量子点—微腔耦合系统激发和输运特性研究
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摘要
量子点-微腔耦合结构广泛应用于集成光学器件中,例如单量子点激光器和单光子源等。研究这种结构的重点是处理光与物质的相互作用。而基于光场量子化的主方程技术是处理微纳米尺度光与物质相互作用的一个有力工具。本论文运用主方程技术研究了量子点-光学微腔耦合结构中光与物质的相互作用：通过构造不同的结构参数,分析了浅束缚势量子点-微腔结构获得激射的条件；研究了深束缚势量子点-微腔在非共振情况下的激发特性,发现利用失谐可以获得低阈值激发；引入波导结构,研究了整个耦合结构的光子输运特性。
本论文的主要研究工作概述如下：
1.利用激光模型模拟了浅束缚势量子点-微腔耦合结构的激发特性。研究了激发特性与微腔损耗速率、微腔非相干泵浦速率和激子激发速率的变化关系。计算结果显示在微腔非相干泵浦速率较小时,整个系统比较容易获得激光发射。在直接求解主方程的基础上,推导出了自发辐射、受激辐射和吸收与密度矩阵元素的关系。探讨了三种激光阈值定义随着量子点-微腔相互作用强度和微腔损耗速率的变化关系。
2.建立了量子点与光子耦合谐振器结合的模型,利用双腔之间的光子阻碍效应取得了单光子发射(g(2)(0)在10-2量级)。分析了结构参数对单光子特性的影响。研究发现两个腔模频率不相等时,二阶关联函数比较靠近0。计算表明与量子点耦合的微腔损耗速率对单光子发射有显著影响。
3.基于双电子多构型量子点模型,提出了非共振深束缚势量子点-微腔耦合结构模型。利用量子点激发能级和腔模之间的失谐来补偿双激子跃迁所导致的能量移动。研究了量子点-腔模之间失谐对激发特性的影响。研究发现,失谐因子大小直接影响激光产生。当失谐为4.36meV时激光阈值取得最小值Pth=0.197/ps(比共振时的激光阈值大概小10倍)。此时交换能完全被失谐抵消,相当于修饰的量子点-微腔共振的情况。由于载流子的捕获机制和s激子-p激子之间可以忽略的能级间距,提出了在深束缚势量子点-光学微腔模型中采用s激子-p激子同时激发的泵浦方式。通过对比三种不同激发方式(s激子泵浦、p激子泵浦、s激子-p激子泵浦)下量子点-微腔系统发射特性的不同,发现在s激子-p激子激发机制下量子点-微腔系统提前进入激射和自淬灭区域,与实验比较吻合。
4.基于单模微腔-波导耦合结构输入-输出关系理论,推导了双量子点-微腔-波导耦合结构的输入-输出关系。在不同量子点-微腔相互作用强度情况下,探讨了耦合结构在波导弱激发和强激发下的光子输运特性。在弱激发条件下,透射谱波谷位于√g12+g22,并随着第二个量子点与微腔相互作用增强而向外移动。强激发情况下,共振位置透过率受到量子点-微腔耦合因子调制。
5.推导了双腔-量子点-波导结构输入-输出关系。基于格林函数理论,解析地定义了微腔和波导之间的耦合速率。通过腔场和量子点下降算符的运动方程,求解出透射谱的解析形式。研究了在双腔共振、非共振情形下透射谱与双腔之间相位的关系。计算发现：双腔共振时透射谱出现单峰结构；双腔非共振情况下透射谱呈现三峰结构,次峰强度紧密依赖于双腔距离,在传感上有潜在应用。这种处理方法可以用来研究单模波导与两个相互作用微腔耦合结构的光子输运特性。
本论文的主要创新点包括：
1.建立了浅量子点-微腔耦合结构激光模型,研究了结构参数对激发特性的影响。找到了一种数值求解自发辐射、受激辐射和吸收的方法。基于偶极子近似和马尔科夫近似,通过数值求解主方程就可以得到跃迁速率,并不需要其它额外近似。
2.基于量子点-光子耦合谐振器结构,分析了结构参数对单光子特性的影响。利用双腔之间的光子阻碍效应获得了单光子发射,二阶关联函数在10-2量级。
3.建立了非共振深束缚势量子点-微腔耦合结构模型。利用量子点激发能级和腔模之间失谐来补偿双激子跃迁所导致的能量移动,实现了较低阈值激发。提出引入s激子激发的必要性。通过对比不同激发方式下系统发射特性的不同,发现在s激子-p激子激发机制下系统提前进入激发区域和自淬灭区域。
4.建立了不同结构输入-输出关系理论,比如双量子点-微腔-波导结构、双腔-量子点-波导系统等。在格林函数理论基础上,解析定义了微腔和波导之间的耦合速率。研究了这两种结构的光子输运特性。对于双量子点结构,波导弱激发时量子点-微腔耦合因子会引起透射谱峰谷的明显位移,波导强激发时共振位置透过率受到量子点-微腔耦合因子调制。对于双腔结构,双腔共振时透射谱出现单峰结构,双腔非共振情况下透射谱呈现三峰结构,次峰强度紧密依赖于双腔距离。
Quantum dot-microcavity system has extensive application in integrated optical device, such as single quantum dot laser and single photon source. How to handle the interaction between light and matter in this structure is crucial. To address it, one usually has recourse to the master equation technique, which bases on the quantization of light field. The research work within this dissertation uses this technique to investigate the interaction between light and matter in coupled quantum dot-cavity system. Through analyzing structural parameters, single exciton emission and single photon emission is obtained in the quantum dot-cavity system with shallow confinement potential. Lasing properties of a non-resonant quantum dot-cavity system with deep confinement poten-tial is investigated and a low laser threshold is achieved. Moreover, we study the photon transport of quantum dot-cavity system coupled with waveguide.
