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GENERAL

Similarity transformations and exact solutions of the generalized ($ n+1 $)-dimensional Schrödinger equation with ($ 2 m+1 $)th order nonlinear terms and spatiotemporally varying coefficients
WANG Gangwei, TAN Zixuan
2025, 74 (11): 110201. doi: 10.7498/aps.74.20250225
Abstract +
Schrödinger-type equations represent a fundamentally important class of differential equations. Research on high-dimensional variable-coefficient Schrödinger-type equations as important theoretical and practical value, providing critical insights into the dynamics of complex wave phenomena. In this paper, we employ similarity transformations to derive a novel class of soliton solutions for the (n + 1)-dimensional (2m + 1)th-order variable-coefficient nonlinear Schrödinger equation. By extending similarity transformations from lower-dimensional to higher dimensionnal equations, we establish the intrinsic relationships among the equation’s coefficients. Furthermore, utilizing the solutions of the stationary Schrödinger equation and using the balancing-coefficient method, we construct both bright and dark soliton solutions for the (n + 1)-dimensional (2m + 1)th-order variable-coefficient nonlinear Schrödinger equation. Finally, for specific cases, we present graphical representations of the bright and dark soliton solutions and conduct a systematic analysis of their spatial structures and propagation characteristics. Our results indicate that bright solitons exhibit a single-peak structure, while dark solitons form trough-like profiles, further confirming the stability of soliton wave propagation.

GENERAL

Quantum steering based weak entanglement detection
QIU Shangfeng, XU Qiao, ZHOU Xiaoqi
2025, 74 (11): 110301. doi: 10.7498/aps.74.20241539
Abstract +
Quantum entanglement is a unique phenomenon of quantum mechanics and the core of many quantum technologies. Although entanglement is often observed in small-scale systems, detecting weak entanglement in large or noisy systems remains a major challenge, as experimental flaws can easily destroy fragile quantum correlations. A new weak entanglement detection criterion based on quantum steering has recently been proposed as a potential alternative to traditional entanglement witnesses. In this work, we provide a theoretical analysis by comparing the detection capabilities of the steering-based criterion with those of traditional entanglement witnesses under realistic measurement errors. The results show that the steering-based approach offers improved sensitivity for detecting weak entanglement. We further experimentally verify the feasibility of this steering-based criterion by using a linear optical setup. The experimental results align well with theoretical predictions, confirming the practicality and reliability of the method. These findings provide the steering-based criterion as a promising and accessible tool for detecting weak entanglement, and are expected to have potential applications in quantum communication, quantum computing, and other areas of quantum information science.

GENERAL

Chaotic spatiotemporal dynamics of Bose-Einstein condensates with nonlinear time- and space-varying interactions in moving optical lattices
LI Fei, LI Wenwu
2025, 74 (11): 110302. doi: 10.7498/aps.74.20241604
Abstract +
The dynamical behaviors of Bose-Einstein condensates (BECs) depend largely on the nonlinear interactions between BEC atoms. The advancement of experimental techniques enables the rapid and effective modulation of the nonlinear interactions through Feshbach resonance technique. At present, both the nonlinear time-varying interaction and nonlinear space-varying interaction have been realized, respectively, thus making it possible to simultaneously modulate the nonlinear interactions in time and space through the combination of techniques. It will provide more options to conduct various studies by manipulating the BECs. Therefore, BECs with time- and space-varying interactions must possess unique advantages in studying BEC dynamics.This paper focuses on the chaotic spatiotemporal dynamics of BECs with nonlinear time- and space-varying interactions in moving optical lattices. When the intensities of the moving optical lattice potential and the modulation of the nonlinear interaction are small, the system satisfies the perturbation conditions and the Melnikov-function method is used in the theoretical analyses to obtain the Melnikov spatiotemporal chaotic criterion of the system. When the system does not meet the perturbation conditions, numerical simulations show that for a BEC with an attractive atomic interaction, increasing the modulation intensity of the nonlinear interaction can deepen the degree of spatiotemporal chaos in the system. In certain parameter regions, the modulation frequency of the nonlinear interaction can have a significant influence on the spatiotemporal dynamical behavior of the system. Further numerical research results show that larger chemical potentials can suppress the spatiotemporal chaos not only in the attractive BEC but also in the repulsive BEC. Based on the above research results, spatiotemporal chaos in BEC system can be avoided or triggered off in experiments as needed.

