Macroscopic quantum effects in a strongly driven nanomechanical resonator

航天返回与遥感第44卷第6期38 SPACECRAFT RECOVERY & REMOTE SENSING2023年12月宏观傅里叶叠层技术远距离成像实验研究田芷铭赵明王森李剑（大连海事大学，大连116026）摘要傅里叶叠层是一新型的宽视场高分辨成像技术，但是其在宏观成像领域的应用中，成像模型在米级成像距离下通常仅有2 cm左右的成像视场，难以满足使用要求。

为了提高宏观傅里叶叠层技术的成像距离和视场，文章开展了远距离宏观反射式傅里叶叠层成像模型的理论研究，提出了一种新的宏观傅里叶叠层成像模型，该模型使用发散光束照明，通过球面波移位对目标傅里叶谱进行扫描重建高分辨率目标图像；此外，还分析了宏观相干成像机理和傅里叶成像模型近似条件，由此推导出模型的近似范围，为模型推广提供了理论基础；最后，利用搭建的实验系统对10 m外目标成像，使目标分辨率从1.4 mm提升到0.35 mm，分辨率提升4倍以上，验证了模型具有通过合成孔径技术提升目标成像分辨率的能力。

关键词宏观成像傅里叶叠层成像模型远距离成像超分辨技术傅里叶叠层实验中图分类号: TP391.41文献标志码: A 文章编号: 1009-8518(2023)06-0038-07 DOI: 10.3969/j.issn.1009-8518.2023.06.004Experimental Research on Long-Range Imaging Using MacroscopicFourier Ptychographic TechnologyTIAN Zhiming ZHAO Ming WANG Sen LI Jian（Dalian Maritime University, Dalian 116026, China）Abstract Fourier ptychography is a promising high-resolution imaging technique that has been gradually applied in the field of macroscopic imaging. However, its imaging model typically provides a limited field-of-view of around 2 cm at meter-level imaging distances, which often falls short of practical requirements. To enhance the imaging distance and field-of-view of macroscopic Fourier ptychography, this article conducted theoretical research on the long-distance macro reflection Fourier stack imaging model. The proposed model utilizes diverging light beams for illumination, scans the target Fourier spectrum using spherical wavefront shifting, and reconstructs high-resolution target images. The article analyzes the mechanism of macroscopic coherent imaging and the approximation conditions of the Fourier imaging model, deriving the approximate range of the model and establishing a theoretical foundation for its extension. Finally, the built experimental system was used to image a target 10 meters away, increasing the target resolution from 1.4 mm to 0.35 mm, a resolution increase of more than 4 times, verifying the model’s capability to improve target imaging resolution through the synthetic aperture technology.收稿日期：2023-06-20引用格式：田芷铭, 赵明, 王森, 等. 宏观傅里叶叠层技术远距离成像实验研究[J]. 航天返回与遥感, 2023, 44(6): 38-44.TIAN Zhiming, ZHAO Ming, WANG Sen, et al. Experimental Research on Long-Range Imaging Using Macroscopic Fourier Ptychographic Technology[J]. Spacecraft Recovery & Remote Sensing, 2023, 44(6): 38-44. (in Chinese)第6期 田芷铭 等: 宏观傅里叶叠层技术远距离成像实验研究 39Keywords macroscopic imaging; Fourier ptychographic model; long-range imaging; super-resolution technology; Fourier ptychographic experiment0 引言目前，在监视、遥感等领域，高分辨率成像问题面临着重要挑战。

