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Molecular dynamics approaches use wave packets as nucleon wave functions to simulate the time evolution of nuclear reactions. It is crucial to activate the momentum fluctuation inherent in each wave packet so that it properly affects the time evolution. In the antisymmetrized molecular dynamics (AMD) model, this has traditionally been done by splitting the wave packets, i.e., by introducing a random fluctuation to the wave packet center of each particle. The present work proposes an improved approach to activate the fluctuation in both the one-body mean-field propagation and the two-nucleon collision processes, consistently based on the gradual or sudden change of the degree of isolation, which is derived from the fragment number function used for the zero-point energy subtraction. This new method is applied to the 12C + 12C and 12C + p reactions at about 100 MeV/nucleon, focusing on the momentum distribution of the 11B fragments produced by one-proton removal from the 12C projectile. The results show that, with the momentum fluctuation suitably activated, the method correctly accounts for the recoil from the removed nucleon to the residue and the 11B momentum distribution is significantly improved, while without activating the fluctuation the distribution is too narrow compared to the experimental data. Furthermore, the AMD results indicate that the momentum distribution consists of two components; one is the high $P_z$ component with a small shift from the beam velocity, resulting from the simple removal of a proton after an energetic collision with a target particle; the other is the low $P_z$ component with a larger peak shift resulting from the decay of an excited 12C nucleus in a longer time scale. The activation of momentum fluctuation mainly affects the high $P_z$ component to broaden it. The role of cluster correlations in this problem is also investigated., Comment: 15 pages, 13 figures

The Zeeman effect, a fundamental quantum phenomenon, demonstrates the interaction between magnetic fields and atomic systems. While precise spectroscopic measurements of this effect have advanced significantly, there remains a lack of simple, visually accessible demonstrations for educational purposes. Here, we present a low-cost experiment that allows for direct visual observation of the Zeeman effect. Our setup involves a flame containing sodium (from table salt) placed in front of a sodium vapor lamp. When a magnetic field is applied to the flame, the shadow cast by the flame noticeably lightens, providing a clear, naked-eye demonstration of the Zeeman effect. Furthermore, we conduct two quantitative experiments using this setup, examining the effects of varying magnetic field strength and sodium concentration. This innovative approach not only enriches the experimental demonstration for teaching atomic physics at undergraduate and high school levels but also provides an open platform for students to explore the Zeeman effect through hands-on experience., Comment: 5 pages, 6 figures, Comments are welcome. This manuscript is intended for submission to American Journal of Physics

The bubble nuclei are important components of exotic nuclear structures characterized by special depletions of central densities. Focusing on bubble structures of $^{36}$Ar, the characterizations of bubble nuclei were explored with the framework of the extended quantum molecular dynamics model. Three density distribution modes were uncovered for the first time, i.e. micro-bubble, bubble, and cluster resonances, which show unique spectral signature compared to the monopole resonance spectrum as the excitation intensity was increased in bubbles. Of pivotal importance is the revelation that the bubble mode's oscillation frequency closely resembles macroscopic bubble dynamics, building a connection between classical macroscopic phenomena and the quantum complexity of the nuclear structure. The discovery marks a crucial step forward in deciphering the relationship between classical and quantum domains within the enigmatic world of atomic nuclei.

The interactions between Rydberg atoms and microwave fields provide a valuable framework for studying the complex dynamics out of equilibrium, exotic phases, and critical phenomena in many-body physics. This unique interplay allows us to explore various regimes of nonlinearity and phase transitions. Here, we observe a phase transition from the state in the regime of bistability to that in multistability in a strongly interacting Rydberg atoms by varying the microwave field intensity, accompanying with the breaking of Z3-symmetry. During the phase transition, the system experiences a hidden critical point, in which the multistable states are difficult to be identified. Through changing the initial state of system, we can identify a hidden multistable state and reveal a hidden trajectory of phase transition, allowing us to track to a hidden critical point. In addition, we observe multiple phase transitions in spectra, suggesting higher-order symmetry breaking. The reported results shed light on manipulating multistability in dissipative Rydberg atoms systems and hold promise in the applications of non-equilibrium many-body physics., Comment: 10 pages, 5 figures

Neural language representation models such as GPT, pre-trained on large-scale corpora, can effectively capture rich semantic patterns from plain text and be fine-tuned to consistently improve natural language generation performance. However, existing pre-trained language models used to generate lyrics rarely consider rhyme information, which is crucial in lyrics. Using a pre-trained model directly results in poor performance. To enhance the rhyming quality of generated lyrics, we incorporate integrated rhyme information into our model, thereby improving lyric generation performance.

