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GENERAL

Many-body localization of a one-dimensional anyon Stark model
YOU Huimin, LIU Jinghu, ZHANG Yunbo, XU Zhihao
2025, 74 (4): 040301. doi: 10.7498/aps.74.20241615
Abstract +
In this work, a one-dimensional interacting anyon model with a Stark potential in the finite size is studied. Using the fractional Jordan Wigner transformation, the anyons in the one-dimensional system are mapped onto bosons, which are described by the following Hamiltonian:         $ \begin{aligned} \hat{H}^{\text{boson}}=-J\sum_{j=1}^{L-1}\left( \hat{b}_{j}^{\dagger}\hat{b}_{j+1}{\mathrm{e}}^{{\mathrm{i}}\theta \hat{n}_{j}}+{\mathrm{h.c.}}\right)+\frac{U}{2}\sum_{j=1}^{L}\hat{n}_{j}\left( \hat{n}_{j}-1\right)+\sum_{j=1}^{L}{h}_{j}\hat{n}_{j},\;\;\;\;\;\;\;\;\;\end{aligned}$where θ is the statistical angle, and the on-site potential is $h_{j}=-\gamma\left(j-1\right) +\alpha\Big( \dfrac{j-1}{L-1}\Big)^{2}$ with γ representing the strength of the Stark linear potential and α denoting the strength of the nonlinear part. Using the exact diagonalization method, the spectral statistics, half-chain entanglement entropy and particle imbalance are numerically analyzed to investigate the onset of many-body localization (MBL) in this interacting anyon system, induced by increasing the linear potential strength. As the Stark linear potential strength increases, the spectral statistics transforms from a Gaussian ensemble into a Poisson ensemble. In the ergodic phase, except for θ = 0 and π, where the average value of the gap-ratio parameter $\left\langle r\right\rangle\approx 0.53$, due to the destruction of time reversal symmetry, the Hamiltonian matrix becomes a complex Hermit matrix and $\left\langle r\right\rangle\approx 0.6$. In the MBL phase, $\left\langle r\right\rangle\approx 0.39$, which is independent of θ. However, in the intermediate γ regime, the value of $\left\langle r\right\rangle$ strongly depends on the choice of θ. The average of the half-chain entanglement entropy transforms from a volume law into an area law, which allows us to construct a θ-dependent MBL phase diagram. In the ergodic phase, the entanglement entropy S(t) of the half chain increases linearly with time. In the MBL phase, S(t) grows logarithmically with time, reaching a stable value that depends on the anyon statistical angle. The localization of particles in a quench dynamics can provide the evidence for the breakdown of ergodicity and is experimentally observable. It is observed that with the increase of γ, the even-odd particle imbalance changes from zero to non-zero values in the long-time limit. In the MBL phase, the long-time average value of the imbalance is dependent on the anyon statistical angle θ. From the Hamiltonian $\hat{H}^{\text{boson}}$, it can be inferred that the statistical behavior of anyon system equally changes the hopping interactions in boson system, which is a many-body effect. By changing the statistical angle θ, the many-body interactions in the system are correspondingly changed. And the change of the many-body interaction strength affects the occurrence of the MBL transition, which is also the reason for MBL transition changing with the anyon statistical angle θ. Our results provide new insights into the study of MBL in anyon systems and whether such phenomena persist in the thermodynamic limit needs further discussing in the future.

