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Chiral optical transport of quantum dots with different diamagnetic behaviors in a waveguide

Shi Shu-Shu Xiao Shan Xu Xiu-Lai

Shi Shu-Shu, Xiao Shan, Xu Xiu-Lai. Chiral optical transport of quantum dots with different diamagnetic behaviors in a waveguide. Acta Phys. Sin., 2022, 71(6): 067801. doi: 10.7498/aps.71.20211858
Citation: Shi Shu-Shu, Xiao Shan, Xu Xiu-Lai. Chiral optical transport of quantum dots with different diamagnetic behaviors in a waveguide. Acta Phys. Sin., 2022, 71(6): 067801. doi: 10.7498/aps.71.20211858

Chiral optical transport of quantum dots with different diamagnetic behaviors in a waveguide

Shi Shu-Shu, Xiao Shan, Xu Xiu-Lai
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  • In order to realize scalable and integrated quantum photonic networks, various functional devices are highly desired. Strip waveguides with unidirectional transmission function have a wide range of applications in devices such as single-photon diodes, transistors and deterministic quantum gate devices. In this work, the separation of circularly polarized light is achieved by exciting a quantum dot light source in a central region of a waveguide at a low temperature of 4.2 K by using a confocal microscope system. By applying a magnetic field with Faraday configuration (along with the quantum dot growth direction), the spin-momentum locking effect in the waveguide is verified. Both forward shift and reverse shift of different values of output photon energy are demonstrated to show the unidirectional transmission of the waveguide. The chiral transmission of quantum dot with anomalous diamagnetic behavior is achieved in experiment, leading to a wider range of wavelength tuning for chrial transmission in a single waveguide. This paper provides a basis for investigating the chiral quantum devices in a wide wavelength range and expands the applications of waveguides in the field of optical quantum information.
      PACS:
      78.20.Ls(Magneto-optical effects)
      84.40.Az(Waveguides, transmission lines, striplines)
      85.35.Be(Quantum well devices (quantum dots, quantum wires, etc.))
      Corresponding author: Xu Xiu-Lai, xlxu@iphy.ac.cn
    • Funds: Project is supported by the National Key R&D Program of China (Grant No. 2021YFA1400700), the National Natural Science Foundation of China (Grant Nos. 62025507, 11934019, 11721404, 11874419), the Guangdong Provincial Key Area R&D Program, China (Grant No. 2018B03032900), and the Strategic Pioneer Science and Technology Special Project of Chinese Academy of Sciences (Grant No. XDB28000000)

    量子信息科学构建的蓝图为一系列前沿理论和技术提供了机遇与挑战[1,2]. 为了提升量子网络中量子节点的性能, 需要开发能够同时处理量子态完整传输和高效读出的量子器件, 从而实现量子态与各类多功能量子器件的有效结合 [3,4]. 最近, 手性量子光学在量子信息领域中受到了广泛的关注[5]. 利用自旋动量锁定效应, 可以在不同微纳结构(光纤[6,7]、波导[8,9]、谐振器[10,11]等)中构建自旋-光子界面, 实现方向性依赖的传输与耦合, 从而为量子态的操控增加了一种新的自由度. 其中, 波导结构对光子的横向传播具有强束缚, 通过波导模式与光子偏振的耦合, 可以实现单向光子传输[12]. 而在条形波导结构中, 光子定向传输的单向性已高达0.95[13]. 到目前为止, 波导已实现单向性的量子光源[14]、能量分束[15]、通道转换[16]等功能. 此外, 具有单向传输功能的波导可作为单光子光学二极管[17,18]、晶体管[19,20]和确定性量子门[21,22]等的关键组成部分. 因此, 研究单向传输波导是实现量子光学网络的一条有探索价值的途径.

    作为研究波导单向传输的常用发光中心, 量子点可以看作一个类二能级系统, 量子点中的电子空穴对复合时的发光具有单光子特性[23,24] . 量子点相较于单个原子具有易于操控和集成的优点, 可以作为高效单光子源[25-27]. 同时光子可以作为飞行量子比特的载体. 此外, 量子点中空穴与电子的自旋可以作为自旋量子比特参与固态量子信息处理[28-30]. 因此, 量子点可以作为沟通两种量子比特的媒介[31,32], 有望实现分布式计算[33].