The interplay between strong long-range interactions and the coherent driving contribute to the formation of complex patterns, symmetry, and novel phases of matter in many-body systems. However, long-range interactions may induce an additional dissipation channel, resulting in non-Hermitian many-body dynamics and the emergence of exceptional points in spectrum. Here, we report experimental observation of interaction-induced exceptional points in cold Rydberg atomic gases, revealing the breaking of charge-conjugation parity symmetry. By measuring the transmission spectrum under increasing and decreasing probe intensity, the interaction-induced hysteresis trajectories are observed, which give rise to non-Hermitian dynamics. We record the area enclosed by hysteresis loops and investigate the dynamics of hysteresis loops. The reported exceptional points and hysteresis trajectories in cold Rydberg atomic gases provide valuable insights into the underlying non-Hermitian physics in many-body systems, allowing us to study the interplay between long-range interactions and non-Hermiticity.

Jet-associated deuteron production in $pp$ collisions at $\sqrt{s}=13$ TeV and $p$-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV is studied in the coalescence model by using the phase-space information of proton and neutron pairs from a multiphase transport (AMPT) model at the kinetic freezeout. In the low transverse momentum ($p_T$) region $p_T/A < 1.5$ GeV/$c$, where $A$ is the mass number of a nucleus, the in-jet coalescence factor $B_2^\text{In-jet}$ for deuteron production, given by the ratio of the in-jet deuteron number to the square of the in-jet proton number, is found to be larger than the coalescence factor $B_2$ in the medium perpendicular to the jet by a factor of about 10 in $pp$ collisions and of 25 in $p-$Pb collisions, which are consistent with the ALICE measurements at the LHC. Such large low-momentum enhancements mainly come from coalescence of nucleons inside the jet with the medium nucleons. Coalescence of nucleons inside the jet dominates deuteron production only at the higher $p_T$ region of $p_T/A\gtrsim 4$ GeV/$c$, where both the yield ratio $d/p$ of deuteron to proton numbers and the $B_2$ are also significantly larger in the jet direction than in the direction perpendicular to the jet due to the strong collinear correlation among particles produced from jet fragmentation. Studying jet-associated deuteron production in relativistic nuclear collisions thus opens up a new window to probe the phase-space structure of nucleons inside jets.

Phase engineering strategies in two-dimensional transition metal dichalcogenides (2D-TMDs) have garnered significant attention due to their potential applications in electronics, optoelectronics, and energy storage. Various methods, including direct synthesis, pressure control, and chemical doping, have been employed to manipulate structural transitions in 2D-TMDs. Metal intercalation emerges as an effective technique to modulate phase transition dynamics by inserting external atoms or ions between the layers of 2D-TMDs, altering their electronic structure and physical properties. Here, we investigate the significant structural phase transitions in Pb(Ta1+xSe2)2 single crystals induced by Ta intercalation using a combination of Raman spectroscopy and first-principles calculations. The results highlight the pivotal role of Ta atoms in driving these transitions and elucidate the interplay between intercalation, phase transitions, and resulting electronic and vibrational properties in 2D-TMDs. By focusing on Pb(Ta1+xSe2)2 as an ideal case study and investigating like metal intercalation, this study advances understanding in the field and paves the way for the development of novel applications for 2D-TMDs, offering insights into the potential of these materials for future technological advancements.