Room -Temperature Quantum Hall Effect in GrapheneK.S. Novoselov 1, Z. Jiang 2, 3, Y. Zhang 2, S.V. Morozov 1, H.L. Stormer 2, U. Zeitler 4, J.C. Maan 4, G.S. Boebinger 3, P. Kim 2* & A.K. Geim 1*1Department of Physics, University of Manchester, M13 9PL, Manchester, UK2Department of Physics, Columbia University, New York, New York 10027, USA3National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA4High Filed Magnet Laboratory, Radboud University Nijmegen, 6525 ED Nijmegen, NetherlandsThe quantum Hall effect (QHE), one example of a quantum phenomenon that occurs on a truly macroscopic scale, has been attracting intense interest since its discovery in 1980 (1). The QHE is exclusive to two-dimensional (2D) metals and has elucidated many important aspects of quantum physics and deepened our understanding of interacting systems. It has also led to the establishment of a new metrological standard, the resistance quantum h /e 2 that contains only fundamental constants of the electron charge e and the Planck constant h (2). As many other quantum phenomena, the observation of the QHE usually requires low temperatures T , typically below the boiling point of liquid helium (1). Efforts to extend the QHE temperature range by, for example, using semiconductors with small effective masses of charge carriers have so far failed to reach T above 30K (3,4). These efforts are driven by both innate desire to observe apparently fragile quantum phenomena under ambient conditions and the pragmatic need to perform metrology at room or, at least, liquid-nitrogen temperatures. More robust quantum states, implied by their persistence to higher T , would also provide added freedom to investigate finer features of the QHE and, possibly, allow higher quantization accuracy (2). Here, we show that in graphene – a single layer of carbon atoms tightly packed in a honeycomb crystal lattice – the QHE can be observed even at room temperature. This is due to the highly unusual nature of charge carriers in graphene, which behave as massless relativistic particles (Dirac fermions) and move with little scattering under ambient conditions (5).Figure 1 shows the room-T QHE in graphene. The Hall conductivity σxy reveals clearplateaux at 2e 2/h for both electrons and holes, while the longitudinal conductivity ρxxapproaches zero (<10Ω) exhibiting an activation energy ∆E ≈600K (Fig. 1B). Thequantization in σxy is exact within an experimental accuracy of ≈0.2% (see Fig. 1C). Thesurvival of the QHE to such high temperatures can be attributed to the large cyclotrongaps ωh characteristic to Dirac fermions in graphene. Their energy quantization inmagnetic field B is described by |2|BN e v E F N h = where v F ≈106m/s is the Fermivelocity and N an integer Landau level (LL) number (5). The expression yields an energygap ∆E ≈2800K at B =45T if the Fermi energy E F lies between the lowest Landau levelN =0 and the first excited one N =±1 (inset, Fig. 1B). This implies that, in our experimentsat room temperature, ωh exceeded the thermal energy k B T by a factor of 10. Importantly,in addition to the large cyclotron gap, there are a number of other factors that help theQHE in graphene to survive to so high temperatures. First, graphene devices allow forvery high carrier concentrations (up to 1013 cm -2) with only a single 2D subband occupied,which is essential to fully populate the lowest LL even in ultra-high B . This is in contrast totraditional 2D systems (for example, GaAs heterostructures) which are either depopulatedalready in moderate B or exhibit multiple subband occupation leading to the reduction ofthe effective energy gap to values well below ωh . Second, the mobility µ of Diracfermions in our samples does not change appreciably from liquid-helium to roomtemperature. It remains at ≈10,000 cm 2/Vs, which yields a scattering time of 1310~−τsecso that the high field limit 1>>⋅=B µωτ is reached in fields of several T.These characteristics of graphene foster hopes for the room-T QHE observable in fieldssignificantly smaller than 30T. In fact, we observe the Hall plateaus developing already inB <20T at 300K. The need for high B is attributed to broadened LLs due to disorder,which reduces the activation energy. We expect that improving sample homogeneity andachieving higher µ (currently limited by static defects) should allow the observation of theroom-T QHE using conventional magnets. This should open up new vistas for developing graphene-based resistance standards (certainly, operational above liquid-nitrogen temperature) and for novel quantum devices working at elevated temperatures. *e-mail: pkim@ and geim@[1] S. Das Sarma and A. Pinczuk, Perspectives in Quantum Hall Effects , Wiley, New York (1997).[2] B. Jeckelmann, B. Jeanneret. Rep. Prog. Phys. 64, 1603 (2001).[3] S.Q. Murphy et al . Physica E 6, 293 (2000).[4] G. Landwehr et al. Physica E 6, 713 (2000).[5] K.S. Novoselov et al . Nature 438, 197 (2005); Y. Zhang, Y.W. Tan, H.L. Stormer, P. Kim. Nature 438, 201 (2005).[6] This work was supported by EPSRC (UK), Royal Society and Leverhulme Trust, NSF (DMR-03-52738), DOE (DE-AIO2-04ER46133, DE-FG02-05ER4615), FOM (Netherlands), Microsoft Corporation, and W. M. Keck Foundation. The experiments were partially performed at the National High Magnetic Field Laboratory (supported by NSF Cooperative Agreement # DMR-0084173, by the state of Florida, and by DOE) and partially at the European High Field Magnet Laboratory (Nijmegen).Figure 1. Room-temperature QHE in graphene. (A ) – Optical micrograph of one of the devices used in the measurements. The scale is given by the Hall bar’s width of 2 µm. Device fabrication procedures were described in (5). (B ) - σxy (red) and ρxx (blue) as a function of gate voltages V g in a magnetic field of 29 T. Positive (negative) gate voltages V g induce electrons (holes) in concentrations n = (7.2⋅1010 cm -2/V)⋅V g (5). The inset illustrates the Landau level quantization for Dirac fermions. (C ) - Hall resistance R xy for electrons (red) and holes (green) shows the accuracy of the observed quantization at 45 T.。