    然而, 在波导单向传输的研究工作中, 通常随着磁场的增加, 光子的能量总是整体向高能方向偏移 [13-16], 限制了单向传输的能量范围. 在针对量子点的研究中, 磁场不仅可以调控量子点的发光能级[34,35], 而且有研究小组观测到磁场下量子点荧光的反常抗磁现象[36-38]. 反常抗磁行为的量子点具有出射光子能量向低能方向偏移的特征, 可以填补波导中定向光子传输的能量移动范围. 目前, 对波导中具有反常抗磁行为量子点光源的单向传输的研究还未见报道.

    本文通过制备悬浮的条形波导, 在法拉第构型(沿量子点生长方向)磁场的调控下, 首次在同一波导器件中实现了具有不同抗磁行为的量子点的圆偏振光的单向传输. 实验研究了不同抗磁行为的量子点的单向传输, 通过对低温荧光光谱进行洛伦兹拟合, 得到正常和反常抗磁行为的量子点中激子的朗德因子分别为gex1=2.57gex2=1.26, 抗磁系数分别为γ1=5.83μeV/T2γ2=3.43μeV/T2, 相应的最高手性对比度分别达到0.84与0.66. 在磁场的作用下同时实现了向高能与低能方向移动的量子点圆偏振光的定向输出, 扩展了波导器件的能量传输范围, 为实现功能更为丰富的手性量子器件提供了途径.

    利用分子束外延的方法, 在未掺杂的GaAs衬底上生长一层厚度为1 μm的AlGaAs作为牺牲层. 接着在牺牲层上生长一层150 nm厚的GaAs薄膜, 单层自组装InGaAs量子点生长于GaAs薄膜中心. 通过电子束曝光技术将结构图案转移到使用正抗蚀剂AR-P 6200旋涂过的样品上, 再使用显影剂AR 600-546对电子束曝光区域进行显影. 定影后, 利用电感耦合等离子体蚀刻工艺将图案转移到GaAs薄膜上. 最后使用氢氟酸溶液去除暴露的AlGaAs牺牲层, 留下悬浮的条形波导.

    我们将样品置在温度恒为4.2 K的共聚焦荧光显微系统中进行光学测试. 样品台两侧环绕的超导线圈可以提供高达9 T的法拉第构型磁场(磁场方向与量子点生长方向平行). 量子点由波长为 532 nm 的连续激光器非共振激发. 通过光路调节, 激发光路用于激发量子点, 收集光路用于收集由光栅耦合器耦合出的量子点荧光光谱. 其中选用的显微物镜数值孔径为0.8. 收集到的荧光信号经过光纤耦合, 由分辨率为60 μeV的光栅光谱仪进行探测.

    条形波导的材质为GaAs, 折射率约为3.46. 由于全反射, 光子被限制在波导中进行低损耗传输. 我们将波导设计成单模波导, 其设计参数详见文献[16]. 虽然条形波导不具备手性的几何结构, 但波导中存在局域的圆偏振场分布, 自旋极化的量子点可以与这种场分布进行模式耦合, 实现量子点自旋与位置相关的单向光子发射. Coles等[13]详细讨论了在无限长条形波导的电场分布, 即以波导横截面中心为零点, 位置分别向零点的正方向和负方向移动时, 电场分量表现出相反的相位. 具体而言, 场极化分布分别由零点处线性分布逐渐演变为左圆极化与右圆极化分布, 由此生成不对称的手性特征. 由于波导的手性行为与电场分布密切相关, 光子传输的手性度由量子点在波导中的位置主导决定, 圆极化光只有与电场相位匹配时才能形成有效耦合[16]. 理论上, 在偏离条形波导中心的某些位置可以实现最佳手性传输. 此时, 波导内电场分布正好为左或右圆极化的状态, 在此放置相同极化方向的圆偏振光可以与波导内电场耦合, 而相反方向的圆偏振光受到抑制, 形成单向传输.