The global spin alignment of vector mesons has been observed by the STAR collaboration at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). It provides a unique opportunity to probe the correlation between the polarized quark and antiquark in the strongly coupled quark-gluon plasma (sQGP) produced in relativistic heavy ion collisions, opening a new window to explore the properties of sQGP. In addition, spin alignments of vector mesons have also been observed in other high-energy particle collisions. The results seem to be strongly dependent on the hadronization mechanism, so comprehensive studies are needed.In this article, we present a brief review of theoretical and experimental advances in the study of vector meson's spin alignments in a variety of high-energy particle collisions, with emphasis on hadronization mechanisms., Comment: ReVTex 4.1, 15 pages, 7 figures

Non-Hermitian dynamics in quantum systems have unveiled novel phenomena, yet the implementation of valid non-Hermitian quantum measurement remains a challenge, because a universal quantum projective mechanism on the complete but skewed non-Hermitian eigenstates is not explicit in experiment. This limitation hinders the direct acquisition of non-Hermitian observable statistics (e.g., non-Hermitian population dynamics), also constrains investigations of non-Hermitian quantum measurement properties such as uncertainty relation. Here, we address these challenges by presenting a non-Hermitian projective protocol and investigating the non-Hermitian uncertainty relation. We derive the uncertainty relation for pseudo-Hermitian (PH) observables that is generalized beyond the Hermitian ones. We then investigate the projective properties of general quantum states onto complete non-Hermitian eigenvectors, and present a quantum simulating method to apply the valid non-Hermitian projective measurement on a direct-sum dilated space. Subsequently, we experimentally construct a quantum simulator in the quantum optical circuit and realize the 3-dimensional non-Hermitian quantum measurement on the single-photon qutrit. Employing this platform, we explore the uncertainty relation experimentally with different PH metrics. Our non-Hermitian quantum measurement method is state-independent and outputs directly the non-Hermitian quantum projective statistics, paving the way for studies of extensive non-Hermitian observable in quantum domain., Comment: 6 pages, 4 figures

In the paper, we discuss the development of the multi-gap resistive plate chamber Time-of-Flight (TOF) technology and the production of the STAR TOF detector in China at the beginning of the 21st century. Then we review recent experimental results from the first beam energy scan program (BES-I) at the Relativistic Heavy Ion Collider (RHIC). Topics cover measurements of collectivity, chirality, criticality, global polarization, strangeness, heavy-flavor, di-lepton and light nuclei productions., Comment: 31 pages, 33 figures. This review is dedicated to Professor Wenqing Shen on the occasion to celebrate his leadership of the Chinese STAR Collaboration, the development and production of the STAR MRPC TOF detector in China and many physics analyses

Active Target Time Projection Chambers (AT-TPCs) are state-of-the-art tools in the field of low-energy nuclear physics, particularly suitable for experiments using low-intensity radioactive ion beams or gamma rays. The Fudan Multi-purpose Active Target Time Projection Chamber (fMeta-TPC) with 2048 channels has been developed to study $\alpha$-clustering nuclei. {\fcb In this work, the focus is on the study of the photonuclear reaction with the Laser Compton Scattering (LCS) gamma source, especially for the decay of the highly excited $\alpha$-cluster state.} The design of fMeta-TPC is described and a comprehensive evaluation of its offline performance is performed by ultraviolet (UV) laser and $^{241}$Am $\alpha$ source. The result shows that the intrinsic angular resolution of the detector is within 0.30$^{\circ}$ and has an energy resolution of 6.85\% for 3.0 MeV $\alpha$ particles. The gain uniformity of the detector is about 10\% (RMS/Mean), tested by the $^{55}$Fe X-ray source., Comment: 10 pages, 12 figures

Automatic code generation has been a longstanding research topic. With the advancement of general-purpose large language models (LLMs), the ability to code stands out as one important measure to the model's reasoning performance. Usually, a two-stage training paradigm is implemented to obtain a Code LLM, namely the pretraining and the fine-tuning. Within the fine-tuning, supervised fine-tuning (SFT), and reinforcement learning (RL) are often used to improve the model's zero-shot ability. A large number of work has been conducted to improve the model's performance on code-related benchmarks with either modifications to the algorithm or refinement of the dataset. However, we still lack a deep insight into the correlation between SFT and RL. For instance, what kind of dataset should be used to ensure generalization, or what if we abandon the SFT phase in fine-tuning. In this work, we make an attempt to understand the correlation between SFT and RL. To facilitate our research, we manually craft 100 basis python functions, called atomic functions, and then a synthesizing pipeline is deployed to create a large number of synthetic functions on top of the atomic ones. In this manner, we ensure that the train and test sets remain distinct, preventing data contamination. Through comprehensive ablation study, we find: (1) Both atomic and synthetic functions are indispensable for SFT's generalization, and only a handful of synthetic functions are adequate; (2) Through RL, the SFT's generalization to target domain can be greatly enhanced, even with the same training prompts; (3) Training RL from scratch can alleviate the over-fitting issue introduced in the SFT phase.