GENERAL

Regulation of resonance and anti-resonance of soliton in ultracold atomic gases
HE Zhangming, ZHAI Dexun, ZHU Qianquan, PAN Xiang
2025, 74 (11): 110501. doi: 10.7498/aps.74.20250177
Abstract +
Kapitza’s pendulum is an inverted pendulum that is dynamically stabilized by rapidly driving its pivot point. Many applications of Kapitza stabilization in quantum systems have been proposed, such as optical molasses, the stability of optical resonators, preparation of molecular ions, the breaking of translation symmetry, the periodically driven sine-Gordon model, polariton Rabi oscillation, and the stabilization of bright solitons in a Bose-Einstein condensate. In particular, Kapitza stabilization can be used to trap particles. The most notable example of such an application is the Paul trap.Recently, the Kapitza trap was created by superimposing time-tuned focused laser beams to produce a periodically driven harmonic potential for ultracold atomic gases. This work opens up new possibilities to study Floquet systems of ultracold atomic gases. So we consider the periodically driven harmonic potential, and investigate the properties of soliton in ultracold atomic gases by numerical simulations. It is found interestingly that when a soliton is located at the center of the harmonic potential, a resonance phenomenon of soliton amplitude oscillation occurs at a specific driven frequency. In addition, the oscillation amplitude increases with the increase of the trapping frequency of the harmonic potential, and the resonance frequency increases with theaugment of soliton initial amplitude.The change of driven frequency and initial phase has a significant effect on soliton motion when the soliton is located at the edge of the harmonic potential. When the initial phase is zero, there is a characteristic driven frequency. For the case where the driven frequency is equal to the characteristic frequency, soliton motion exhibits periodic oscillations. For the case where the driven frequency is slightly lower than the characteristic frequency, the resonance of soliton oscillation can be found. When the driven frequency is slightly higher than the characteristic frequency, the anti-resonance of soliton oscillation can be found. In addition, it is found that the characteristic driven frequency increases linearly with the increase of the trapping frequency of the harmonic potential. When the initial phase is not equal to zero, the irregular oscillation, quasi-periodic oscillation, and periodic oscillation can be observed with the increase of driven frequency. When the driven frequency is equal to a specific value, the resonance of soliton oscillation can also obtained. Furthermore, the fast driving has no effect on the motion trajectory of solitons. These results can help to precisely control ultracold atomic gases.

INSTRUMENTATION AND MEASUREMENT

A high-capacity 1-K cryogenic system pre-cooled by pulse tube cryocooler
LIU Xuming, ZHA Kuifan, MA Shuai, HAN Liming, XIE Xiaolin, GUO Weijie, PAN Changzhao
2025, 74 (11): 110701. doi: 10.7498/aps.74.20250181
Abstract +
A 1-K cryogenic system can provide a stable and necessary low-temperature environment for some fields such as quantum computing, condensed matter physics research, and cryogenic scientific instruments. Specifically, in the field of basic research, 1 K is an ideal condition for studying quantum phenomena in low-temperature physics, such as quantum Hall effect and topological phase transition; in the field of technical applications, 1 K is a necessary condition for some quantum devices, such as superconducting quantum interferometers and single-photon detectors, to achieve high-sensitivity operation; in the field of ultra-low temperature technology, 1 K is the pre-cooling stage of refrigeration technologies, such as dilution refrigerators, and is also the basis for further achieving mK temperature ranges and lower temperatures. At present, in most of domestic 1-K systems, GM (Gifford-McMahon) cryocoolers are used for pre-cooling. These systems encounter some difficulties in achieving lower vibration control, lower electrical noise interference, lower pre-cooling temperature, and higher liquefaction efficiency. The 1-K systems based on pulse tube cryocoolers pre-cooling have inherent advantages in solving these problems. In this work, a 4-K GM-type pulse tube cryocooler is first developed by using a domestic helium compressor and a developed rotary valve, and the cold-end heat exchanger and the room-temperature phase shifters are redesigned in order to achieve a minimum cooling temperature of 2.14 K, and provide 1.5 W at 4.2 K and 45 W at 45 K cooling capacity simultaneously. With the home-made pulse tube cryocooler as the pre-cooling stage, a 1-K cryogenic system is further constructed. By designing key components such as JT flow resistance, combined thermal switch, and anti-superflow structure, a minimum cooling temperature of 1.1 K is achieved, with a cooling capacity of 100 mW at 1.6 K. This study lays an important foundation for subsequently developing dilution refrigerators with larger cooling capacity.

