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Here we investigate the internal sublattice symmetry, and thus the enriched topological classification of bosonic Bogoliubov excitations of thermodynamically stable free-boson systems with non-vanishing particle-number-nonconserving terms. Specifically, we show that such systems well described by the bosonic Bogoliubov-de Gennes Hamiltonian can be in general reduced to particle-number-conserving (single-particle) ones. Building upon this observation, the sublattice symmetry is uncovered with respect to an excitation energy, which is usually hidden in the bosonic Bogoliubov-de Gennes Hamiltonian. Thus, we obtain an additional topological class, i.e., class AIII, which enriches the framework for the topological threefold way of free-boson systems. Moreover, a construction is proposed to show a category of systems respecting such a symmetry. For illustration, we resort to a one-dimensional (1D) prototypical model to demonstrate the topological excitation characterized by a winding number or symplectic polarization. By introducing the correlation function, we present an approach to measure the topological invariant. In addition, the edge excitation together with its robustness to symmetry-preserving disorders is also discussed., Comment: 18 pages, 4 figures

Let $(S,\mathcal{F})$ be a foliated surface over the complex number of general type, i.e., the Kodaira dimension $\mathrm{Kod}(\mathcal{F})=2$. We study the geometry of the canonical map $\varphi$ of the foliated surface $(S,\mathcal{F})$, and prove several boundedness results on the canonical map $\varphi$, generalizing Beauville's beautiful work on the canonical maps of algebraic surfaces to foliated surfaces. As an application, we prove three Noether type inequalities for $(S,\mathcal{F})$ depending on the Kodaira dimension of the surface $S$., Comment: Comments are welcome. arXiv admin note: text overlap with arXiv:2404.16293

We explore the collective Zeno dynamics of giant artificial atoms that are coupled, via multiple coupling points, to a common photonic or acoustic reservoir. In this regime, the establishment of atomic cooperativity and the revivification of exponential decay, are highly intertwined, which is utterly beyond the non-Markovian regime with only retarded backaction. We reveal that giant atoms build up their collective emission smoothly from the decay rate of zero to that predicted by Markovian approximation, and show great disparity between different waveguide QED setups. As a comparison, the step-like growth of instantaneous decay rates in the retardation-only picture has also been shown. All of these theoretical pictures predict the same collective behavior in the long time limit. From a phenomenological standpoint, we observe that the atomic superradiance exhabits significant directional property. In addition, the subradiant photons feature prolonged oscillation in the early stage of collective radiance, where the energy is exchanged remarkably between giant emitters and the field. Our results might be probed in state-of-art waveguide QED experiments, and fundamentally broaden the fields of collective emission in systems with giant atoms., Comment: 14 pages, 6 figures

Genuine multipartite entanglement (GME) is not only fundamental interesting for the study of quantum-to-classical transition, but also is essential for realizing universal quantum computing and quantum networks. Here we investigate the multipartite entanglement (ME) dynamics in a linear chain of N LC resonators interacting optomechanically with a common thermal acoustic reservoir. By presenting the exact analytical solutions of system evolution, we predict the periodic generation of non-Gaussian ME, including the discrete and continuous variables entanglement. Interestingly, the GME is obtained even though the system is in a heat bath. The mechanism relies on the special acoustic environment featuring frequency comb structure. More importantly, our proposed model also allows the periodic generation of entangled multipartite cat states (MCSs), i.e., a typical GHZ state, with high fidelity. This work fundamentally broadens the fields of ME, and have wide applications in implementing thermal-noise-resistant quantum information processing and many-body quantum simulation., Comment: 25 pages, 9 figures

