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SPECIAL TOPIC—Heat conduction and its related interdisciplinary areas

Preface to the special topic: Heat conduction and its related interdisciplinary areas
2024, 73 (3): 030101. doi: 10.7498/aps.73.030101
Abstract +

GENERAL

Application of high-order SF-SFDTD scheme to solving a time-dependent Schrödinger equation
Xie Guo-Da, Pan Pan, Ren Xin-Gang, Feng Nai-Xing, Fang Ming, Li Ying-Song, Huang Zhi-Xiang
2024, 73 (3): 030201. doi: 10.7498/aps.73.20230771
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The traditional finite-difference time-domain (FDTD (2, 2)) method with second-order numerical accuracy in time and space has been extensively employed in the field of quantum mechanics to solve the Schrödinger equation. Nevertheless, the presence of the Courant-Friedrichs-Lewy (CFL) condition imposes limitations on the grid size in the computational space, thereby constraining the admissible range of time steps. Accordingly, the efficiency of the FDTD(2, 2) method significantly decreases. In addition, the second-order numerical accuracy of the FDTD(2, 2) method both in time domain and in space domain often results in significant error accumulation during calculations, thereby undermining the fidelity of the simulation results. To surmount the constraints imposed by the CFL stability conditions and enhance the accuracy of computations, a novel approach termed SF-SFDTD(3, 4) method has been proposed, with 3 and 4 referring to the accuracy in space and time, respectively. This method combines spatial filtering (SF) with the high-order symplectic finite-difference time-domain (SFDTD) method. Its primary objective is to solve the time-dependent Schrödinger equation while ensuring time stability and scalability. The SF-SFDTD(3, 4) method obviates the need for further deriving the iterative formula employed in the conventional SFDTD(3, 4) method. Therefore, the method under consideration exhibits a remarkable degree of compatibility with its traditional counterpart. It is merely necessary to include a spatial filtering operation during each numerical iteration to eliminate spatial high-frequency components arising from the utilization of time step sizes that fail to satisfy the CFL stability condition, thereby ensuring the stability of the numerical scheme. Moreover, when the time step value satisfies the CFL stability condition, the amplitude of the high-frequency component approaches zero, thereby exerting a minimal influence on the accuracy of the computational results. The adoption of time steps that do not meet the CFL stability conditions leads to an amplification in the amplitude of the high-frequency component. However, this finding solely affects the stability of the computational results, and the elimination of these unstable high-frequency components scarcely affect the accuracy of the computational results. The SF-SFDTD(3, 4) retains the simplicity and efficacy inherent in the traditional SFDTD(3, 4) methods, while enhancing computational efficiency. Additionally, the numerical stability and dispersion error of the SF-SFDTD(3, 4) method are analyzed theoretically. Finally, the validity and efficacy of the proposed method are corroborated through numerical illustrations.

GENERAL

Quantum game— “PQ” problem
Yang Xiao-Kun, Li Wei, Huang Yong-Chang
2024, 73 (3): 030301. doi: 10.7498/aps.73.20230592
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This paper reviews the coin flipping problem of “PQ” in a classical two-player game, and shows that when one player adopts quantum strategy, he can beat his classical opponent and gain higher returns. By using quantitative means, the whole “PQ” problem is put under a more general and fair condition, and it is generalized and studied again from many aspects and angles. Finally, we obtain some more essential and important conclusions, and explain the conclusions and its practical significance through some practical examples. At the same time, this paper gives the definition of imperfect fair game and the definition of perfect fair game, revises the quantum coin flipping game to make the game fair, and studies a multi-round version of quantum coin flipping. Some basic conclusions of fair quantum game are obtained, and the meaning of perfectly fair game is explained in practice.

The 90th Anniversary of Acta Physica Sinica

Majorana zero mode and its lattice construction in iron-based superconductors
Li Geng, Ding Hong, Wang Zi-Qiang, Gao Hong-Jun
2024, 73 (3): 030302. doi: 10.7498/aps.73.20232022
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Majorana zero modes (MZMs) obey non-Abelian braiding statistics. The braiding of MZMs can be used to construct the basic unit − topological qubit − of the topological quantum computation, which is immune to environmental noise and can achieve fault-tolerant quantum computation. The existing MZM platforms include hybrid structures such as topological insulator/superconductor, semiconducting nanowire/superconductor and 1d magnetic atomic chain/superconductor, and single materials such as 2M-WS2, 4Hb-TaS2, and iron-based superconductors (IBSs). The IBSs have advantages such as easy to fabricate, pure MZMs and high surviving temperatures of MZMs. Recently, a large-scale, ordered and tunable MZM lattice has been observed in LiFeAs, which provides a promising platform to future topological quantum computation. In this paper, first, we review the experimental observations of MZMs in IBSs, focusing on FeTe0.55Se0.45, (Li0.84Fe0.16)OHFeSe, CaKFe4As4 and LiFeAs. Next, we introduce the critical experimental evidences of the MZMs. We also review the recent research work on the ordered and tunable MZM lattice in LiFeAs. Finally, we give conclusion and perspective on future Majorana research.