SPECIAL TOPIC—Technology of magnetic resonance

Atomic vapor cells with Herriott-cavity sealed under vacuum and their applications in atomic magnetometry
XIE Ziping, HAO Chuanpeng, SHENG Dong
2025, 74 (11): 110702. doi: 10.7498/aps.74.20250220
Abstract +
This paper focuses on standardized fabrications of atomic vapor cells with multipass cells. For this purpose, we build a vacuum system that enables the sealing of the multipass-cavity-assisted cell under vacuum. Alkali atoms are prepared inside a glass holder, and the tip of the holder is broken by controlled collisions under vacuum. Atoms are then transferred to a cell glass body part by heating. Once enough atoms accumulate inside the glass part, buffer and quenching gases are filled into the system, and the glass body part is moved to contact the silicon wafer which is bonded with a Herriott-cavity. Then the cavity part and the glass part are sealed together using the anodic bonding technique. The resulting vapor cells provide enhanced measurement sensitivity and improved device standardization, which allows for seamless replacements of each other in practical applications. The performances of these cells are tested, including a test in a double-resonance alkali-metal atomic magnetometer. A magnetic field sensitivity of 95 fT/Hz1/2 is achieved in a frequency range from 10 to 20 Hz with a multipass cell filled with 400 Torr (1 Torr = 1.33×102 Pa) N2 and natural Rb atoms at 100 ℃. The technology and cells developed in this work are expected to have wide applications in atomic devices, especially in He magnetometers and nuclear-spin atomic co-magnetometers, which have special requirements for cell qualities.

The 90th Anniversary of Acta Physica Sinica

Intermediate/high-energy heavy-ion collisions and nuclear matter equation of state
ZHANG Yapeng, SUN Zhiyu, YONG Gaochan, FENG Zhaoqing
2025, 74 (11): 112101. doi: 10.7498/aps.74.20241650
Abstract +
The equation of state (EoS) of nuclear matter is a description of the macroscopic properties of nuclear matter under different thermodynamic conditions or external fields, which is critical for understanding the theory of the strong interaction—quantum chromodynamics (QCD), the nature of nuclei, the dynamics of heavy-ion collisions (HICs), the internal structure of compact stars, the merger of binary neutron stars, and other physical phenomena. Heavy-ion collisions (HICs) are the only method in laboratories to create nuclear matter with extreme conditions such as high temperatures and high densities. HICs at different energy levels offer the possibility to quantitatively study the properties of nuclear matter under diverse thermodynamic conditions. This paper mainly presents the current research status of the EoS of nuclear matter and introduces the fundamental observables in HICs that are sensitive to the EoS, as well as the typical experiments and results used to explore the EoS. The progress in studying the EoS containing strangeness is also described and its possible research directions in the future are also discussed. The status and progress of worldwide heavy-ion accelerators and experimental spectrometers in the high-baryon density region are introduced, including China’s large-scale scientific facilities, i.e HIRFL-CSR and HIAF, as well as the CEE experiment. Additionally, the opportunities and challenges for experimental research on the EoS of nuclear matter in China are discussed.