GENERAL

Experimental verification of on-chip quantum key distribution based on advantage distillation
ZHANG Rui, TIAN Yu, ZHANG Bin, CHEN Gaohui, DING Huajian, ZHOU Xingyu, WANG Qin
2025, 74 (4): 040302. doi: 10.7498/aps.74.20241375
Abstract +
Quantum key distribution (QKD) has been extensively studied for practical applications. Advantage distillation (AD) represents a key technique to extract highly correlated bit pairs from weakly correlated ones, thus improving QKD protocol performance, particularly in large-error scenarios. However, its practical implementation remains under-explored. In this study, the AD is integrated into the three-intensity decoy-state BB84 protocol and its performance is demonstrated on a high-speed phase-encoding platform. The experimental system employs an asymmetric Mach-Zehnder interferometer (AMZI) fabricated on a silicon dioxide optical waveguide chip for phase encoding, which is benefited from its low coupling loss and minimum waveguide transmission loss. Phase-randomized weak coherent pulses, generated by a distributed feedback laser at 625 MHz, are modulated into decoy states of varying intensities. The signals are encoded via an AMZI and attenuated to single-photon levels before transmission. At the receiver, another AMZI demodulates the signals detected by avalanche photodiodes in gated mode. Experiments conducted at 50 km and 105 km demonstrate secure key rates of 104 kbits/s and 59 bits/s, respectively. The results at shorter distances closely match theoretical predictions, while slight deviations at 105 km are attributed to signal attenuation and noise. Despite these challenges, the results obtained at 105 km highlight the effectiveness of AD in enhancing secure key rates in the large-error scenario. This study confirms the potential of AD in extending secure communication range of QKD. By leveraging the high integration and scalability of silicon dioxide photonic chips, the proposed system lays a foundation for large-scale QKD deployment, paving the way for developing advanced protocols and real-world quantum networks.

GENERAL

Effects of ambient noise on quantum speed limit time and quantum discord dynamics of a double “gravitational cat state” system
DAI Youcheng, HAN Wei, ZHANG Yingjie
2025, 74 (4): 040303. doi: 10.7498/aps.74.20241514
Abstract +
The exploration of the quantum nature of gravity has always been the focus of academic research. In this work, we consider a double “gravitational cat state” quantum system consisting of a pair of massive particles coupled with gravitational interaction confined in their respective double potential wells. Specifically, we model the double “gravitational cat state” system as a two-qubit system by assuming that the system is initially in the two-qubit Bell state, and investigate the effects of stable classical field and decayed field noise on the quantum speed limit time (QSLT) and trace distance discord (TDD) dynamics of the double “gravitational cat state”. The results show that the QSLT can be controlled by changing the parameters of the system and the environment, and the quantum state dynamic evolution of the system with massive particles can be accelerated. The quantum state evolution can be accelerated by increasing the gravitational coupling intensity between the two massive particles. The decay rate of the decaying field can also regulate the QSLT of the system to a certain extent, so as to accelerate the quantum state evolution. Under the influence of decaying field noise, it is worth noting that the intensity of gravitational coupling affects the frequency of quantum discord oscillations in this two-particle system. The QSLT shows an oscillating trend with time: rapidly increasing to a certain value in a short period of time, then beginning to decline, and then oscillating until it reaches a stable value. That is to say, the evolution of quantum states goes through an oscillatory cycle of first deceleration and then acceleration until the evolution rate becomes stable after a certain period of time. At the same time, there are similar oscillations in the dynamics of quantum discord. Moreover, by comparing these two, it is found that the QSLT decreases in the process of increasing the quantum discord in the system. When the discord oscillation has regularity, the QSLT tends to a certain value, and the quantum discord of the double “gravitational cat state” system has a certain relationship with the QSLT. In other words, the quantum discord will affect the rate of quantum state evolution to some extent, and the increase of quantum discord between systems will be more conducive to the evolution of quantum states.

GENERAL

A method of modeling saddle point movement driven by multiple radio frequency fields
MAI Jun, WANG Zhao, YUAN Chang, XIAO Jie, MA Wei, WANG Xu
2025, 74 (4): 040304. doi: 10.7498/aps.74.20241552
Abstract +
In an integrated ion trap with integrated optical modules, the problem of misalignment between the optical focus and the trapped ion saddle point is very likely to occur, which seriously hinders the practicality of the experimental method. To solve this problem, the multi-RF field method can be used to compensate for and move the ion saddle point position. However, in the actual experimental process, the application of the multi-RF method requires the knowledge of the amplitude of the RF voltage to be loaded corresponding to the actual spatial position of the saddle point. Therefore, a set of mathematical models is established to describe the relationship. The accuracy of the model determines the control accuracy of the spatial position of the saddle point, and the simplicity of the model determines the speed of the solution process. Therefore, in this work, a mathematical model of the relationship between the multi-RF electric field voltage and the saddle point position is proposed based on the numerically simulated electric field distribution and the polynomial fitting method. It can quickly and accurately give a mathematical description between the two without considering the physical mechanism or model. Numerical method is adopted to verify and discuss the correctness and scope of application of the model, and can quickly and accurately provide the amplitude of the RF voltage to be loaded in the experiment, causing the saddle point to move and coincide with the optical focus. This method greatly reduces the time delay caused by the solution and improves the feedback loop bandwidth during the movement of the saddle point position.