Realizing precise control over multiquanta emission is crucial for quantum information processing, especially when integrated with advanced techniques of manipulating quantum states. Here, by spinning the resonator to induce the Sagnac effect, we can obtain nonreciprocal photon-phonon and photon-magnon super-Rabi oscillations under conditions of optically driving resonance transitions. Opening dissipative channels for such super-Rabi oscillations enables the realization of directional bundle emissions of entangled photon-phonon pairs and photon-magnon pairs by transferring pure multiquanta state to bundled multiquanta outside of the system. This nonreciprocal emission is a flexible switch that can be controlled with precision, and simultaneous emissions of different entangled pairs (such as photon-phonon or photon-magnon pairs) can even emerge but in opposite directions by driving the resonator from different directions. This ability to flexibly manipulate the system allows us to achieve directional entangled multiquanta emitters, and has also potential applications for building hybrid quantum networks and on-chip quantum communications., Comment: 16 pages, 4 figures, accepted by Physical Review Letters

We theoretically predict a kind of power-law-exponential (PLE) dipole-dipole interaction between quantum emitters in a 1D waveguide QED system. This unconventional long-range interaction is the combination of power-law growth and exponential decay couplings. Applying PLE interaction to a spin model, we uncover the rich many-body phases. Most remarkably, we find that PLE interaction can induce the ordered and critical spiral phases. These spiral phases emerge from the strong frustration generated by the power-law factor of PLE interaction, hence they are absent for other types of long-range interaction, e.g., pure exponential and power-law decay interactions. Our work is also applicable for the higher dimensional systems. It fundamentally broadens the realm of many-body physics and has the significant applications in quantum simulation of strong correlated matters., Comment: 16 pages, 12 figures

We demonstrate the emergence of nonreciprocal superradiant phase transitions and novel multicriticality in a cavity quantum electrodynamics (QED) system, where a two-level atom interacts with two counter-propagating modes of a whispering-gallery-mode (WGM) microcavity. The cavity rotates at a certain angular velocity, and is directionally squeezed by a unidirectional parametric pumping $\chi^{(2)}$ nonlinearity. The combination of cavity rotation and directional squeezing leads to nonreciprocal first- and second-order superradiant phase transitions. These transitions do not require ultrastrong atom-field couplings and can be easily controlled by the external pump field. Through a full quantum description of the system Hamiltonian, we identify two types of multicritical points in the phase diagram, both of which exhibit controllable nonreciprocity. These results open a new door for all-optical manipulation of superradiant transitions and multicritical behaviors in light-matter systems, with potential applications in engineering various integrated nonreciprocal quantum devices, Comment: 18 pages, 10 figures

We propose an innovative design for quantum batteries (QBs) that involves coupling two-level systems to a topological photonic waveguide. Employing the resolvent method, we analytically explore the thermodynamic performances of QBs. First, we demonstrate that in the long-time limit, only bound states significantly contribute to the stored energy of QBs. We observe that near-perfect energy transfer can occur in the topologically nontrivial phase. Moreover, the maximum stored energy exhibits singular behavior at the phase boundaries, where the number of bound states undergoes a transition. Second, when a quantum battery and a quantum charger are coupled at the same sublattice within a unit cell, the ergotropy becomes immune to dissipation at that location, facilitated by a dark state and a topologically robust dressed bound state. Third, we show that as dissipation intensifies along with the emergence of the quantum Zeno effect, the charging power of QBs experiences a temporary boost. Our findings offer valuable guidance for improving quantum battery performance through structured reservoir engineering., Comment: 8 + 16 pages, 3 + 7 figures. Revised version