maccormack scheme 麦科马克格式 mach angle 马蒜⾓ mach cone 马蒜锥；马赫锥 mach criterion 马赫判据 mach disk 马赫盘 mach fringe 马赫条纹 mach line 马赫线 mach net 马赫 mach number 马赫数 mach pendulum 马赫摆 mach principle 马赫原理 mach quadrangle 马赫四⾓形 mach reflection 马赫反射 mach scale law 马赫相似律 mach wave 马蒜波 mach wave machine 马赫波发⽣器 mache 马谢 machine 机械 machine time 机票间 machmeter 马赫数表 macro brownian movement 宏观布朗运动 macro fluid 宏观铃 macrocrack 宏观裂缝 macrodynamics 宏观动⼒学 macrographic test 宏观组织检验 macrohardness 宏观硬度 macromechanics 宏观⼒学 macromixing 宏观混合 macromolecule ⼤分⼦ macrorheology 宏观龄学 macroscopic 宏观的 macroscopic state 宏观状态 macroseismic phenomenon 强震现象 macroseisms 强震 macrostructure 宏观结构 macroturbulence 宏观湍流 macroviscosity 宏观粘性 magnesyn 磁⾃动同步机 magnetic convection effect 磁传输效应 magnetic diffusion 磁扩散 magnetic energy 磁能 magnetic field 磁场 magnetic flux 磁通量 magnetic force 磁⼒ magnetic friction 磁摩擦 magnetic hardness coefficient 磁硬度系数 magnetic inertia 磁惯性 magnetic knudsen number 磁克努曾数 magnetic line of force 磁⼒线 magnetic mach number 磁马赫数 magnetic moment 磁矩 magnetic plasma 磁等离⼦体 magnetic potential 磁位 magnetic prandtl number 磁普朗特数 magnetic pressure 磁压强 magnetic resonance absorption 磁共振吸收 magnetic resonance frequency 磁共振频率 magnetic reynolds number 磁雷诺数 magnetic stress tensor 磁应⼒张量 magnetic surface 磁⾯ magnetic tension 磁张⼒ magnetic transformation 磁性转变 magnetic viscosity 磁粘性 magnetized plasma 磁化等离⼦体 magnetizing force 磁化⼒ magnetoaerodynamics 磁性空⽓动⼒学 magnetocaloric effect 磁热效应 magnetodynamics 磁动⼒学 magnetoelastic constant 磁弹性常数 magnetoelastic effect 磁弹性效应 magnetoelastic energy 磁弹性能 magnetoelastic field 磁弹性场 magnetoelastic hysteresis 磁弹性滞后 magnetoelastic wave 磁弹性波 magnetofluiddynamics 磁铃动⼒学 magnetogasdynamics 磁⽓体动⼒学 magnetohydrodynamic 磁铃动⼒学的 magnetohydrodynamic approximation 磁铃动⼒学近似 magnetohydrodynamic conversion 磁铃动⼒学转换 magnetohydrodynamic dynamo 磁铃发电机 magnetohydrodynamic equations 磁铃⼒学⽅程 magnetohydrodynamic generator 磁铃发电机 magnetohydrodynamic instability 磁铃动⼒学不稳定性 magnetohydrodynamic shock wave 磁铃动⼒激波 magnetohydrodynamic turbulence 磁铃动⼒湍流 magnetohydrodynamic wake 磁铃动⼒尾迹 magnetohydrodynamic wave 磁铃动⼒波 magnetohydrodynamics 磁铃动⼒学 magnetohydrostatic 磁铃静⼒学的 magnetomechanical 磁⼒学的 magnetomechanical factor 磁⼒学因数 magnetomotive force 起磁⼒ magnetoplasma 磁等离⼦体 magnetoplasmadynamics 磁等离⼦体动⼒学 magnetosonic wave 磁声波 magnetosphere 磁层 magnetostatic energy 静磁能 magnetostatic energy density 静磁能量密度 magnetostatic oscillation 静磁振荡 magnetostatic stress tensor 静磁应⼒张量 magnetostatic unit 静磁单位 magnetostriction 磁致伸缩 magnetostrictive senser 磁致伸缩传感器 magnetostrictive strain 磁致伸缩应变 magnetostrictive stress 磁致伸缩应⼒ magnetothermal effect 磁热效应 magnetoviscous 磁粘性的 magnification 放⼤率 magnitude ⼤⼩ magnitude of angular velocity ⾓速度值 magnus effect 马格努斯效应 magnus force 马格努斯⼒ magnus formula 马格努斯公式 main axis of dilatation 膨胀轴 main axis of expansion 膨胀轴 main bar 拄 main flow 主 main