SPECIAL TOPIC—Heat conduction and its related interdisciplinary areas

Research progress of heat transport in trapped-ion crystals
Li Ji, Chen Liang, Feng Mang
2024, 73 (3): 033701. doi: 10.7498/aps.73.20231719
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Heat transport is one of the most important research topics in physics. Especially in recent years, with the in depth study on single-molecule devices, heat transport in low-dimensional (i.e. one- and two-dimensional) microsystems has received more and more attention. In the research of Fermi-Pasta-Ulam crystals and harmonic crystals, it is widely accepted that heat conduction in low-dimensional system does not follow Fourier’s law. Due to the lack of the equipment that can directly measure heat current, it has been proven to be a challenging task to carry out relevant experiments. Ion crystal in ion trap is located in vacuum and does not exchange energy with the external environment. The crystal structure and temperature can be accurately controlled by electric field and optical field, providing an ideal experimental platform for studying thermal conduction in low-dimensional crystals in classical state or quantum state. Herein we summarize the recent theoretical research on thermal conduction in ion crystals, including the methods of calculating temperature distribution and steady-state heat current in one-dimensional, two-dimensional, and three-dimensional models, as well as the characteristics of heat current and temperature distribution under different ion crystal configurations. Because the nonlinear effect caused by the imbalance among three dimensions hinders the heat transport, the heat current in ion crystal is largest in the linear configuration while smallest in the zig-zag configuration. In addition, we also introduce the influence of disorder on the thermal conductivity of ion crystal, including the influence on the heat current across various ion crystal configurations such as the linear, the zig-zag and the helical configuration. Notably, the susceptibility of ion crystal to disorder increases with crystal size increasing. Specifically, the zig-zag ion crystal configuration exhibits the largest susceptibility to disorder, whereas the linear configuration is least affected. Finally, we provide a concise overview of experimental studies of the heat conduction in low-dimensional systems. Examination of the heat conduction in ion crystal offers a valuable insight into various cooling techniques employed in ion trap systems, including sympathetic cooling, electromagnetically induced transparency cooling, and polarization gradient cooling. Just like macroscopic thermal diodes made by thermal metamaterials, it is possible that the microscopic thermal diodes can also be made in low-dimensional systems.

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

Miniaturized electronically controlled notched band filter based on spoof surface plasmon polaritons
Sun Shu-Peng, Cheng Yong-Zhi, Luo Hui, Chen Fu, Yang Ling-Ling, Li Xiang-Cheng
2024, 73 (3): 034101. doi: 10.7498/aps.73.20231447
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In this paper, a novel miniaturized electronical controlled notch band filter based on spoof surface plasmon polaritons (SSPPs) with inverted “山”-shaped unit is designed and experimentally demonstrated. The notch band filter is mainly composed of four parts: microstrip transmission line, transition structure, inverted “山”-shaped SSPPs, and split ring resonator (SRR) structure, and a varactor diode is embedded in the slit notch of the SRR structure to realize electronic control. Comparing with the traditional SSPP unit with the same lateral size, the dispersion curve of the proposed inverted “山”-shaped unit shows better slow wave characteristics, and the asymptotic frequency is reduced to 55%. The frequency of the notch band can be dynamically controlled by adjusting the external bias voltage at both ends of the varactor diode. As the external bias voltage increases from 0.5 V to 30 V, the notch band frequency can be changed from 2.1 GHz to 2.3 GHz and achieve easily electronic regulation. The simulation results show that the notched band filter achieves low insertion loss (S21 < –1 dB) and great return loss (S11 > –10 dB) in the pass band, which has the advantage of miniaturization with the size only 0.78λg × 0.35λg. It is worth noting that when the equivalent capacitance of the slit notch is changed, the transmission coefficient of the notched band is always less than –15 dB, showing superior band-stop performance. At the same time, by comparing and analyzing the electric field distribution of notch band filter, the transmission mechanism of microwave signal is further verified. In order to verify the its effectiveness, the traditional printed circuit board technology is used to fabricate notch band filter. The measurement results are in good agreement with the simulation ones, verifying the feasibility of the design. The electronically controlled notch band filter has higher integration and can effectively suppress the interference frequency band.