Let $\mathcal F$ be a foliation on a smooth projective surface $S$ over the complex number $\mathbb{C}$. We introduce three birational non-negative invariants $c_1^2(\mathcal F)$, $c_2(\mathcal F)$ and $\chi(\mathcal F)$, called the Chern numbers. If the foliation $\mathcal F$ is not of general type, the first Chern number $c_1^2(\mathcal F)=0$, and $c_2(\mathcal F)=\chi(\mathcal F)=0$ except when $\mathcal F$ is induced by a non-isotrivial fibration of genus $g=1$. If $\mathcal F$ is of general type, we obtain a slope inequality when $\mathcal F$ is algebraically integral. As a corollary, $\mathcal F$ is always transcendental if the slope is less than $2$. On the other hand, we also prove three sharp Noether type inequalities if $\mathcal F$ is of general type. As applications, we obtain a criterion for foliations to be transcendental using Noether type inequalities, and we also give a partial positive answer to the question on the lower bound on the volume of a foliation of general type., Comment: The title is changed and one more author is added. In this new version, we provide two approaches to study the Poincare's problem on the algebraic integrability of foliations on smooth surfaces: the first one is to use the Chern numbers and slope inequalities; the other one is to use the Noether type inequalities obtained in the earlier version.of this paper. Any comment is warmly welcome

Based on the scattering matrix method, we theoretically demonstrate that the chiral interaction can induce the almost perfect photon blockade (PB) in the waveguide-cavity quantum electrodynamics (QED) system. The mechanism relies on the multi-photon-paths interference within the waveguide, which is clearly shown by the analytical parameter regime for $g^{(2)}(0)\approx0$. When $N$ cavities are introduced into the system, there are $N$ optimal parameter points accordingly for the almost perfect PB, and the required chirality decreases exponentially with increasing $N$. Under the conditions of resonant driving and specific chirality, the output light only relies on the parity of $N$ ($N\ge2$), where the coherent state and single-photon state correspond to the case of system including the odd and even number of cavities, respectively. Our work offers an alternative route for achieving almost perfect PB effects by employing the chirality of system, with potential application in the on-chip single-photon source with integrability., Comment: 5 pages, 4 figures + Supplemental Material

The Schr\"{o}dinger cat state produced differently in two directions is anticipated to be a critical quantum resource in quantum information technologies. By exploring the interplay between quantum nonreciprocity and topology in a one-dimensional microcavity array, we obtain the Schr\"{o}dinger cat state ({\it a pure quantum state}) in a chosen direction at the edge cavity, whereas a {\it classical state} in the other direction. This {\it nonreciprocal generation of the cat state} originates from the {\it topologically protected chirality-mode excitation} in the nontrivial phase, but in the trivial phase the {\it nonreciprocal generation of cat state} vanishes. Thus, our proposal is switchable by tuning the parameters so that a topological phase transition occurs. Moreover, the obtained cat state has nonreciprocal high fidelity, nonclassicality, and quantum coherence, which are sufficient to be used in various one-way quantum technologies, e.g., invisible quantum sensing, noise-tolerant quantum computing, and chiral quantum networks. Our work provides a general approach to control quantum nonreciprocities with the topological effect, which substantially broadens the fields of nonreciprocal photonics and topological physics., Comment: 8 pages, 4 figures, accepted by SCIENCE CHINA Physics, Mechanics & Astronomy

We derive a compact analytical solution of the $n$th-order equal-time correlation functions by using scattering matrix ($S$ matrix) under a weak coherent state input. Our solution applies to any dissipative quantum system that respects the U(1) symmetry. We further extend our analytical solution into two categories depending on whether the input and output channels are identical. The first category provides a different path for studying cross-correlation and multiple-drive cases, while the second category is instrumental in studying waveguide quantum electrodynamics systems. Our analytical solution allows for easy investigation of the statistical properties of multiple photons even in complex systems. Furthermore, we have developed a user-friendly open-source library in Python known as the quantum correlation solver, and this tool provides a convenient means to study various dissipative quantum systems that satisfy the above-mentioned criteria. Our study enables using $S$ matrix to study the photonic correlation and advance the possibilities for exploring complex systems., Comment: 22 pages, 8 figures, the QCS open-source library is available at http://github.com/ZhiGuangLu/qcs/