foundation 基板 main motion 炙动 main pipe 周 main shaft 轴 main stream 主⼲流 main tide 直 main water table 潜⽔⾯ major cycle ⼤循环 man carrying rocket 载⼈⽕箭 man made satellite ⼈造卫星 maneuver 机动飞⾏ maneuverability 机动性 maneuvering 机动 manifold 分淋 manned rocket 载⼈⽕箭 manning formula 曼宁公式 manograph 压⼒记录仪 manometer 压⼒计 manometer head 液压计⽰压头 manometric balance 压⼒秤 manometric flame 感压焰 manual ⼿动的 many body force 多体⼒ many body problem 多体问题 many degrees of freedom system 多⾃由度系统 many level resonance formula 多能级共振公式 many particle force 多粒⼦⼒ mapping 映射 marangoni effect 马朗⼽尼效应 marangoni gibbs effect 马朗⼽尼吉布斯效应 margin 限界 margin of error 误差界限 margin of safety 安全系数 marginal force 边缘⼒ marking 标⽰ markoff distribution 马尔科夫分布 markoff process 马尔科夫过程 marzetti plasticity 马泽蒂塑性 mask 掩模 mass 质量 mass absorption coefficient 质量吸收系数 mass action 质量酌 mass action constant 质量酌常数 mass action law 质量酌定律 mass attenuation coefficient 质量衰减系数 mass balance 质量平衡 mass center 质⼼ mass center integral 质⼼积分 mass concentration 质量浓度 mass conductivity coefficient 传质系数 mass conservation law 质量守恒定律 mass decrement 质量减量 mass density ⽐质量 mass energy relation 质能关系 mass energy transfer coefficient 质能转移系数 mass flow 质量流 mass flow rate 质量潦 mass flow ratio 质量量⽐ mass flow velocity 质量临 mass flux 质量量 mass force 质量⼒ mass inertia 质量惯性 mass matrix 质量矩阵 mass mean diameter 质量平均径 mass moment 质量矩 mass moment of inertia 质量惯性矩 mass motion 地块运动 mass of system 系统质量 mass point 质点 mass point mechanics 质点⼒学 mass ratio 质量⽐ mass separation 质量分离 mass tensor 质量张量 mass to thrust ratio 质量推⼒⽐ mass transfer 传质 mass transfer coefficient 传质系数 mass transfer rate 传质速率 mass velocity 质量速度 mass velocity relation 质量速度关系 mast 帆柱 master pulse 嘱冲 material 物质 material acceleration 物质加速度 material balance 物质平衡 material constant 材料常数 material continuity equation 物质连续性⽅程 material coordinates 物质坐标 material derivative 物质导数 material discontinuity 物质不连续性 material field 物质场 material flow 物质流 material line 物质线 material nonlinearity 材料⾮线性 material point 质点 material reference frame 物质参考系 material surface 物质表⾯ material testing machine 材料试验机 material testing reactor 材料试验反应堆 material transfer 物质转移 material transmitting pressure only 单纯传压材料 material transmitting traction only 单纯传拉材料 material viscoelasticity 材料粘弹性 materialization 质化 materials science 材料科学 materials testing 材料试验 mathematical model 数学模型 mathematical pendulum 单摆 mathematical similarity 数学相似 mathematical simulation 数学模拟 mathieu equation 马提厄⽅程 mathieu function 马提厄函数 matrices of composite material 复合材料基体 matrix 矩阵 matrix calculation 矩阵计算 matrix element 矩阵元 matrix mechanics 矩阵⼒学 matrix of the coefficients 系数矩阵 matrix structural analysis 矩阵法结构分析 matter 物质 matter constant 材料常数 matter tensor 物质张量 maximum maximum deflection 挠度 maximum deviation 偏差 maximum discharge 量 maximum freezing point 凝固点 maximum height ⾼度 maximum intensity of shear 切应⼒ maximum limit of size 极限尺⼨ maximum load 负载 maximum moment ⼒矩 maximum normal stress 法向应⼒ maximum output 输出功率 maximum overpressure 过压 maximum permeability 磁导率 maximum permissible unbalance 容许不平衡 maximum phase angle deviation 相⾓偏差 maximum pressure 压⼒ maximum principal deformation 咒形 maximum principal stress theory 枝⼒理论 maximum principle 极⼤值原理 maximum range 射程 maximum shear stress 切应⼒ maximum speed 速度 maximum strain energy theory 应变能理论 maximum stress 应⼒ maximum stress theory 应⼒理论 maximum stretching strain 伸长应变 maximum tensile stress 拉伸应⼒ maximum thrust 推⼒ maximum usable frequency 可⽤频率 maximum value 值 maximum velocity 速度 maximum with constraints 条件极⼤ maximum work 功 maxwell body 麦克斯韦体 maxwell boltzmann equaion 麦克斯韦玻⽿兹曼⽅程 maxwell construction of streamlines 麦克斯韦吝准法 maxwell diagram 麦克斯韦⼒图 maxwell energy stress tensor 麦克斯韦能量应⼒张量 maxwell equation 麦克斯韦⽅程 maxwell field 麦克斯韦场 maxwell fluid 麦克斯韦铃 maxwell formula 麦克斯韦公式 maxwell law of viscosity 麦克斯韦粘度定律 maxwell liquid 麦克斯韦液体 maxwell material 麦克斯韦体 maxwell model 麦克斯韦模型 maxwell reciprocal theorem 麦克斯韦倒易定理 maxwell relaxation equation 麦克斯韦弛豫⽅程 maxwell relaxation model 麦克斯韦弛豫模型 maxwell solid 麦克斯韦体 maxwell theorem 麦克斯韦定理 maxwellian distribution 麦克斯韦分布 maxwellian gas 麦克斯韦⽓体 maxwellian relaxation time 麦克斯韦弛豫时间 maxwellian stress 麦克斯韦应⼒ mean 平均 mean acceleration 平均加速度 mean angular motion 平均⾓运动 mean angular velocity 平均⾓速度 mean anomaly 平近点⾓ mean camber of the wing 翼型中线曲度 mean collision frequency 平均碰撞频率 mean collision time 平均碰撞时间 mean deviation 平均偏差 mean diameter 平均直径 mean diurnal motion 平均周⽇运动 mean effective pressure 平均有效压⼒ mean error 平均误差 mean free path 平均⾃由程 mean free path for fission 裂变平均⾃由程 mean free time 平均⾃由时间 mean high tide 平均⾼潮位 mean hydraulic depth 平均⽔⼒深度 mean life 平均寿命 mean mass velocity 质⼼速度 mean motion 平均运动 mean orbital element 平均轨迹元 mean pressure 平均压⼒ mean pulse power 平均脉冲功率 mean range 平均射程 mean range of tide 平均潮差 mean resistance 平均阻⼒ mean speed 平均速度 mean speed vector 平均速度⽮量 mean square 均⽅ mean square deviation 均⽅差 mean square error 均⽅误差 mean temperature 平均温度 mean value 平均值 mean velocity 平均速度 meander 曲流 meander pattern 曲两样 meandering 迂曲运动 measure 测 measure of strain 应变量度 measured value 实测值 measurement 测量 measuring 测量 measuring apparatus 测量仪器 measuring device 测量设备 measuring machine 测量机 measuring pulse 试验脉冲 measuring range 测定范围 measuring rod 测量杆 mechanical action ⼒学酌 mechanical admittance ⼒导纳 mechanical aeration 机械曝⽓ mechanical analogue 机械横拟 mechanical analysis of soil ⼟壤粒度分析 mechanical efficiency ⼒学效率 mechanical energy ⼒学能 mechanical equilibrium ⼒学平衡 mechanical equivalent of heat 热功当量 mechanical hysteresis ⼒学滞后 mechanical impedance ⼒学阻抗 mechanical kinematics 机械运动学 mechanical loss 机械损耗 mechanical mass ⼒学质量 mechanical model ⼒学模型 mechanical motion ⼒学运动 mechanical oscillation ⼒学振荡 mechanical oscillator ⼒学振荡器 mechanical passivity ⼒学钝性。