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

Propagation properties of partially coherent vector beam with multiple off-axis vortex phases
Xu Hua-Feng, Zhang Xing-Yu, Wang Ren-Jie
2024, 73 (3): 034201. doi: 10.7498/aps.73.20231484
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In this paper, we investigate the propagation properties of radially polarized rectangular-symmetric cosine-Gaussian Schell-model (RCGSM) beam with multiple off-axis vortex phases by using Fourier transform and convolution method based on the unified theory of coherence and polarization. The results indicate that the radially polarized RCGSM beam has self-splitting properties and can be split into four identical lobes due to its unique spatial coherence structure. Furthermore, the modulation of multiple off-axis vortex phases can be acted on each lobe. For high coherence, the spot arrays with triangular or square hollow light intensity distribution can be generated in the focal plane by modulating the number of off-axis vortices (N0) and the beam order, and the corresponding state of polarization on each lobe presents an inverted triangular or oblique square elliptic distribution. However, for small coherence, the modulation effect of multiple off-axis vortex phases disappears and the light intensity of each lobe degenerates into a quasi-Gaussian distribution, whereas its state of polarization keeps invariant, which is independent of the beam order and coherence length. In addition, the beam still has a certain self-healing ability for one of the off-axis vortex phases partially blocked by an obstacle, but it will be destroyed for completely blocking, resulting in a notch on each lobe.

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

Analysis and optimization of optical frequency comb spectra of magnesium fluoride microbottle resonator
Guo Zhuang, Ouyang Feng, Lu Zhi-Zhou, Wang Meng-Yu, Tan Qing-Gui, Xie Cheng-Feng, Wei Bin, He Xing-Dao
2024, 73 (3): 034202. doi: 10.7498/aps.73.20231126
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Optical frequency comb has shown great potential applications in many areas including molecular spectroscopy, RF photonics, millimeter wave generation, frequency metrology, atomic clock, and dense/ultra-dense wavelength division multiplexed high speed optical communications. Optical frequency comb in the microresonator supporting whispering-gallery mode has attracted widespread interest because of its advantages such as flexible repetition rate, wide bandwidth, and compact size. The exceptionally long photon lifetime and small modal volume enhance light-matter interaction, which enables us to realize intracavity nonlinear frequency conversions with low pump threshold. With the advantages of small size, low power consumption, wide spectral coverage and adjustable dispersion, the magnesium fluoride microresonator optical frequency comb has potential applications in optical communication and mid-infrared spectroscopy.In this work, the spectral characteristics of the optical frequency comb generated by a magnesium fluoride whispering-gallery mode microbottle resonator platform are investigated. In order to optimize the spectral distribution of the optical frequency comb of the magnesium fluoride microbottle resonator, the second-order dispersion and higher-order dispersion of the bottle resonator structure under different curvatures and axial modes are solved iteratively by the finite element method, and the spectral evolutions of the optical frequency comb under different axial mode excitations are simulated by solving the nonlinear Schrödinger equation through the split-step Fourier method. The results show that near-zero anomalous dispersion tuning can be achieved in a wide bandwidth range by exciting low-order axial mode at an optimal radius of curvature, while the high-order axial mode will lead the microbottle resonator to present the weak normal dispersion. The weaker anomalous dispersion in the lower-order axial mode broadens the bandwidth of the optical comb, demonstrating that the third-order dispersion and the negative fourth-order dispersion can broaden the Kerr soliton optical comb; the weak normal dispersion in the higher-order axial mode suppresses the generation of the Kerr optical comb, and the Raman optical comb dominates. The selective excitation of Kerr soliton combs and Raman combs can be achieved by modulating the axial mode of the microbottle resonator under suitable pumping conditions. The present work provides guidance for designing the dispersion in magnesium fluoride microresonator and the experimental tuning of broadband Kerr soliton optical combs and Raman optical combs.