    图1(a)展示了实验制备的条形波导的扫描电子显微镜图像(scanning electron microscope, SEM). 条形波导尾端分别连接到左右两侧的光栅耦合器上. 波导中间包含一层InGaAs量子点, 以波导方向为y轴, 则量子点随机分布在波导中平行于波导的xy面. 图1(a)中右边的插图为波导横截面(xz面)中量子点分布的示意图. 量子点能级能量较体材料更低, 光激发产生的电子与空穴弛豫到量子点中形成束缚态, 称为激子态. 在实验中, 激光激发波导中心区域的量子点时, 激子态产生的荧光会经过波导传输进入左右两个光栅耦合器. 光栅耦合器可以将平面内传输的光信号从竖直方向上输出, 以便于共聚焦显微系统的光谱收集. 图1(b)为量子点在法拉第构型的磁场下量子点激子态能级发生Zeeman分裂的示意图. 由于载流子能级不再简并, 量子点中电子与空穴对应的自旋态进行自发辐射跃迁后, 将产出两支极化相反的圆偏振光(σ+, σ). 这样的一对左旋与右旋圆偏振光可以作为研究波导手性特征的量子光源.

    图 1 条形波导的结构和量子点的能级示意图 (a)条形波导的SEM图像, 实验中激光激发波导中心区域的量子点, 并从左右两侧光栅耦合器分别收集量子点的荧光; 右边的插图为波导中心区域横截面中量子点分布的示意图; (b)量子点能级的Zeeman分裂示意图, Zeeman分裂导致了两支极化相反的圆偏振光σ-和σ+的产生.\r\nFig. 1. Schematic diagram of the structure of the strip waveguide and the energy levels of a quantum dot (QD). (a) SEM image of a strip waveguide. In the experiment, the QDs in the central area of the waveguide were excited by the laser, and the photoluminescence (PL) spetra of the QDs were collected from the left and right grating couplers, respectively. Illustration on the right is the schematic diagram of QDs distributed in the central area of the cross section of the waveguide. (b) Zeeman splitting of the QD energy levels. Zeeman splitting results in two branches of circularly polarized light with opposite polarization σ- and σ+.
    图 1  条形波导的结构和量子点的能级示意图 (a)条形波导的SEM图像, 实验中激光激发波导中心区域的量子点, 并从左右两侧光栅耦合器分别收集量子点的荧光; 右边的插图为波导中心区域横截面中量子点分布的示意图; (b)量子点能级的Zeeman分裂示意图, Zeeman分裂导致了两支极化相反的圆偏振光σ和σ+的产生.
    Fig. 1.  Schematic diagram of the structure of the strip waveguide and the energy levels of a quantum dot (QD). (a) SEM image of a strip waveguide. In the experiment, the QDs in the central area of the waveguide were excited by the laser, and the photoluminescence (PL) spetra of the QDs were collected from the left and right grating couplers, respectively. Illustration on the right is the schematic diagram of QDs distributed in the central area of the cross section of the waveguide. (b) Zeeman splitting of the QD energy levels. Zeeman splitting results in two branches of circularly polarized light with opposite polarization σ and σ+.

    量子点在磁场下的能级劈裂程度通常用朗德g因子来描述, Zeeman分裂的能量大小可写为ΔEZeeman=gexμBB, 其中B为磁场强度, μB为玻尔磁子. 则量子点激子态的朗德因子gex可记为gex=ΔEZeemanμBB=E(σ+)E(σ)μBB, 其中E(σ+)E(σ)分别表示在磁场作用下分开的σ+σ中心能量. 除此之外, 法拉第构型磁场对量子点内部的电子与空穴的行为存在束缚作用, 在洛伦兹力的影响下电子与空穴将产生额外的回旋运动, 从而影响载流子复合发光的速率, 产生抗磁效应. 量子点激子态的抗磁大小与磁场强度的关系可表述为ΔEEnergy shift=γB2, 即为γ=ΔEEnergy shiftB2 = E(σ+) + E(σ)2B2, 其中ΔEEnergy shiftσ+σ的中心能量的平均值来定义, 用于描述其能量整体偏移的程度; B代表磁场强度, γ为抗磁系数. 磁场下, 量子点的抗磁效应通常表现为σ+σ中心能量的平均值随磁场增强向高能方向偏移[39-41]. 然而随着量子点研究的深入, 发现了σ+σ中心能量的平均值随磁场增强向低能方向移动的情况[36-38]. 为表区分, 本文中将这两种抗磁行为称为正常抗磁与反常抗磁.