纳米材料的表征特性1:表面与界面效应球形颗粒的表面积与直径的平方成正比，其体积与直径的立方成正比，故其比表面积(表面积/体积)与直径成反比。

随着颗粒直径变小，比表面积将会显著增大，说明表面原子所占的百分数将会显著增加。

对直径大于0.1μm的颗粒的表面效应可忽略不计，当尺寸小于0.1μm时，其表面原子百分数急剧增长，甚至1g超微颗粒表面积的总和可高达l00m2，这时的表面效应将不容忽略。

超微颗粒的表面与大块物体的表面是十分不同的，若用高倍率电子显微镜对金超微颗粒(直径为2×10-3μm)进行电视摄像，实时观察发现这些颗粒没有固定的形态，随着时间的变化会自动形成各种形状(如立方八面体，十面体，二十面体多粒晶等)，它既不同于一般固体，又不同于液体，是一种准固体。

在电子显微镜的电子束照射下，表面原子仿佛进入了“沸腾”状态，尺寸大于10nm后才观察不到这种颗粒结构的不稳定性，这时微颗粒具有稳定的结构状态。

超微颗粒的表面具有很高的活性，在空气中金属颗粒会迅速氧化且燃烧。

如要防止自燃，可采用表面包覆或有意识地控制氧化速率，使其缓慢氧化生成一层极薄且致密的氧化层，确保表面稳定化。

利用表面活性，金属超微颗粒有望成为新一代的高效催化剂、储气材料或低熔点材料。

2:小尺寸效应当纳米粒子的尺寸与光波的波长、传导电子的德布罗意波长以及超导态的相干长度或透射深度等物理尺寸相当或比它们更小时，周期性的边界条件被破坏，声、光、电、磁、热力学特性等均会随着粒子尺寸的减小发生显著的变化。

这种因尺寸的减小而导致的变化称为小尺寸效应，也叫体积效应。

如纳米粒子的熔点可远低于块状固体，此特性为粉末冶金工业提供了新工艺；利用等离子共振频移随颗粒尺寸变化的性质，可以通过改变颗粒尺寸，控制吸收边的位移，构造具有一定频宽的微波吸收纳米材料，用于电磁波屏蔽、隐形飞机等。

材料的硬度和强度随着晶粒尺寸的减小而增大，不少纳米陶瓷材料的硬度和强度比普通材料高4—5倍，如纳米TiO2的显微硬度为12.75kPa，而普通TiO2陶瓷的显微硬度低于1.96kPa。