We theoretically predict the squeezing-induced point-gap topology together with a {\it symmetry-protected $\mathbb{Z}_2$ skin effect} in a one-dimensional (1D) quadratic-bosonic system (QBS). Protected by a time-reversal symmetry, such a topology is associated with a novel $\mathbb{Z}_2$ invariant (similar to quantum spin-Hall insulators), which is fully capable of characterizing the occurrence of $\mathbb{Z}_2$ skin effect. Focusing on zero energy, the parameter regime of this skin effect in the phase diagram just corresponds to a {\it real-gap and point-gap coexisted topological phase}. Moreover, this phase associated with the {\it symmetry-protected $\mathbb{Z}_2$ skin effect} is experimentally observable by detecting the steady-state power spectral density. Our work is of fundamental interest in enriching non-Bloch topological physics by introducing quantum squeezing, and has potential applications for the engineering of symmetry-protected sensors based on the $\mathbb{Z}_2$ skin effect., Comment: 6 pages, 4 figures + Supplemental Material

We theoretically study the superradiant phase transition (SPT) in an indirect Rabi model, where both a two-level system and a single mode bosonic field couple to an auxiliary bosonic field. We find that the indirect spin-field coupling induced by the virtual excitation of the auxiliary field can allow the occurrence of a SPT at a critical point, and the influence of the so-called $A^2$ term in the normal Rabi model is naturally avoided. In the large detuning regime, we present the analytical expression of quantum critical point in terms of the original system parameters. The critical atom-field coupling strength is tunable, which will loosen the conditions on realizing the SPT. Considering a hybrid magnon-cavity-qubit system, we predict the squeezed cat state of magnon generated with feasible experimental parameters, which has potential applications in quantum metrology and quantum information processing., Comment: 12 pages, 8 figures

We propose a physical witness for dynamically detecting topological phase transitions (TPTs) via an experimentally observable out-of-time-order correlation (OTOC). The distinguishable OTOC dynamics appears in the topological trivial and non-trivial phases due to the topological locality. In the long-time limit, the OTOC undergoes a {\it zero-to-finite-value transition} at the critical point of the TPTs. This transition is robust to the choices of the initial state of the system and the used operators in OTOC. The proposed OTOC witness can be applied into the systems with and without chiral symmetry, e.g., the lattices described by the SSH model, Creutz model, and Haldane model. Moreover, our proposal, as a physical witness in real space, is still valid even in the presence of disorder. Our work fundamentally offers a new prospect of exploring topological physics with quantum correlations., Comment: 8 pages, 4 figures + Supplemental Material

We investigate theoretically the collective radiance characteristics of an atomic ensemble with the simultaneous decay of two atoms. We show that the two-atom decay can significantly suppress the steady-state collective radiance of the atoms, expanding the region of subradiance. In the steady-state subradiance regime, the system is in an entangled state, and the mean populations of the system in the excited state and ground state of the atoms are almost equal. The processes of the two-atom decay can be demonstrated by the population distribution of the system state on the Dicke ladder. Moreover, we show the correlation property of the emitted light from the atomic ensemble, where the correlation function is rewritten in the presence of the two-atom decay. We find that the emitted photons of steady state only show bunching in the case of two-atom decay. This work broadens the realm of collective radiance, with potential applications for quantum information processing., Comment: 8 pages, 5 figures

We investigate the non-Markovian dynamics of two giant artificial atoms interacting with a continuum of bosonic modes in a one-dimensional (1D) waveguide. Based on the diagrammatic method, we present the exact analytical solutions, which predict the rich phenomena of collective radiance. For the certain collective states, the decay rates are found to be far beyond that predicted in the the Dicke model and standard Markovian framework, which indicates the occurrence of super-superradiance. The superadiance-to-subradiance transition could be realized by adjusting the exchange symmetry of giant atoms. Moreover, there exists multiple bound states in continuum (BICs), with photons/phonons bouncing back and forth in the cavity-like geometries formed by the coupling points. The trapped photons/phonons in the BICs can also be re-released conveniently by changing the energy level splitting of giant atoms. The mechanism relies on the joint effects of the coherent time-delayed feedback and the interference between the coupling points of giant atoms. This work fundamentally broadens the fields of giant atom collective radiance by introducing non-Markovianity. It also paves the way for a clean analytical description of nonlinear open quantum system with more complex retardation., Comment: 8 pages, 5 figures + Supplemental Material (15 pages, 3 figures)