GENERAL

Extraction of nonlinear feature parameters based on multi-channel dataset
LI Weijia, SHEN Xiaohong, LI Yaan, ZHANG Kui
2025, 74 (4): 040501. doi: 10.7498/aps.74.20241512
Abstract +
Phase space reconstruction plays a pivotal role in calculating features of nonlinear systems. By mapping one-dimensional time series onto a high-dimensional phase space using phase space reconstruction techniques, the dynamical characteristics of nonlinear systems can be revealed. However, existing nonlinear analysis methods are primarily based on phase space reconstruction of single-channel data and cannot directly utilize the rich information contained in multi-channel array data. The reconstructed data matrix shows the structural similarities with multi-channel array data. The relationship between phase space reconstruction and array data structure, as well as the gain in nonlinear features brought by array data, has not been sufficiently studied. In this paper, two classical nonlinear features: multiscale sample entropy and multiscale permutation entropy are adopted. The array multi-channel data are used to replace the phase space reconstruction step in algorithms so as to enhance the algorithmic performance. Initially, the relationship between phase space reconstruction parameters and actual array structures is analyzed, and conversion relationships are established. Then, multiple sets of simulated and real-world array data are used to evaluate the performances of the two entropy algorithms. The results show that substituting array data for phase space reconstruction effectively improves the performances of both entropy algorithms. Specifically, the multiscale sample entropy algorithm, when applied to array data, allows for distinguishing between noisy target signals from background noise at low signal-to-noise ratios. At the same time, the multiscale permutation entropy algorithm using array data reveals the complex structure of signals on different time scales more accurately.

GENERAL

Fuzzy permutation time irreversibility for nonequilibrium analysis of complex system
YAO Wenpo
2025, 74 (4): 040502. doi: 10.7498/aps.74.20241271
Abstract +
Permutation time irreversibility is an important method to quantify the nonequilibrium characteristics; however, ordinal pattern is a coarse-graining alternative of temporal structure and cannot accurately represent detailed structural information. In this paper, a fuzzy permutation time irreversibility (fpTIR) is proposed by measuring the difference between vector elements based on a negative exponential function. Amplitude permutation of vector is constructed and its membership degree is calculated, then the difference in probability distribution between the forward sequence and backward sequence is measured for fpTIR. For comparison, Shannon entropy is calculated as the average amount of information in the fuzzy permutation probability distribution, i.e. fuzzy permutation entropy (fPEn), to measure the complexity of the system. According to the surrogate theory, mode series are generated by logistic, Henon, and first-order autoregressive systems to verify the fpTIR, which is then used to analyze heart rates of congestive heart failure, healthy elderly and healthy young subjects from PhysioNet database. The results suggest that fpTIR effectively measures the nonequilibrium characteristic of system and improves the accuracy of heart rate analysis. Since fpTIR and fPEn are different in analyzing probability distributions, they have discrepancies in chaotic series and even opposite results in the heart rate signals, where the results of fpTIR are consistent with theory of complexity loss in aging and disease. In conclusion, the fpTIR not only accurately characterizes the structure of sequences and enhances the effect of the nonequilibrium analysis of complex systems, but also provides a new perspective and theoretical basis for exploring complex systems from the perspectives of nonequilibrium dynamics and entropy complexity.

