices. We show that photon hopping naturally organizes the possible superradiant configurations according to the lattice symmetry, providing a unified interpretation of the nonequilibrium phase diagram and the emergence of multistability. For the dissipative four-site Dicke lattice, we obtain the complete phase diagram and identify the coexistence of up to four stable superradiant phases. The proposed classification is further extended to five- and six-site lattices. Moreover, we demonstrate that the same configuration-based understanding also applies to the closed Dicke lattice, where the ground state uniquely selects one of the allowed configurations. Finally, we show that different configurations may belong to either same or distinct nonequilibrium universality classes in the dissipative Dicke lattice, while they share the same equilibrium universality class in the closed Dicke lattice. Our results provide a unified picture for understanding equilibrium and nonequilibrium superradiant phase transitions in Dicke lattices.

Chiral quantum optics is central to developing scalable quantum networks, yet existing approaches rely predominantly on linear single-photon regimes. It remains unclear how to generate directional multiphotons. Here we show that giant emitters coupled to nonlinear quantum optical baths enable tunable directional correlated photons, revealing a mechanism for multiphoton directional emission. We demonstrate that the propagation phases of correlated photons, together with the coupling phases of giant emitters, can generate destructive interference in one direction while enhancing emission in the opposite direction, making directionality fully tunable. Building on this mechanism, we introduce a nonlinear cascaded quantum network paradigm mediated by "correlated flying qubits", providing a configurable building block enabling distinct many-body applications beyond linear unidirectional setups. These results reveal a rich landscape for engineering multiphoton propagation and correlations through interference in giant emitter-nonlinear bath architectures, offering pathways for quantum networks and strongly correlated light-matter platforms.

Giant atoms, which couple to a waveguide through multiple spatially separated connection points beyond the dipole approximation, provide a versatile route for quantum information processing based on interference-induced bound states in the continuum (BICs). While multi-giant-atom architectures are being developed toward giant-atom quantum networks, the role of direct coupling between the giant atoms, in particular the associated coupling phase, in atomic dynamics remains insufficiently understood. Here we take a first step toward addressing this issue by studying a two-giant-atom waveguide-QED model. We show that the coupling phase can be used to control both the number of BICs and their profiles for both of photon and atoms. More interestingly, the presence of BICs gives rise to a variety of dynamical behaviors, providing an effective mechanism for tailoring quantum-state evolution in giant-atom waveguide-QED systems. Our results highlight coupling-phase engineering as a useful tool for controlling interference, bound states, and quantum dynamics in nonlocal light–matter interfaces.

In open quantum systems, reduced dynamics is commonly described by a master equation, whose Liouvillian gap closing (LGC) typically signals the emergence of decoherence-free subspace. By contrast, the dynamics of the full system-environment compound is governed by the underlying Hamiltonian spectrum, where bound states in the continuum (BICs) can protect long-lived quantum resources. Despite these parallel perspectives, the relation between LGC and BIC formation has remained largely unexplored. Here we bridge this gap in a paradigmatic giant-atom waveguide platform and show that the occurrence of LGC necessarily benchmarks the presence of a BIC in the full Hamiltonian description. By engineering the giant-atom geometry, we further demonstrate rich dynamical regimes-including Rabi oscillations, fractional decay, and complete exponential relaxation-depending on the number of supported BICs, which can be tuned from three to zero. Remarkably, when two BICs become frequency-degenerate, the long-time dynamics approaches a steady state rather than exhibiting persistent oscillations. Our results establish a direct spectral-dynamical connection between effective Markovian and underlying non-Markovian descriptions, and provide a route toward flexible control of open-system dynamics.

We investigate the superradiance of two-level target atoms (TAs) coupled to a photonic waveguide, demonstrating that the scaling of the superradiance strength can be controlled on demand by an ensemble of control atoms (CAs). The scaling with respect to the number of TAs can be lower, higher, or equal to the traditional Dicke superradiance, depending on the relative positioning of the ensembles and the type of CAs (e.g., small or giant). These phenomena are attributed to unconventional atomic correlations. Furthermore, we observe chiral superradiance of the TAs, where the degree of chirality can be enhanced by giant CAs instead of small ones. The effects discussed in this work could be observed in waveguide QED experiments, offering a potential avenue for manipulating superradiance.

Photonic state engineering in waveguide QED is typically based on local light-matter interactions. This limits its control over the spatial structure of bound photonic states. Here, we demonstrate a distinct mechanism arising from the interplay between nonlocal giant-atom coupling and topological band structure. Specifically, we consider giant atoms coupled to a Su-Schrieffer-Heeger waveguide and show that this configuration enables a controllable energy-level crossing protected by the topological gap. Adiabatically sweeping the atomic detuning across the crossing leads to a controlled exchange between distinct photonic bound states. In a two-giant-atom configuration, this mechanism achieves high-fidelity conversion of a spatially splitting state into a combining state. Extending this scheme to three-giant atoms, we further realize robust, shape-preserving photon transfer mediated by sequential in-gap crossings. Our results demonstrate how topology and nonlocal light-matter coupling can be combined to achieve programmable control of bound photonic states in waveguide QED platforms.