The main research works are as follows:
1. Based on the laser model, we investigate the lasing properties of quantum dot-cavity system with shallow confinement potential. The dependence of lasing on cavity decay rate, cavity pump rate and exciton pump rate is amply investigated. The calculation reveals that the whole system achieves lasing easier when the cavity pump rate is smaller. By directly solving the master equation, we derive the spontaneous emission rate, stimulated emission and absorption rate from the density matrix elements. The difference between three different definitions of lasing threshold is investigated by varying coupling rate and cavity decay rate.
2. We propose a structure with a quantum dot integrated with coupled photonic res-onators to investigate single photon emission. Due to photon blockade effect be-tween the coupled photonic resonators, single photon emission is generated with second order correlation on the magnitude of10-2. The effect of structural param- eters on single photon emission is studied. It reveals that, the coupled photonic resonators detune with the excitation frequency asymmetrically, second order cor-relation is more close to0. In addition, the calculation reveals that the decay rate of the cavity coupled with quantum dot has a drastic influence on single photon emission.
3. Based on the two electrons multi-configuration quantum dot model, we propose a non-resonant quantum dot-cavity model. The detuning between s-exciton and cavity in some way offsets the energy loss caused by the biexciton transition. The influence of detuning on lasing is detailedly investigated. The result reveals that the detuning directly influences the generation of lasing. When the detuning is4.36meV, the laser threshold achieves its optimum Pth=0.197/ps. At this time, the effect of exchange energy is totally offset by the detuning, where the dressed quantum dot is resonant with the cavity. Due to the capture mechanism and the negligible energy space of s and p-exciton, s-exciton pump is introduced. Through comparing the three different excitations, the whole system goes into the lasing and self-quenching regime in advance under s-and p-exciton pump, which fits the experiment better.
4. Based on the Input-output theory of coupled cavity-waveguide system, we de-rive the Input-output relation of different structures, such as two quantum dots-cavity system coupled with waveguide. By gradually increased coupling strength, the photon transport is investigated under weak and strong excitation. For weak excitation case, the dips of the transmission appear at the position of√g12+g22which shifts outward with increased coupling rate. At strong excitation, the on-resonance transmissivity is modulated by the quantum dot-cavity coupling rate.
5. We derive the Input-output relation of cavities-quantum dot-waveguide system. By means of the Green's function, the coupling rate between cavity and waveg-uide is analytically defined. With the aid of Heisenberg equation of system op-erators, the analytic transmission is derived under weak excitation limit. The dependence of transmission on the distance and detuning between two cavities is studied. The results reveal that, the transmission is singlet when the left cav-ity resonant with right cavity, and the transmission behaves three-peak structure when the left cavity detuned with right cavity. This method can be applied to treat coupled photonic resonators.
Highlights of the dissertation are in the following:
1. We establish a laser model for two level quantum dot-cavity system and study the influence of system parameters on lasing. By directly solving the master equa-tion, we relate the spontaneous emission rate, stimulated emission and absorp-tion rate with the density matrix elements. On the basis of dipole approximation and Markov approximation, this derivation doesn't need addition approximation-s. Through violently solving the master equation, we can get the three emission rates. Using the two level quantum dot-cavity system, we comparing the three definitions of lasing threshold.
2. A structure with quantum dot-cavity coupled with another single mode microcav-ity is designed. We systematically investigate the influence of the relative param-eters on the single photon emission. Using the photon blockade effect between two cavities, the system behaves better single photon emission.