COVER ARTICLE

Simulation study of precision spectroscopy of dielectronic recombination for highly charged heavy ions at HIAF
HUANG Houke, WEN Weiqiang, HUANG Zhongkui, WANG Shuxing, TANG Meitang, LI Jie, MAO Lijun, YUAN Yang, WAN Mengyu, LIU Chang, WANG Hanbing, ZHOU Xiaopeng, ZHAO Dongmei, YAN Kaiming, ZHOU Yunbin, YUAN Youjin, YANG Jiancheng, ZHANG Shaofeng, ZHU Linfan, MA Xinwen
2025, 74 (4): 043101. doi: 10.7498/aps.74.20241589
Abstract +
Dielectronic recombination (DR) experiments of highly charged ions not only provide essential atomic benchmark data for astrophysical and fusion plasma research but also serve as a stringent test for strong-field quantum electrodynamics (QED) effects, relativistic effects, and electron correlation effects. High-intensity heavy-ion accelerator facility (HIAF), currently under construction at Huizhou, China, will have a high-precision spectrometer ring (SRing) equipped with a 450 kV electron-cooler and an 80 kV ultracold electron-target. This advanced setup facilitates precise measurements of the DR process for highly charged ions in a broad range of center-of-mass energy, from meV to tens of keV. In this work, we carry out the molecular dynamics simulation of the electron beam temperature distribution of the ultracold electron-target at the SRing. The simulation results indicate that after treatment by the designed adiabatic magnetic field and acceleration field, the transverse and longitudinal electron beam temperature generated by the thermionic electron gun can be reduced from 100 meV to below 5 meV and 0.1 meV, respectively. Furthermore, we analyze the influence of this ultracold electron beam temperature on the resonance peak and energy resolution in DR experiment. The resolution gain at the SRing electron-target is particularly pronounced at small electron-ion collision energy, which provides unique experimental conditions for the DR experiments. Taking lithium-like $ {}_{~\,54}^{129}{{\mathrm{X}}{\mathrm{e}}}^{51+} $ and $ {}_{~\,92}^{238}{{\mathrm{U}}}^{89+} $ ions for example, we simulate the DR resonance spectra at the SRing and compare them with the simulated results from the experimental cooler storage ring CSRe. The results reveal that the SRing experiments can resolve fine DR resonance structures with ultra-high energy resolution compared with those from the CSRe. This work lays a solid foundation for precise DR spectroscopy of highly charged ions at the SRing to stringent test of strong field QED effect and extraction nuclear structure information.

ATOMIC AND MOLECULAR PHYSICS

Rydberg atom electric field based quantum measurement method and polarization influence analysis
DING Chao, HU Shanshan, DENG Song, SONG Hongtian, ZHANG Ying, WANG Baoshuai, YAN Sheng, XIAO Dongping, ZHANG Huaiqing
2025, 74 (4): 043201. doi: 10.7498/aps.74.20241362
Abstract +
The interaction between an electric field and the energy levels of Rydberg states results in the Stark effect, which can be used for quantum detection by measuring the frequency shift in electromagnetically induced transparency (EIT) spectra. By using the functional relationship between the frequency shift and the electric field, it is possible to measure the electric field in question. However, the mismatch between the probe laser and the polarization direction of the coupled laser leads to errors in the measurement of the frequency shift, affecting the accurate measurement of the electric field. In this work, the Schrödinger equation is solved by perturbation method to derive the functional relationship between the energy offset and the electric field strength. Then, the functional relationship between the energy offset and the electric field strength is brought into the solution of the density matrix equation, and the influences of the polarization direction of the detected light and coupled light on the EIT-Stark mathematical model are analyzed. Then an internal electrode method is used to prevent shielding effects caused by alkali metal atoms adhering to the surface of the atomic vapor cell, thereby enabling the application of the electric field. The calibration of the Rydberg state polarisation rate is achieved by using a standard source and measuring the frequency shift of the EIT spectrum. Finally, the effects of polarisation mismatch on the measurement results of EIT spectrum and the electric field are verified by modulating the laser polarization direction. The experimental data show that when the polarization directions of the probe laser and coupled laser are parallel to each other, it is the most matched polarization direction for the lasers, the peak value of the EIT spectrum is the largest, and the maximum relative error of the electric field measurement is 1.67%. When the angle between the polarisation directions of the probe light and the coupled light laser is 45°, the laser polarisation mismatch is the most severe, the EIT spectral peak is the lowest and the maximum relative error of the electric field measurement is 10.24%.