    拥有正常抗磁行为的量子点在波导中的手性传输结果如图2(a)所示. 图中, 在波导中心区域的量子点受激光激发后, 辐射出的荧光的中心能量向高能方向发生偏移, 其中红色或黑色实线分别代表从右侧或左侧光栅耦合器中收集到的量子点荧光光谱, 外加磁场从0 T逐渐增强到8 T, 测量步长为0.5 T. 相同磁场强度下左右两侧收集到的荧光信号表现出明显的单向传输行为, 即手性现象. 在强磁场下, 从左侧收集到的荧光信号σ正常传输而σ+受到抑制, 反之亦然. 通过观察可以发现, 单向传输与荧光峰位或量子点激子态的Zeeman分裂程度无关. 通过洛伦兹拟合, 提取图2(a)中各个峰值位置对应的中心能量, 结果如图2(b)所示, 其中黑色表示σ, 红色表示σ+. 为了进一步得到朗德因子, 将σ+σ中心能量的差值进行线性拟合, 如图2(c)所示. 根据定义, 激子态Zeeman分裂程度随磁场强度变化的斜率即为朗德因子, 其拟合结果为朗德因子gex1=2.57. 图2(d)表示σ+σ中心能量的平均值随磁场的变化. 对其进行二次拟合, 可得到抗磁系数γ1=5.83μeV/T2, 与文献[42]中自由激子的抗磁系数基本一致.

    图 2 正常抗磁行为量子点的手性传输实验结果 (a) 施加0—8 T的磁场, 从左右两侧光栅耦合器分别收集到的量子点激子态的圆极化荧光光谱; (b) 随磁场变化的荧光光谱的峰值; (c) 激子态的Zeeman分裂随磁场的变化和对应的g因子; (d)激子态劈裂峰的能量平均值随磁场的变化和对应的抗磁系数.\r\nFig. 2. Experimental results of chiral transport of QDs with normal diamagnetic behavior: (a) Circularly polarized PL spectra of excitonic states of QDs collected from the left and right grating couplers by applying a magnetic field from 0 T to 8 T, respectively; (b) PL peak energies as a function of an applied magnetic field; (c) Zeeman splitting of the exciton state with a magnetic field and the corresponding g-factor; (d) average energy of the splitting peaks with a magnetic field and the corresponding diamagnetic coefficient.
    图 2  正常抗磁行为量子点的手性传输实验结果 (a) 施加0—8 T的磁场, 从左右两侧光栅耦合器分别收集到的量子点激子态的圆极化荧光光谱; (b) 随磁场变化的荧光光谱的峰值; (c) 激子态的Zeeman分裂随磁场的变化和对应的g因子; (d)激子态劈裂峰的能量平均值随磁场的变化和对应的抗磁系数.
    Fig. 2.  Experimental results of chiral transport of QDs with normal diamagnetic behavior: (a) Circularly polarized PL spectra of excitonic states of QDs collected from the left and right grating couplers by applying a magnetic field from 0 T to 8 T, respectively; (b) PL peak energies as a function of an applied magnetic field; (c) Zeeman splitting of the exciton state with a magnetic field and the corresponding g-factor; (d) average energy of the splitting peaks with a magnetic field and the corresponding diamagnetic coefficient.

    在同一根波导中, 实验观测到了表现为反常抗磁的另一个量子点的单向传输现象, 如图3(a)所示. 在相同的实验条件下, 施加0—8 T的磁场, 从左右两侧光栅耦合器分别观测到量子点的发光能量向低能方向偏移, 即产生了反常抗磁现象. 在0 T时, 图3(a)中含有3个量子点的荧光. 可以观察到随着磁场的变化, 每个单峰的Zeeman分裂以及抗磁行为均不相同. 绿色区域反映了其中1个反常抗磁量子点在磁场下的发光光谱. 图3(b)为洛伦兹拟合得到的σ+σ的中心能量位置, 整体趋势与图2(b)正好相反. 如图3(c), 提取σ+σ中心能量的差值, 经过线性拟合得到朗德因子gex2=1.26. 对于图3(d), 提取σ+σ中心能量的平均值, 经二次拟合得到抗磁系数γ2=3.43μeV/T2, 符合文献[38]中反常抗磁激子的一般情形. 本文中正常抗磁与反常抗磁现象来源于不同的两个量子点, 量子点之间具有形貌大小方面的制备差异, 这是造成不同的朗德因子以及抗磁系数的重要因素.