Schrödinger cat states, representing coherent superpositions of macroscopically distinguishable states, are indispensable nonclassical resources for continuous-variable quantum information processing. Existing generation protocols typically rely on strong nonlinear interactions, complicated control techniques, or engineered dissipation, posing challenges for experimental implementation. Here, we propose a simple measurement-based protocol for generating Schrödinger cat states in a cavity-QED system by combining coherent driving, dispersive atom–cavity interactions, and atomic postselection. The atom–cavity interaction establishes coherent correlations between the atomic and photonic degrees of freedom, while the subsequent atomic postselection projects the cavity field onto a non-Gaussian superposition state with pronounced Wigner negativity. Numerical simulations based on the Lindblad master equation show that the generated Schrödinger cat states remain robust against moderate cavity dissipation. Our results demonstrate that conditional atomic measurements provide an effective and experimentally accessible approach for preparing nonclassical cavity states without relying on strong optical nonlinearities or engineered dissipation.

Bound states in the continuum (BICs) have attracted intense interest, yet their many-particle counterparts remain largely unexplored in waveguide quantum electrodynamics. We identify and characterize a bound state embedded in the doublon continuum (BIDC) that emerges when four atoms couple to a coupled-resonator waveguide with strong on-site interaction. Exploiting this interaction-enabled BIDC, we show that (i) a distant, four-atom entangled state can be prepared with high fidelity, and (ii) quantum entangled states can be coherently transferred between spatially separated nodes. Our results establish a scalable mechanism for multi-particle state generation and routing in waveguide platforms, opening a route to interaction-protected quantum communication with many-particle BICs.

Bound states in the continuum (BICs) have been extensively exploited to enhance light-matter interactions in metamaterials, yet their emergence and utility in multiatom waveguide platforms remain far less explored. Here we study atom-waveguide-dressed BICs in a one-dimensional coupled-resonator waveguide, where two spatially separated atomic arrays couple to distinct resonators with time-dependent strengths. We show that these BICs host standing-wave photonic components and enable the transfer of unknown atomic quantum states encoded in the single-excitation subspace between the two arrays, with fidelities exceeding 99%. Going beyond traditional cascaded-quantum-network protocols, our scheme leverages BIC-assisted interference to remain robust against both disorder and intrinsic dissipation. Our results establish BICs as long-lived resources for high-fidelity quantum information processing in waveguide-QED architectures.

Spontaneous breaking of continuous time-translation symmetry in driven-dissipative systems gives rise to boundary time crystals (BTCs), characterized by persistent oscillations sustained by coherent driving and collective dissipation. Conventional BTCs, however, typically require strong driving and exact atom-drive resonance, imposing stringent constraints on their realization. Here we consider two atomic ensembles coupled to a common Markovian reservoir and show that shared dissipation organizes dissipation-free and low-dissipation modes into dynamically accessible low-dissipation channels, enabling BTCs under weak driving and finite detuning. Finite detuning further selects a unique stable limit cycle from an initial-state-dependent family of oscillatory trajectories. Our results establish low-dissipation dynamical channels as a route to robust BTCs under relaxed driving and resonance conditions.

Non-trivial dispersion relations engineered in photonic waveguide for the precise control of atomic dynamics has recently attracted considerable attention. Here, we study a system in which atoms are coupled to one-dimensional coupled-resonator waveguides with long-range hoppings. By carefully engineering the jth-order nearest neighbor (JNN) hoppings between resonators, we construct linear dispersion relations with the chiral characteristic. To quantify the degree of linearity, we analyze the propagation fidelities of Gaussian wave packets in these waveguides. Furthermore, we demonstrate that such coupled-resonator waveguides can serve as versatile platforms for enabling directional atomic radiation and absorption. Beyond linear dispersion relations, more general forms, including quadratic and cubic relations, can also be achieved through tailored JNN-hoppings. Our study thus provides a unified framework for simulating atom-environment couplings with arbitrary dispersion relations.

The superradiant phase transition in the dissipative Dicke lattice model, driven by on-site collective atom-photon interactions and inter-site photon hopping, is a cornerstone of nonequilibrium quantum many-body physics. However, little is still known about the influence of boundaries in experimental achievable systems of finite size. Here we investigate the dissipative superradiant phase transition in the Dicke lattice model with a small number of sites and reveal a striking sensitivity of this model to the nature of the boundary conditions. Specifically, we find that under open boundary conditions a whole zoo of superradiant phases with broken translational symmetry appears, which is not observed in the corresponding infinite lattice system. Our results demonstrate the crucial influence of boundary effects on the stationary phases of dissipative lattice models, which offers intriguing new opportunities for studying these phenomena in near term experimental realizations of such models in quantum optics and circuit QED.