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

Underwater polarization de-scattering imaging independent of target-free region
ZHU Yeqing, WANG Xing, ZHU Zhuqing
2025, 74 (4): 044201. doi: 10.7498/aps.74.20241582
Abstract +
Underwater optical imaging technology possesses broad application prospects in fields such as marine resource exploration, underwater ecological environment monitoring, and seabed topography detection. The technology employs the polarization characteristics of light, particularly those of the background and target, to achieve a clear image. However, the traditional methods rely on target-free regions to compute the backscattered light information, which is infrequently present in the actual scene captured by the camera. Then the full-space resolution of target information light and backscattered light information are required. At this time, the traditional methods may be difficult to adapt in practical application.In this work, an underwater polarization de-scattering method independent of target-free regions is proposed by combining active polarization imaging and transmittance de-scattering model. Initially, the total light intensity within the camera’s field of view is decomposed into its polarized and unpolarized components. By removing the backscattered light with polarized and unpolarized information from the total light intensity, a clear underwater target can be obtained. Based on the active polarization imaging model, the backscattered light with polarization information is calculated, in which the polarization angle of the backscattered light is considered to be zero in the full-space. Thus, the polarization degree of the target information light occupying the camera’s entire field of view can be derived. According to the polarization correlation, the polarization degree of the backscattered light can be characterized, and the intensity of the backscattered light with polarization information in the camera’s entire field of view can also be obtained. Then the unpolarized component is calculated using the minimum intensity image with Stokes vector transformation. Finally, the underwater scene is obtained by combining the transmittance de-scattering principle and introducing adjustment parameters.Experimental and real-world underwater imaging results demonstrate that the proposed method can effectively remove the majority of the backscattered light and improve the image contrast and entropy, regardless of whether there are target-free regions. Additionally, this method possesses a certain rate advantage, which can facilitate the real-time complex underwater imaging technology.

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

Adaptive gating for low signal-to-noise ratio non-line-of-sight imaging
LI Min, LUO Yihan, LI Tailin, ZHAO Kaiyuan, TAN Yi, XIE Zongliang
2025, 74 (4): 044202. doi: 10.7498/aps.74.20241535
Abstract +
Non-line-of-sight (NLOS) imaging is an emerging optical imaging technique used for detecting hidden targets outside the line of sight. Due to multiple diffuse reflections, the signal echoes are weak, and gated single-photon avalanche diode (SPAD) plays a pivotal role in signal detection under low signal-to-noise ratio (SNR) conditions. However, when gated SPAD is used for detecting a target signal, existing methods often depend on prior information to preset the gate width, which cannot fully mitigate non-target signal interference or signal loss. Additionally, these methods encountered some problems such as large data acquisition volumes and lengthy processing times. To address these challenges, an adaptive gating algorithm is proposed in this work based on the principle of maximizing the distance from the vertex of a triangle to its base. The algorithm possesses advantages of the linear variation in scan point positions and the echo information from specific feature points. It can automatically identify echo signals and compute their widths without additional prior information or manual intervention. This method reduces the amount of data collected, improves processing efficiency, and has other benefits. Moreover, a confocal NLOS imaging system based on gated SPAD is developed to validate the proposed algorithm. The work further quantitatively evaluates the enhancement of target signal detection and image quality achieved by gated SPAD, and compares its imaging performance with leading NLOS image reconstruction algorithms. Experimental results demonstrate that the adaptive gating algorithm can effectively identify echo signals, facilitate automatic adjustment of gating parameters, and significantly improve target imaging quality while reducing data acquisition volume and enhancing processing efficiency.
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