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

Design of optical frequency comb based on dual frequency pumped normal dispersion silicon carbide microresonator
Gao Rong, Yang Ya-Nan, Zhan Chen-Yi, Zhang Zong-Zhen, Deng Yi, Wang Zi-Xiao, Liang Kun, Feng Su-Chun
2024, 73 (3): 034203. doi: 10.7498/aps.73.20231442
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The scheme of generating optical frequency comb (OFC) mainly includes mode-locked laser, electro-optic modulation comb, and nonlinear Kerr micro-resonator comb. The OFC with frequency spacing on the order of 10–200 GHz can be employed in optical communication, microwave photonics, and other fields. Silicon carbide (SiC) has aroused the considerable research interest in integrated nonlinear photonics owing to its high second nonlinear coefficient and third order nonlinear coefficient, low optical loss, without multiphoton absorption loss owing to the wide bandgap. Single soliton microcomb in anomalous group velocity dispersion regime based on a 4H-SiC-on-insulator thin film has been demonstrated with the relative lower pump to comb efficiency, while the OFC in normal dispersion regime based on the SiC microresonator has not been reported. The pump conversion efficiency of OFC in the normal dispersion regime is high, and the pump frequency detuning range for the OFC generation is large, which is conducive to the OFC generation and long-term stable operation. Since there is no modulation instability effect in normal dispersion regime, the key to generating the OFC in normal dispersion regime is that the initial state needs the assistance of a multi-frequency laser (or four-wave mixing sideband). The phase-locked dual-frequency laser can be regarded as a pulse pump laser source with wide pulse duration, which can be realized by integrated distributed feedback laser.In this paper, a scheme of generating OFC by pumping the normal dispersion SiC microresonator with phase locked dual-frequency laser is proposed. The flat normal dispersion in 1550 nm band is realized through dispersion engineering of the SiC microresonator. The effective mode field area of the TE0 fundamental mode at 1550 nm in the optimized SiC ridge waveguide is about 0.94 μm2, and the nonlinear coefficient is about 3.69 $ {{\mathrm{W}}}^{-1}{\cdot} {{\mathrm{m}}}^{-1} $. Meanwhile, dispersion parameters of the microresonator with 100 GHz FSR are also obtained. The OFC generation pumped by a phase-locked dual-frequency laser based on normal dispersion SiC microresonator is simulated through using the Lugiato-Lefever equation. The evolution process of the OFC in time and frequency domain related to the pump detuning is studied. The effects of several parameters such as the pump power, microresonator waveguide loss, microresonator dispersion, proportion of the dual-frequency laser, and the frequency interval of dual-frequency laser on the performance of the OFC are also investigated. The conclusions can be obtained through the OFC generation simulation as follows, 1) When the microresonator waveguide loss is larger, the pump detuning range for the OFC generation becomes smaller, and the pulse peak power under the same pulse intensity filling rate decreases. 2) When the input pump power is larger, the pump detuning range for the OFC generation becomes larger, the pulse peak power under the same pulse intensity filling rate increases, and the corresponding spectrum becomes wider. 3) With the increase of absolute dispersion value, the spectrum bandwidth of the generated OFC decreases obviously. 4) The power proportion of dual-frequency laser has little influence on the OFC generation. 5) The frequency spacing of the generated OFC can be tuned through changing the frequency spacing of the two phase-locked lasers with integral multiple of free spectral range.The OFC with spectrum bandwidth of about 70 nm can be generated in a range of 1500—1600 nm through the simulation. The simulation results are beneficial to promoting the research and practical application of high repetition rate broadband optical frequency comb in a 1550 nm band based on the normal dispersion silicon carbide microresonator.

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

Acoustic scattering modeling and sound field characteristics of rough seafloor in shallow sea
Wang Lei, Huang Yi-Wang, Guo Lin, Ren Chao
2024, 73 (3): 034301. doi: 10.7498/aps.73.20231472
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Acoustic scattering is an important part of ocean acoustics, and the acoustic scattering caused by the unevenness of the seafloor surface is one of the reasons for the fluctuation of acoustic propagation in the ocean. In order to solve the acoustic scattering problem of sea bottom surface roughness, normal wave theory is used to model the acoustic field. To simplify the problem, Lambert’s law is used to establish the seafloor rough scattering model in horizontal layered shallow sea waveguides, and the scattering field is assumed to be isotropic in the horizontal direction. Based on this model, the amplitude distribution and the phase distribution of the scattered sound pressure are obtained, and the intensity of the scattered sound field and its spatial correlation coefficient are simulated numerically. The prediction of the scattered sound field under rough interface conditions is realized, and the variation of the spatial characteristics of the scattered sound field with the roughness of the seafloor is revealed. The results show that when Lambert’s law is used to describe the rough interface acoustic scattering and when the seafloor roughness is smaller than the wavelength, the spatial correlation coefficient of the scattered sound field at two different positions in space has a change rule of periodic oscillation attenuation with the increase of spatial distance, and in the vertical direction, the oscillation period is larger and the attenuation is slower. When the roughness increases, the oscillation amplitude of the horizontal and the vertical correlation coefficient gradually increase, the oscillation period of the horizontal correlation coefficient gradually decreases, and the vertical correlation coefficient no longer attenuates in the direction near the seafloor, which is the result of the weakening of the seafloor acoustic scattering. The model theory in this paper can also be extended to the acoustic scattering modeling of rough sea surface. For the case of non-horizontal seabed, the scattered sound field of the rough interface in the waveguide can be obtained by using coupled normal wave or adiabatic normal wave theory.
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