We study the dynamics of two giant atoms interacting with a coupled resonator waveguide (CRW) beyond the Markovian approximation. The distinct atomic configurations determine the number of bound states in the continuum (BIC), leading to different dynamical behaviors. Our results show that when the system supports two BICs, Rabi oscillations dominate the dynamics, whereas fractional population dynamics emerge in the presence of a single BIC. The connection between these dynamics and the existence of BICs is further verified by analyzing the photonic distribution in the CRW during time evolution. These findings challenge the conventional notion that the environment always induces dissipation and decoherence. Instead, the bound states in the CRW-emitters coupled system can suppress complete dissipation of the emitters. This work offers an effective approach for controlling dissipative dynamics in open quantum systems.

We study single photon scattering in a one-dimensional coupled resonator waveguide, which is dressed by a small and a giant artificial atom simultaneously. Here, we have set the small atom to be a neighbor to one leg of the giant atom, and the giant atom couples to the waveguide via two distant sites. When the small and giant atoms are both resonant with the bare resonator in the waveguide, we observe the perfect reflection of the resonant incident photon. On the other hand, when the small atom is detuned from the giant atom, the single photon reflection is characterized by a wide window and Fano line shape. We hope our work will pave the way for the potential application of small and giant atom hybrid systems in the study of photonic control in the low-dimensional waveguide structure.

The coherent emission of multiple atoms gives rise to superradiance, a cornerstone phenomenon in quantum optics with wide-ranging applications in quantum information processing and precision metrology. Despite its importance, how the superradiant scaling with respect to the number of participating atoms can be effectively controlled remains largely unexplored. In this work, we investigate a cavity-QED system and demonstrate that atom-photon coupling can significantly alter the emission behavior–suppressing the collective superradiant scaling while enhancing the scaling associated with individual atomic emissions. Our study provides a pathway toward controllable collective emission in state-of-the-art experimental platforms.

Nonlocal interactions between photonic resonator array and giant atoms have attracted extensive attentions. Optimization and control of quantum states via giant atoms have been shown. We here study the dynamical scattering of a single-photon wave packet by a giant atom coupled to a two-dimensional photonic resonator array via multiple spatial points. Using several iterations of time evolutions, we can prepare an expected wave packet with a stable size and use it as the incident state for the scattering process. We show that spatially symmetric or asymmetric target scattering states of single-photon wave packet can be generated by adjusting the coupling strengths between the giant atom and different lattice sites of the resonator array. Furthermore, the dynamical scattering of the wave packets enables us to study the atomic excitation and propagating properties of the scattering states. We find that the atomic excitation has negligibly small probability during the scattering process. Our study may provide a new way to generate an expected photon state via photon scattering by a giant atom in two-dimensional photonic array.

In this paper, we propose a high-fidelity scheme for generating entangled states in a system of two and three giant atoms coupled to the coupled resonator waveguide. Our approach leverages the bound state in the continuum, which is robust against waveguide disorder. Specifically, we achieve a fidelity exceeding 98% for Bell state generation, overcoming the limitations of conventional decoherence-free interaction mechanisms. This scheme can be readily extended to a three-giant-atom system for generating W states. In both the twoand three-atom setups, the maximally entangled states are generated in a short time and remain stable even as time approaches infinity. Our proposal is feasible for implementation on state-of-the-art solid-state quantum platforms and significantly broadens the applications of giant atoms and waveguide QED systems in quantum information processing.

Going beyond traditional chemical batteries, we investigate a quantum battery system under both external driving and dissipation. The system consists of a coupled two-level charger and battery immersed in non-equilibrium fermionic reservoirs. By considering the changes in the energy spectrum induced by external driving and charger-battery coupling in a non-perturbative manner, we go beyond the secular approximation to derive the Redfield master equation. In the non-equilibrium scenario, both charging efficiency and power of the quantum battery can be optimized through a compensation mechanism. When the charger and battery are off-resonance, a significant chemical potential difference between the reservoirs, which characterizes the degree of non-equilibrium, plays a crucial role. Specifically, the charger's frequency should be higher (lower) than that of the battery when the average chemical potential is negative (positive) to achieve enhanced charging efficiency and power under strong non-equilibrium conditions. Remarkably, the efficiency in the non-equilibrium case can surpass that in the equilibrium setup. Moreover, we find no positive correlation between entanglement and efficiency; therefore, entanglement is not necessary to enhance the performance of quantum devices. Our results provide insights into the design and optimization of quantum batteries in non-equilibrium open systems.

Leveraging the sensitive dependence of a giant atom's relaxation rate on its frequency [A. F. Kockum et al., Phys. Rev. A 90, 013837 (2014)], we propose an effective magnetometer model based on a single giant emitter. In this model, the emitter's frequency is proportional to the applied bias magnetic field. The self-interference effect causes the slope of the decay rate to vary linearly with the number of emitter-waveguide coupling points. The giant emitter magnetometer achieves a sensitivity as high as 10-8-10-9 T/ Hz, demonstrating the significant advantages of the self-interference effect compared to small emitters. We hope our proposal will expand the applications of giant emitters in precision measurement and magnetometry.