In the extended thermodynamics of black holes, there exists a thermodynamical pressure and its conjugate volume. Extensive studies have been conducted on the phase structure of numerous black holes, which have demonstrated striking similarities to the phase structure of various ordinary matter systems. A comparison of the thermodynamic properties of spherically symmetric AdS black holes with those of ordinary thermodynamic systems reveals that the isovolumetric heat capacity of the former is zero, whereas that of the latter is non-zero. It is a subject of interest for the intrinsic reason for this discrepancy. The effective thermodynamic quantities, based on the context of the boundary between the black hole horizon and the cosmological horizon in dS spacetime, as well as the interaction between the two horizons, are presented. The heat capacity in the Reissner-N\"{o}rdstrom-de Sitter (RN-dS) spacetime is then investigated, and it is demonstrated that the behavior of the heat capacity in the RN-dS spacetime is analogous to that of Schottky specific heat. Treating the two horizon interfaces in the RN-dS spacetime as two distinct energy levels in a two-energy system, and the thermodynamic properties in the RN-dS spacetime are discussed with the method of studying the thermodynamic properties in an ordinary two-energy system, to elucidate the intrinsic reasons for the occurrence of Schottky specific heat in the RN-dS spacetime. The heat capacity observed in the RN-dS spacetime is not only consistent with that of the Schottky specific heat described by the effective thermodynamic quantities in the RN-dS spacetime, but also with that of the heat capacity in an ordinary two-energy-level system. The quantum properties in the RN-dS spacetime are reflected, thereby providing a new avenue for further in-depth study of the quantum properties of black holes and dS spacetime.

Large Language Models (LLMs) have shown excellent performance in language understanding, text generation, code synthesis, and many other tasks, while they still struggle in complex multi-step reasoning problems, such as mathematical reasoning. In this paper, through a newly proposed arithmetical puzzle problem, we show that the model can perform well on multi-step reasoning tasks via fine-tuning on high-quality synthetic data. Experimental results with the open-llama-3B model on three different test datasets show that not only the model can reach a zero-shot pass@1 at 0.44 on the in-domain dataset, it also demonstrates certain generalization capabilities on the out-of-domain datasets. Specifically, this paper has designed two out-of-domain datasets in the form of extending the numerical range and the composing components of the arithmetical puzzle problem separately. The fine-tuned models have shown encouraging performance on these two far more difficult tasks with the zero-shot pass@1 at 0.33 and 0.35, respectively., Comment: Accept by Findings of ACL 2024

Macromolecules can gain special properties by adopting knotted conformations, but engineering knotted macromolecules is a challenging task. Here we surprisingly observed that knotting can be very effectively produced in active polymers. When one end of an actively reptative polymer is anchored, it can undergo continual self-knotting as a result of intermittent giant conformation fluctuations and the outward reptative motion. Once a knot is formed, it migrates to the anchored point due to a non-equilibrium ratchet effect. Moreover, when the active polymer is grafted on the end of a passive polymer, it can function as a self-propelling soft needle to either transfer its own knots to the passive polymer or directly braid knots on the passive polymer. We further show that these active needles can create inter-molecular bridging knots between two passive polymers. Our finding highlights the non-equilibrium effects in modifying the dynamic pathways of polymer systems, which have potential applications in macromolecular topology engineering, e.g., manipulating topological states of proteins and nucleic acids, as well as macromolecular braiding.