An experimentally feasible magnetometer based on a dual-coupling optomechanical system is proposed, where the radiation-pressure coupling transduces the magnetic signal to the optical phase, and the quadratic optomechanical interaction induces a periodic squeezing effect. The latter not only amplifies the signal to be measured, but also accelerates the signal transducing rate characterized by an experimentally observable phase accumulation efficiency. In the vicinity of opto-mechanical decoupled time, the ultimate bound to the estimability of magnetic signal is proportional to $\exp(-6r)$, and then the optimized accuracy of estimation can be enhanced nearly 3 orders with a controllable squeezing parameter $r<1$. Moreover, our proposal is robust against the mechanical thermal noise, and the sensitivity of a specific measurement can reach to the order of $10^{-17}{\rm T/\sqrt{Hz}}$ in the presence of dissipations and without ground state cooling of mechanical oscillator. Our proposal fundamentally broadens the fields of quantum metrology and cavity optomechanics, with potential application for on-chip magnetic detection with high precision., Comment: 7 pages, 4 figures + Supplementary Material

We introduce the notion of topological hyperbolicity to characterize the largeness of the topological fundamental group of a complex variety. Inspired by the Shafarevich conjecture, we propose to study the topological hyperbolicity of moduli spaces of polarized manifolds. We provide two pieces of supporting evidence: first, we show that moduli spaces where the infinitesimal Torelli theorem holds are very close to being topologically hyperbolic. Second, we establish a weak form of topological hyperbolicity for moduli spaces of elliptic surfaces of Kodaira dimension one without multiple fibers, where the infinitesimal Torelli theorem generally does not hold., Comment: 14 pages, comments welcome

We demonstrate symmetry protected bundle emission in the cavity QED system under the ultrastrong coupling regime. Parity symmetry of Rabi model only permits the super-Rabi oscillations with periodic generation of even photons in cavity, which is realized by the laser driven flip of qubit and the parity conserved transitions induced by Rabi interaction. Combined with dissipation, only 2$n$-photon correlated emissions are allowed, and the corresponding purities are significantly enhanced by the parity symmetry, due to the almost perfect suppression of bundle emissions with odd correlated photons. The switching of bundle emissions between even and odd correlated photons can be controlled by manipulating the parity symmetry of system with an added magnetic field. This work extends multi-photon bundle emission to the ultrastrong coupling regime, and offers the prospect of exploring symmetry-protected multi-quanta physics., Comment: 6 pages, 4 figures

Objectives.--To estimate the basic reproduction number of the Wuhan novel coronavirus (2019-nCoV). Methods.--Based on the susceptible-exposed-infected-removed (SEIR) compartment model and the assumption that the infectious cases with symptoms occurred before January 25, 2020 are resulted from free propagation without intervention, we estimate the basic reproduction number of 2019-nCoV according to the reported confirmed cases and suspected cases, as well as the theoretical estimated number of infected cases by other research teams, together with some epidemiological determinants learned from the severe acute respiratory syndrome. Results The basic reproduction number falls between 2.8 to 3.3 by using the real-time reports on the number of 2019-nCoV infected cases from People's Daily in China, and falls between 3.2 and 3.9 on the basis of the predicted number of infected cases from colleagues. Conclusions.--The early transmission ability of 2019-nCoV is closed to or slightly higher than SARS. It is a controllable disease with moderate-high transmissibility. Timely and effective control measures are needed to suppress the further transmissions. Notes Added.--Using a newly reported epidemiological determinants for early 2019-nCoV, the estimated basic reproduction number is in the range [2.2,3.0]., Comment: 8 pages, 1 table and 1 figure