    图 3 反常磁行为量子点的手性传输实验结果 (a) 施加0—8 T的磁场, 从左右两侧光栅耦合器分别收集到的量子点激子态的圆极化荧光光谱; (b) 随磁场变化的荧光光谱的峰值; (c) 激子态的Zeeman分裂随磁场的变化和对应的g因子; (d)激子态劈裂峰的能量平均值随磁场的变化和对应的抗磁系数.\r\nFig. 3. Experimental results of chiral transport of QDs with anomalous diamagnetic behavior: (a) Circularly polarized PL spectra of excitonic states of QDs collected from the left and right grating couplers by applying a magnetic field from 0 T to 8 T, respectively; (b) PL peak energies as a function of an applied magnetic field;  (c) Zeeman splitting of the exciton state with a magnetic field and the corresponding g-factor; (d) average energy of the splitting peaks with a magnetic field and the corresponding diamagnetic coefficient.
    图 3  反常磁行为量子点的手性传输实验结果 (a) 施加0—8 T的磁场, 从左右两侧光栅耦合器分别收集到的量子点激子态的圆极化荧光光谱; (b) 随磁场变化的荧光光谱的峰值; (c) 激子态的Zeeman分裂随磁场的变化和对应的g因子; (d)激子态劈裂峰的能量平均值随磁场的变化和对应的抗磁系数.
    Fig. 3.  Experimental results of chiral transport of QDs with anomalous diamagnetic behavior: (a) Circularly polarized PL spectra of excitonic states of QDs collected from the left and right grating couplers by applying a magnetic field from 0 T to 8 T, respectively; (b) PL peak energies as a function of an applied magnetic field; (c) Zeeman splitting of the exciton state with a magnetic field and the corresponding g-factor; (d) average energy of the splitting peaks with a magnetic field and the corresponding diamagnetic coefficient.

    反常抗磁产生的原因在于带电激子中电子空穴对复合辐射出光子后, 量子点中仍残存电子, 此时电子运动不再受到初始状态下量子点中空穴的库仑束缚作用, 使得终态量子点中的电子波函数分布范围扩散, 从而在实验上表现为反常抗磁现象, 具有负的抗磁系数[36,38]. 据此可知图3(a)中反常抗磁现象量子点激子态为带负电激子态. 反常抗磁现象一般发生在小尺寸量子点中[36]. 由此, 在量子点的生长过程中对其半径进行调控, 可以实现对量子点的正常和反常抗磁行为的调控, 从而在波导中获得向低能方向和高能方向移动的量子点荧光的单向传输.

    为了定量描述波导的手性性质, 即光子传输的单向性, 引入手性对比度(contrast, C). 以计算σ+的单向性为例, 对圆极化荧光光谱中某磁场强度下的σ+进行洛伦兹拟合分别得到荧光信号的峰值强度Iσ+Iσ, 代入手性对比度公式

    C=Iσ+IσIσ++Iσ

    进而得到σ+σ分别与波导模式耦合后向左与向右传输的手性对比度. 图4(a)图4(b)展示了正常抗磁行为与反常抗磁行为的量子点激子态的手性对比度随磁场强度的变化. 红色圆点表示从右侧光栅耦合器收集到的σ+相对于σ的手性对比度, 而黑色方块表示从左侧光栅耦合器收集到的σ相对于σ+的手性对比度. 抗磁与反常抗磁量子点在较强磁场下的手性对比度最高分别达到了0.84与0.66.

    图 4 不同量子点的手性对比度 (a)正常抗磁行为量子点的手性对比度随磁场的变化; (b)反常抗磁行为量子点的手性对比度随磁场的变化.\r\nFig. 4. Chiral contrast for different QDs: (a) Variation of chiral contrast with a magnetic field for the QD with a normal diamagnetic behavior; (b) variation of chiral contrast with a magnetic field for the QD with an anomalous diamagnetic behavior.
    图 4  不同量子点的手性对比度 (a)正常抗磁行为量子点的手性对比度随磁场的变化; (b)反常抗磁行为量子点的手性对比度随磁场的变化.
    Fig. 4.  Chiral contrast for different QDs: (a) Variation of chiral contrast with a magnetic field for the QD with a normal diamagnetic behavior; (b) variation of chiral contrast with a magnetic field for the QD with an anomalous diamagnetic behavior.