The Extended Quantum Molecular Dynamics (EQMD) model is one of the few QMD-like transport approaches that can describe the $\alpha$-clustering structure with efficient computational power. However, compared to most QMD-like models, the choice of equation of state (EOS) for nuclear matter is very limited. In this work, a Monte Carlo integral method is employed to calculate the density integration with non-integer exponent. We demonstrate the superiority of our approach by studying the isovector giant dipole resonance (IVGDR). This improvement will be beneficial for the EQMD model to study more valuable effects for heavy ion collisions in the near future., Comment: 10 pages, 8 figures

The extended quantum molecular dynamics (EQMD) model is one of the few quantum molecular dynamics (QMD)-like transport approaches that can be used to study the effective clustering structure as well as heavily deformed nuclei in both ground state nuclei and nuclear reactions. However, there are only two parameter sets that lead to hard incompressibility for long times. The aim of the present work is to obtain a soft equation of state (EoS) in the EQMD model. In this context, we take the isoscalar giant monopole resonance (ISGMR), which is sensitive to the EoS, as an example to check our work. By introducing a kind of standard Skyrme energy density functional with different parameter sets, such as SkP, SkT1, and SKXce, whose incompressibility value ranges from 200 to 268 MeV, the ISGMR of $^{208}$Pb and other nuclei are studied. When the SkP parameter sets are adopted, our new soft interaction in the EQMD model gives reasonable agreement with the experimental data in the heavy ion regime., Comment: 10 pages, 8 figures

Particles of non-zero spin produced in non-central heavy-ion collisions are expected to be polarized along the direction perpendicular to the reaction plane because of their spin-orbit interactions in the produced matter, and this has indeed been observed for many hyperons and vector mesons. Here, we show that the hypertriton ($^3_\Lambda\text{H}$), which is the lightest hypernucleus, is also polarized in these collisions. Using the coalescence model based on the kinetic freezeout baryons for light (hyper-)nuclei production, we find that the angular distribution of the decay product of polarized $^3_\Lambda\text{H}$ is highly sensitive to the spin configuration of its wavefunction, providing a novel way to determine its spin structure. We also predict the beam energy dependence of $^3_\Lambda\text{H}$ and ${^3_{\bar{\Lambda}}}\overline{\rm H}$ polarizations in heavy-ion collisions from a few GeV to several TeV based on the measured $\Lambda$ and $\bar{\Lambda}$ polarizations. We further discuss the possibility of studying the spin correlations among nucleons and $\Lambda$ hyperons in the produced hadronic matter from the measured $^3_\Lambda\text{H}$ polarization in non-central heavy-ion collisions., Comment: 6 pages, 2 figures

The production of light nuclei in isobaric $^{96}_{44}$Ru + $^{96}_{44}$Ru and $^{96}_{40}$Zr + $^{96}_{40}$Zr collisions, ranging from $\sqrt{s_{NN}}$ = 7.7 to 200 GeV, are studied using the string melting version of A Multi Phase Transport (AMPT) model in combination with a coalescence approach to light nuclei production. From the calculated yields, transverse momentum $p_{T}$ spectra, and rapidity dependences of light nuclei $p$, $n$, $d$, $t$, ${}^{3}$He, we find that the Ru+Ru/Zr+Zr ratios for the yields of these particles exceed unity with the inclusion of a quadrupole deformation $\beta_{ 2 }$ and octupole deformation $\beta_{ 3 }$ as well as the neutron skins. We also find that heavier particles have a larger deviation from unity. Furthermore, we find that as the collision energy increases, the influence of isospin effects on the production of light nuclei in isobar collisions gradually decreases, while the influence of nuclear structure becomes more significant, particularly evident from the energy dependence of the deuteron ratio, which is unaffected by isospin effects., Comment: 9 pages, 5 figures

Developing an integrated many-to-many framework leveraging multimodal data for multiple tasks is crucial to unifying healthcare applications ranging from diagnoses to operations. In resource-constrained hospital environments, a scalable and unified machine learning framework that improves previous forecast performances could improve hospital operations and save costs. We introduce M3H, an explainable Multimodal Multitask Machine Learning for Healthcare framework that consolidates learning from tabular, time-series, language, and vision data for supervised binary/multiclass classification, regression, and unsupervised clustering. It features a novel attention mechanism balancing self-exploitation (learning source-task), and cross-exploration (learning cross-tasks), and offers explainability through a proposed TIM score, shedding light on the dynamics of task learning interdependencies. M3H encompasses an unprecedented range of medical tasks and machine learning problem classes and consistently outperforms traditional single-task models by on average 11.6% across 40 disease diagnoses from 16 medical departments, three hospital operation forecasts, and one patient phenotyping task. The modular design of the framework ensures its generalizability in data processing, task definition, and rapid model prototyping, making it production ready for both clinical and operational healthcare settings, especially those in constrained environments.