NUCLEAR PHYSICS

Shape coexistence and shell effect of medium mass nuclei
LIU Dong, GUO Jianyou
2025, 74 (11): 112102. doi: 10.7498/aps.74.20250095
Abstract +
The atomic nucleus is an extremely complex quantum many- body system composed of nucleons, and its shape is determined by the number of nucleons and their interactions. The study of atomic nuclear shapes is one of the most fascinating topics in nuclear physics, providing rich insights into the microscopic details of nuclear structure. Physicists have observed significant shape coexistence phenomena and stable triaxial deformation in isotopes of Zn, Ge, Se, and Kr. This paper aims to delve deeper into the influences of shape coexistence and triaxiality on the ground-state properties of atomic nuclei, as well as to verify new magic numbers. We employ the density-dependent meson-exchange model within the framework of the relativistic Hartree-Bogoliubov (RHB) theory to systematically study the ground-state properties of even-even Zn, Ge, Se, and Kr isotopes with neutron numbers N = 32–42. The calculated potential energy surfaces clearly demonstrate the presence of shape coexistence and triaxial characteristics in theseisotopes. By analyzing the ground-state energy, deformation parameters, two-neutron separation energy, neutron radius, proton radius, and charge radius of the atomic nucleus, we discuss the closure of nuclear shells. Our results reveal that at N = 32, there is anotable abrupt change in the two-neutron separation energy values of 62Zn and 64Ge. At N = 34, a significant decrease in the two-neutron separation energy values of 68Se and 70Kr is observed, accompanied by an abrupt change in their charge radii. Meanwhile, at N = 40, clear signs of shell closure are observed. The maximum specific binding energy may be correlated with the emergence of spherical nuclear structures. The shell closure not only enhances nucleon binding energy but also suppresses nuclear deformation through symmetry constraints. Our findings support N = 40 as a new magic number, and some results also suggest that N = 32 and N = 34 can be new magic numbers. Notably, triaxial deformation plays a crucial role here. Furthermore, we explore the potential correlation between triaxiality and shape coexistence in the ground-state properties of atomic nuclei and analyze the physical mechanisms behind these changes.The discrepancies between current theoretical predictions and experimental data reflect the limitations of modeling higher-order many-body correlations (e.g. three-nucleon forces) and highlight challenges in experimental measurements for extreme nuclear regions(including neutron-rich and near-proton-drip-line regions). Future studies will combine tensor force corrections, large-scale shell model calculations, and high-precision data from next-generation radioactive beam facilities (e.g. FRIB and HIAF) to clarify the interplay among nuclear force parameterization, proton-neutron balance, and emergent symmetry, thereby providing a more comprehensive theoretical framework for studying the nuclear structures under extreme conditions.

NUCLEAR PHYSICS

Research on α decay properties of superheavy nuclei with Z = 118–120
XING Fengzhu, LE Xiankai, WANG Nan, WANG Yanzhao
2025, 74 (11): 112301. doi: 10.7498/aps.74.20240907
Abstract +
An unified fission model (UFM) has been improved by considering the nuclear deformation effect and introducing an analytical expression of preformation factor. The improved version of the UFM by taking into consideration the nuclear deformation effect is named IMUFM1. Based on the IMUFM1, the further improved version is termed IMUFM2, which incorporates an analytical expression of the preformation factor. Within the UFM, the IMUFM1 and the IMUFM2, the α decay half-lives of heavy and superheavy nuclei with $ Z \geqslant 92 $are systematically calculated. The calculated standard deviation between the calculation results and the experimental data shows that the accuracy of the IMUFM1 is improved by 2.45% compared with that of the UFM. The accuracy of the IMUFM2 will be further improved by 32.09% compared with that of the IMUFM1, which implies that the nuclear deformation effect and the preformation factor are both important in prediction. Then, the α decay half-lives of Z = 118–120 isotopes are predicted from the IMUFM1 and the IMUFM2 by inputting the α decay energy values that are extracted from the sinite-range droplet model (FRDM), the Weizsäcker-Skyrme-4 (WS4) model and the Koura-Tachibaba-Uno-Yamads (KTUY) formula, respectively. The observed evolution of the α decay half-lives indicates that the evolution trends obtained from the above-mentioned three mass models are consistent with each other and the shell effects occur at N = 178 and 184, but their orders of magnitude, obtained from different mass models, are different from each other. Meanwhile, the comparison of half-lives between α decay and spontaneous fission shows that the dominant decay modes of the superheavy nuclei with N < 186 are α decay. Finally, the decay modes of 296Og, 297119 and 298120 α decay chains are predicted within the IMUFM1 and the IMUFM2 by using these three mass models, showing that the predictions from the WS4 mass model and KTUY mass model are more consistent with the experimental measurements. Form the FRDM2012 mass model, the predictions of 288Fl, 285Nh and 286Fl within the IMUFM1 mass model are not consistent with the experimental measurements, however, the prediction of 288Fl from the IMUFM2 is good agreement with the experimental measurement, which once again verifies the rationality and reliability of the IMUFM2. This study may be helpful for identifying new nuclide in future experiments.