    需要强调的是, 由于在低磁场强度下单量子点产生的两个分裂峰未完全劈开, 重叠部分较大, 难以从圆极化荧光光谱中直接分辨出手性对比度. 因此统计手性对比度时仅对磁场强度在2.5 T以上的结果进行计算. 同一现象中σ+σ手性对此度呈现的差异归因于两侧光栅耦合器的制备误差、量子点制备过程中产生的形貌不对称以及波导中的背向散射. 手性对比度结果与量子点正常抗磁与反常抗磁的行为无关. 两个量子点关于最佳手性位置的偏移距离不同, 导致具有正常抗磁行为的量子点与反常抗磁行为的量子点中σ+σ的手性对比度产生较大差异.

    本文实现了具有正常抗磁与反常抗磁现象的不同量子点中σ+σ在同一个条形波导中的单向传输. 该结果表明σ+σ的单向传输在磁场的作用下除高能方向外, 也能向低能方向进行偏移, 完善了波导器件的传输功能. 通过调节0—8 T的法拉第构型磁场, 观测到波导中量子点激子态的Zeeman分裂以及抗磁效应随磁场的变化, 并通过拟合得到了正常抗磁与反常抗磁条件下对应的朗德因子与抗磁系数. 分别计算了具有正常抗磁与反常抗磁现象的单量子点在单向传输过程中的手性对比度, 分析了较高磁场下手性对比度产生差异的原因. 本文首次聚焦具有反常抗磁现象量子点在波导中的单向传输, 为宽波段范围的手性量子器件的研究奠定了实验基础.

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    期刊类型引用(3)

    1. 白靖,马文浩,葛城显,吴振森,许彤. 驻波场中非均匀手征分层粒子的辐射力特性. 物理学报. 2024(18): 151-167 . 百度学术
    2. SAI YAN,JINGNAN YANG,SHUSHU SHI,ZHANCHUN ZUO,CAN WANG,XIULAI XU. Transport of a topologically protected photonic waveguide on-chip. Photonics Research. 2023(06): 1021-1028 . 必应学术
    3. 李函聪,陈浠庆,杨静南,史书姝,许秀来. 单量子点的发光与应用. 发光学报. 2023(07): 1251-1272 . 百度学术

    其他类型引用(0)

  • 图 1  条形波导的结构和量子点的能级示意图 (a)条形波导的SEM图像, 实验中激光激发波导中心区域的量子点, 并从左右两侧光栅耦合器分别收集量子点的荧光; 右边的插图为波导中心区域横截面中量子点分布的示意图; (b)量子点能级的Zeeman分裂示意图, Zeeman分裂导致了两支极化相反的圆偏振光σ和σ+的产生.

    Figure 1.  Schematic diagram of the structure of the strip waveguide and the energy levels of a quantum dot (QD). (a) SEM image of a strip waveguide. In the experiment, the QDs in the central area of the waveguide were excited by the laser, and the photoluminescence (PL) spetra of the QDs were collected from the left and right grating couplers, respectively. Illustration on the right is the schematic diagram of QDs distributed in the central area of the cross section of the waveguide. (b) Zeeman splitting of the QD energy levels. Zeeman splitting results in two branches of circularly polarized light with opposite polarization σ and σ+.

    图 2  正常抗磁行为量子点的手性传输实验结果 (a) 施加0—8 T的磁场, 从左右两侧光栅耦合器分别收集到的量子点激子态的圆极化荧光光谱; (b) 随磁场变化的荧光光谱的峰值; (c) 激子态的Zeeman分裂随磁场的变化和对应的g因子; (d)激子态劈裂峰的能量平均值随磁场的变化和对应的抗磁系数.

    Figure 2.  Experimental results of chiral transport of QDs with normal diamagnetic behavior: (a) Circularly polarized PL spectra of excitonic states of QDs collected from the left and right grating couplers by applying a magnetic field from 0 T to 8 T, respectively; (b) PL peak energies as a function of an applied magnetic field; (c) Zeeman splitting of the exciton state with a magnetic field and the corresponding g-factor; (d) average energy of the splitting peaks with a magnetic field and the corresponding diamagnetic coefficient.