Flat bands and Dirac cones in materials are at the source of the exotic electronic and topological properties. The Lieb lattice is expected to host these electronic structures, arising from quantum destructive interference. Nevertheless, the experimental realization of a two-dimensional Lieb lattice remained challenging to date due to its intrinsic structural instability. After computationally designing a Platinum-Phosphorus (Pt-P) Lieb lattice, we have successfully overcome its structural instability and synthesized it on a gold substrate via molecular beam epitaxy. Low-temperature scanning tunneling microscopy and spectroscopy verified the Lieb lattice's morphology and electronic flat bands. Furthermore, topological Dirac edge states stemming from pronounced spin-orbit coupling induced by heavy Pt atoms have been predicted. These findings convincingly open perspectives for creating metal-inorganic framework-based atomic lattices, offering prospects for strongly correlated phases interplayed with topology., Comment: 24 pages,11 figures

Crystal seeding enables a deeper understanding of phase behavior, leading to the development of methods for controlling and manipulating phase transitions in various applications such as materials synthesis, crystallization processes, and phase transformation engineering. How to seed a crystalline in time domain is an open question, which is of great significant and may provide an avenue to understand and control time-dependent quantum many-body physics. Here, we utilize a microwave pulse as a seed to induce the formation of a discrete time crystal in Floquet driven Rydberg atoms. In the experiment, the periodic driving on Rydberg states acts as a seeded crystalline order in subspace, which triggers the time-translation symmetry breaking across the entire ensemble. The behavior of the emergent time crystal is elaborately linked to alterations in the seed, such as the relative phase shift and the frequency difference, which result in phase dependent seeding and corresponding shift in periodicity of the time crystal, leading to embryonic synchronization. This result opens up new possibilities for studying and harnessing time-dependent quantum many-body phenomena, offering insights into the behavior of complex many-body systems under seeding.

The identification of tipping points is essential for prediction of collapses or other sudden changes in complex systems. Applications include studies of ecology, thermodynamics, climatology, and epidemiology. However, detecting early signs of proximity to a tipping is made challenging by complexity and non-linearity. Strongly interacting Rydberg atom gases offer a model systems that offer both complexity and non-linearity, including phase transition and critical slowing down. Here, via an external probe we observe prior warning of the proximity of a phase transition of Rydberg thermal gases. This warning signal is manifested as a cessation of the variance growth with increasing probe intensity. We also observed the dynamics of the critical slowing down behavior versus different time scales, driving intensities, and atomic densities, thus providing insights into the study of a Rydberg atom system's critical behavior. Our experiment suggests that the full critical slowing down dynamics of strongly-interacting Rydberg atoms can be probed systematically, thus providing a benchmark with which to identify critical phenomena in quantum many-body systems.

Investigating nucleon-nucleon correlations inherent to the strong nuclear force is one of the core goals in nuclear physics research. We showcase the unique opportunities offered by collisions of $^{16}$O nuclei at high-energy facilities to reveal detailed many-body properties of the nuclear ground state. We interface existing knowledge about the geometry of $^{16}$O coming from \textit{ab-initio} calculations of nuclear structure with transport simulations of high-energy $^{16}$O+$^{16}$O collisions. Bulk observables in these processes, such as the elliptic flow or the fluctuations of the mean transverse momentum, are found to depend significantly on the input nuclear model and to be sensitive to realistic clustering and short-range repulsive correlations, effectively opening a new avenue to probe these features experimentally. This finding demonstrates collisions of oxygen nuclei as a tool to elucidate initial conditions of small collision systems while fostering connections with effective field theories of nuclei rooted in quantum chromodynamics (QCD).