ATOMIC AND MOLECULAR PHYSICS

Numerical studies of three-step selective photoionization of neodymium-150 isotope
WANG Lide, ZHANG Junyao, LU Xiaoyong
2025, 74 (11): 113201. doi: 10.7498/aps.74.20250262
Abstract +
The enriched neodymium-150 (Nd-150) isotope has important applications in fields such as nuclear industry and basic scientific research. The Nd isotope separation can be conducted by atomic vapor laser isotope separation (AVLIS), where the target isotope is selectively ionized through the λ1 = 596 nm → λ2 = 579 nm → λ3 = 640 nm photoionization scheme, and non-target isotopes remain neutral due to the frequency-detuned excitation. Subsequently, an external electric field is applied to extract the ions from the laser-produced plasma. The Nd-150 abundance in the product cannot meet the requirement of the application, attributed to the nearly negligible isotope shift of the λ2 = 579 nm transition, thus resulting in the excess ionization of non-target isotopes. A new high-selectivity photoionization scheme is desirable to address this limitation, and its expected parameter values can be determined through numerical calculations prior to the time-consuming atomic spectroscopy experiments. In this study, a three-step selective photoionization model is established based on the density matrix theory, with the consideration of the hyperfine structures and magnetic sublevels. This model allows the flexible adjustments of atomic parameters (e.g. branching ratio, isotope shift, hyperfine constant) and laser parameters (e.g. frequency, power density, bandwidth, polarization), while the ionization probabilities of magnetic sublevel transitions can be quantitatively predicted. For the existing schemes, the branching ratios are determined by comparing literature data with numerical results, and the Nd-150 abundance values under different laser bandwidths are evaluated. Further, an alternative scheme is numerically explored on the assumption that the first transition remains unchanged and the second transition has a more significant isotope shift and a smaller branching ratio, and the Nd-150 abundance values under different combinations of isotope shifts, hyperfine structures, and laser bandwidths are evaluated, with all the natural Nd isotopes included. From the numerical results, a scheme with the angular momentum of the second excited state J3 = 6, the isotope shift between Nd-148 and Nd-150 IS23,148 ≥ 300 MHz, and a lower reduced dipole matrix element of the second transition reaching approximately 30% of that of λ2 = 579 nm, can produce the high-abundance Nd-150 (>95%, equivalent to that of the electromagnetic separation method) under the bandwidths: b12 ≤ 0.5 GHz and b23 ≤ 1.0 GHz, and parallel linear-polarized lasers. Using the lasers with narrower bandwidth can achieve higher abundance, which is superior to the electromagnetic separation method. The expected high-abundance Nd-150 can be attributed to the combined effects of multi-factors: the larger isotope shift between Nd-150 and Nd-148 than that between other adjacent isotope pairs, the insignificant hyperfine splitting of odd isotopes, and the match between narrow-bandwidth lasers and Nd I spectroscopic parameters. These parameter values can serve as benchmarks helpful for experimental parameter selection in the forthcoming high-precision spectroscopy experiments.
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