    图 3  反常磁行为量子点的手性传输实验结果 (a) 施加0—8 T的磁场, 从左右两侧光栅耦合器分别收集到的量子点激子态的圆极化荧光光谱; (b) 随磁场变化的荧光光谱的峰值; (c) 激子态的Zeeman分裂随磁场的变化和对应的g因子; (d)激子态劈裂峰的能量平均值随磁场的变化和对应的抗磁系数.

    Figure 3.  Experimental results of chiral transport of QDs with anomalous diamagnetic behavior: (a) Circularly polarized PL spectra of excitonic states of QDs collected from the left and right grating couplers by applying a magnetic field from 0 T to 8 T, respectively; (b) PL peak energies as a function of an applied magnetic field; (c) Zeeman splitting of the exciton state with a magnetic field and the corresponding g-factor; (d) average energy of the splitting peaks with a magnetic field and the corresponding diamagnetic coefficient.

    图 4  不同量子点的手性对比度 (a)正常抗磁行为量子点的手性对比度随磁场的变化; (b)反常抗磁行为量子点的手性对比度随磁场的变化.

    Figure 4.  Chiral contrast for different QDs: (a) Variation of chiral contrast with a magnetic field for the QD with a normal diamagnetic behavior; (b) variation of chiral contrast with a magnetic field for the QD with an anomalous diamagnetic behavior.

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    Bennett C H, DiVincenzo D P 2000 Nature 404 247Google Scholar

    [2]

    Monroe C 2002 Nature 416 238Google Scholar

    [3]

    Northup T E, Blatt R 2014 Nat. Photonics 8 356Google Scholar

    [4]

    Kues M, Reimer C, Roztocki P, Cortés L R, Sciara S, Wetzel B, Zhang Y, Cino A, Chu S T, Little B E, Moss D J, L Caspani, Azaña J, Morandotti R 2017 Nature 546 622Google Scholar

    [5]

    Lodahl P, Mahmoodian S, Stobbe S, Rauschenbeutel A, Schneeweiss P, Volz J, Pichler H, Zoller P 2017 Nature 541 473Google Scholar

    [6]

    Petersen J, Volz J, Rauschenbeutel A 2014 Science 346 67Google Scholar

    [7]

    Mitsch R, Sayrin C, Albrecht B, Schneeweiss P, Rauschenbeutel A 2014 Nat. Commun. 5 5713Google Scholar

    [8]

    Söllner I, Mahmoodian S, Hansen S L, Midolo L, Javadi A, Kiršanskė G, Pregnolato T, El-Ella H, Lee E H, Song J D, Stobbe S, Lodahl P 2015 Nat. Nanotechnol. 10 775Google Scholar

    [9]

    Mehrabad M J, Foster A P, Dost R, Fox A M, Skolnick M S, Wilson L R 2020 Optica 7 1690Google Scholar

    [10]

    Rodríguez-Fortuño F J, Barber-Sanz I, Puerto D, Griol A, Martínez A 2014 ACS Photonics 1 762Google Scholar

    [11]

    Tang L, Tang J, Zhang W, Lu G, Zhang H, Zhang Y, Xia K, Xiao M 2019 Phys. Rev. A 99 043833Google Scholar

    [12]

    Mahmoodian S, Prindal-Nielsen K, Söllner I, Søren S, Peter L 2017 Opt. Mater. Express 7 43Google Scholar

    [13]

    Coles R, Price D, Dixon J, Royall B, Clarke E, Kok P, Skolnick M, Fox A M, Makhonin M 2016 Nat. Commun. 7 11183Google Scholar

    [14]

    Barik S, Karasahin A, Flower C, Cai T, Miyake H, DeGottardi W, Hafezi M, Waks E 2018 Science 359 666Google Scholar

    [15]

    Xiao S, Wu S Y, Xie X, Yang J N, Wei W Q, Shi S S, Song F L, Sun S B, Dang J C, Yang L L, Wang Y N, Zuo Z C, Wang T, Zhang J J, Xu X L 2021 Appl. Phys. Lett. 118 091106Google Scholar

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    Shen Y, Bradford M, Shen J T 2011 Phys. Rev. Lett. 107 173902Google Scholar

    [18]

    Yan W B, Ni W Y, Zhang J, Zhang F Y, Fan H 2018 Phys. Rev. A 98 043852Google Scholar

    [19]