We present an integral density method for calculating the multifractal dimension spectrum for the nucleon distribution in atomic nuclei. This method is then applied to analyze the non-uniformity of the density distribution in several typical types of nuclear matter distributions, including the Woods-Saxon distribution, the halo structure and the tetrahedral $\alpha$ clustering. The subsequent discussion provides a comprehensive and detailed exploration of the results obtained. The multifractal dimension spectrum shows remarkable sensitivity to the density distribution, establishing it as an effective tool for studying the distribution of nucleons in nuclear multibody systems., Comment: 9 pages, 6 figures

We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger (SSH) model with long-range hopping terms. By computing the quantum geometry tensor, we derive exactly expressions for the quantum metric and Berry curvature of the energy band electrons, and we obtain the phase diagram of the model marked by the first Chern number. Furthermore, we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. However, some regions where the Berry curvature is identically zero in the first Brillouin zone results in the degeneracy of the quantum metric, which leads to ill-defined non-integer topological Euler numbers. Nevertheless, the non-integer "Euler number" provides valuable insights and provide an upper bound for absolute values of the Chern numbers., Comment: 6 pages, 4 figures

Engineering a Terahertz (THz) frequency comb spectroscopy at atomic level advances the precisely measurement in spectroscopy and sensing. Current progresses on THz frequency comb rely on difference-frequency generation, optical parametric oscillation, and other methods. Generating a THz frequency comb poses challenges in source stability and achieving a narrow bandwidth, which traditional THz devices are difficult to achieve. Furthermore, accurately measuring the generated THz frequency comb necessitates a high-performance THz detector. Rydberg atoms are well-suited for electric field sensing due to their ultra-wide radio frequency transition energy levels, making them especially sensitive to external electric fields in the DC to THz bandwidth. However, there have been no reports about generating THz frequency comb spectroscopy at the atomic level until now. This work presents a THz frequency comb spectroscopy with Rydberg atoms, in which a Floquet comb-like transition is engineered through a time-periodic drive field. Our approach simplifies the setup required for THz frequency comb spectroscopy while extending the working bandwidth for Rydberg atomic sensors. The THz frequency comb spectroscopy at the atomic level reported in this article shows great potential for various applications in astronomy, remote sensing, spectral detection of biological samples, and other related fields.

Developing microwave electric field sensing based on Rydberg atom has received significant attention due to its unique advantages. However, achieving effective coupling between Rydberg atom and the microwave electric field in the sensing process is a challenging problem that greatly impacts the sensitivity. To address this, we propose the use of a microwave resonant cavity to enhance the effective coupling between the Rydberg atoms and the microwave electric field. In our experiment, we use a three-photon excitation scheme to prepare Rydberg atoms, make measurements of electric fields without and with a microwave cavity in which the vapor cell is put inside. Through experimental testing, we achieve an 18 dB enhancement of power sensitivity. The experiment shows an effective enhancement in electric field pulse signal detection. This result provides a promising direction for enhancing the sensitivity of Rydberg atomic electric field sensors and paves the way for their application in precision electric field measurements.

Multiplicity information entropy in central $^{197}$Au + $^{197}$Au collisions at impact parameters of 0$-$3 fm are calculated at various center of mass energies ($\sqrt{s_{\rm NN}}$) of 5.0, 7.7, 11.5, 14.5, 19.6, 27.0, 32.0, 35.0, 39.0, and 54.4 GeV using the Ultra-relativistic Quantum Molecular Dynamics model (UrQMD). The simulations in UrQMD model are compared with hydro modes with three different equations of state (EoS) and also with a default mode without hydrodynamics. The study reveals that the information entropies of baryons, net-baryons and net-protons with different equations of state in the hydro modes exhibit first decreases and then slowly increases with the increase of $\sqrt{s_{\rm NN}}$, while those of hadrons and anti-hadrons, antibaryons show a monotonous increase with $\sqrt{s_{\rm NN}}$. An enhancement is found around $\sqrt{s_{\rm NN}}$ $\sim$ 30 GeV potentially corresponding to the critical endpoint with chiral hadron gas EoS and Bag model EoS., Comment: 7 pages, 7 figures