    Javadi A, Söllner I, Arcari M, Hansen S L, Midolo L, Mahmoodian S, Kiršanskė G, Pregnolato T, Lee E H, Song J D, Stobbe S, Lodahl P 2015 Nat. Commun. 6 8655Google Scholar

    [20]

    Javadi A, Ding D P, Appel M H, Mahmoodian S, Löbl M C, Söllner I, Schott R, Papon C, Pregnolato T, Stobbe S, Midolo L, Schröder T, Wieck A D, Ludwig A, Warburton R, Lodahl P 2018 Nat. Nanotechnol. 13 398Google Scholar

    [21]

    Li T, Miranowicz A, Hu X, Xia K, Nori F 2018 Phys. Rev. A 97 062318Google Scholar

    [22]

    Yan C H, Li Y, Yuan H, Wei L F 2018 Phys. Rev. A 97 023821Google Scholar

    [23]

    Tang J, Xu X L 2018 Chin. Phys. B 27 027804Google Scholar

    [24]

    Kiraz A, Atatüre M, Imamoğlu A 2004 Phys. Rev. A 69 032305Google Scholar

    [25]

    Xu X, Toft I, Phillips R T, Mar J, Hammura K, Williams D A 2007 Appl. Phys. Lett. 90 061103Google Scholar

    [26]

    Sapienza L, Davanço M, Badolato A, Srinivasan K 2015 Nat. Commun. 6 7833Google Scholar

    [27]

    Senellart P, Solomon G, White A 2017 Nat. Nanotechnol. 12 1026Google Scholar

    [28]

    Imamog A, Awschalom D D, Burkard G, DiVincenzo D P, Loss D, Sherwin M, Small A 1999 Phys. Rev. Lett. 83 4204Google Scholar

    [29]

    Gao W B, Fallahi P, Togan E, Miguel-Sánchez J, Imamoglu A 2012 Nature 491 426Google Scholar

    [30]

    Warburton R J 2013 Nat. Mater. 12 483Google Scholar

    [31]

    Qian C J, Wu S Y, Song F L, Peng K, Xie X, Yang J N, Xiao S, Steer M J, Thayne I G, Tang C C, Zuo Z C, Jin K J, Gu C Z, Xu X L 2018 Phys. Rev. Lett. 120 213901Google Scholar

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    Jun L, Qiong W, Le-Man K, Hao-Sheng Z 2010 Chin. Phys. B 19 030313Google Scholar

    [34]

    Wu S Y, Peng K, Xie X, Yang J N, Xiao S, Song F L, Dang J N, Sun S B, Yang L L, Wang Y N, Shi S S, He J J, Zuo Z C, Xu X L 2020 Phys. Rev. Appl. 14 014049Google Scholar

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    Fu Y J, Lin S D, Tsai M F, Lin H, Lin C H, Chou H Y, Cheng S J, Chang W H 2010 Phys. Rev. B 81 113307Google Scholar

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    Lin T C, Li L C, Lin S D, Suen Y W, Lee C P 2011 J. Appl. Phys. 110 013522Google Scholar

    [38]

    Cao S, Tang J, Sun Y, Peng K, GaoY N, Zhao Y H, Qian C J, Sun S B, Ali H, Shao Y T, Wu S Y, Song F L, Williams D A, Sheng W D, Jin K J, Xu X L 2016 Nano Res. 9 306Google Scholar

    [39]

    Bayer M, Walck S N, Reinecke T L, Forchel A 1998 Phys. Rev. B 57 6584Google Scholar

    [40]

    Schulhauser C, Haft D, Warburton R J, Karrai K, Govorov A O, Kalameitsev A V, Chaplik A, Schoenfeld W, Garcia J M, Petroff P M 2002 Phys. Rev. B 66 193303Google Scholar

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    Glazov M M, Ivchenko E L, Krebs O, Kowalik K, Voisin P 2007 Phys. Rev. B 76 193313Google Scholar

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    Tsai M F, Lin H, Lin C H, Lin S D, Wang S Y, Lo M C, Cheng S J, Lee M C, Chang W H 2008 Phys. Rev. Lett. 101 267402Google Scholar

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Metrics
  • Abstract views:  5776
  • PDF Downloads:  107
  • Cited By: 3
Publishing process
  • Received Date:  07 October 2021
  • Accepted Date:  09 November 2021
  • Available Online:  26 January 2022
  • Published Online:  20 March 2022

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