3. A non-resonant quantum dot-cavity system is established. By compensating for the energy loss of biexciton transition with the detuning between s-exciton and cavity, a lower laser threshold is achieved. Furthermore, s-exciton pump is intro-duced. By investigating the emission properties under different excitation mech-anism, we find that the system goes into lasing and self-quenching regime in ad-vance under s-and p-exciton pump.
4. Based on the Input-output theory of coupled cavity-waveguide system, we derive the Input-output relation of different structures, such as two quantum dots-cavity-waveguide system and two cavities-quantum dots-waveguide system. By means of the Green's function, the coupling rate between cavity and waveguide is an-alytically defined. The photon transport is investigated in detail using different parameters. For the two quantum dots case, the dip of transmission is shifted outward with increased quantum dot-cavity coupling rate at weak excitation, at strong pump the on-resonance transmission is modulated by quantum dot-cavity coupling rate. While for two cavities, the transmission is singlet when the left cav-ity resonant with right cavity, and the transmission behaves three-peak structure when the left cavity detuned with right cavity.
本论文的主要研究工作概述如下：
1.利用激光模型模拟了浅束缚势量子点-微腔耦合结构的激发特性。研究了激发特性与微腔损耗速率、微腔非相干泵浦速率和激子激发速率的变化关系。计算结果显示在微腔非相干泵浦速率较小时,整个系统比较容易获得激光发射。在直接求解主方程的基础上,推导出了自发辐射、受激辐射和吸收与密度矩阵元素的关系。探讨了三种激光阈值定义随着量子点-微腔相互作用强度和微腔损耗速率的变化关系。
2.建立了量子点与光子耦合谐振器结合的模型,利用双腔之间的光子阻碍效应取得了单光子发射(g(2)(0)在10-2量级)。分析了结构参数对单光子特性的影响。研究发现两个腔模频率不相等时,二阶关联函数比较靠近0。计算表明与量子点耦合的微腔损耗速率对单光子发射有显著影响。
3.基于双电子多构型量子点模型,提出了非共振深束缚势量子点-微腔耦合结构模型。利用量子点激发能级和腔模之间的失谐来补偿双激子跃迁所导致的能量移动。研究了量子点-腔模之间失谐对激发特性的影响。研究发现,失谐因子大小直接影响激光产生。当失谐为4.36meV时激光阈值取得最小值Pth=0.197/ps(比共振时的激光阈值大概小10倍)。此时交换能完全被失谐抵消,相当于修饰的量子点-微腔共振的情况。由于载流子的捕获机制和s激子-p激子之间可以忽略的能级间距,提出了在深束缚势量子点-光学微腔模型中采用s激子-p激子同时激发的泵浦方式。通过对比三种不同激发方式(s激子泵浦、p激子泵浦、s激子-p激子泵浦)下量子点-微腔系统发射特性的不同,发现在s激子-p激子激发机制下量子点-微腔系统提前进入激射和自淬灭区域,与实验比较吻合。
4.基于单模微腔-波导耦合结构输入-输出关系理论,推导了双量子点-微腔-波导耦合结构的输入-输出关系。在不同量子点-微腔相互作用强度情况下,探讨了耦合结构在波导弱激发和强激发下的光子输运特性。在弱激发条件下,透射谱波谷位于√g12+g22,并随着第二个量子点与微腔相互作用增强而向外移动。强激发情况下,共振位置透过率受到量子点-微腔耦合因子调制。
5.推导了双腔-量子点-波导结构输入-输出关系。基于格林函数理论,解析地定义了微腔和波导之间的耦合速率。通过腔场和量子点下降算符的运动方程,求解出透射谱的解析形式。研究了在双腔共振、非共振情形下透射谱与双腔之间相位的关系。计算发现：双腔共振时透射谱出现单峰结构；双腔非共振情况下透射谱呈现三峰结构,次峰强度紧密依赖于双腔距离,在传感上有潜在应用。这种处理方法可以用来研究单模波导与两个相互作用微腔耦合结构的光子输运特性。
本论文的主要创新点包括：
1.建立了浅量子点-微腔耦合结构激光模型,研究了结构参数对激发特性的影响。找到了一种数值求解自发辐射、受激辐射和吸收的方法。基于偶极子近似和马尔科夫近似,通过数值求解主方程就可以得到跃迁速率,并不需要其它额外近似。
2.基于量子点-光子耦合谐振器结构,分析了结构参数对单光子特性的影响。利用双腔之间的光子阻碍效应获得了单光子发射,二阶关联函数在10-2量级。
3.建立了非共振深束缚势量子点-微腔耦合结构模型。利用量子点激发能级和腔模之间失谐来补偿双激子跃迁所导致的能量移动,实现了较低阈值激发。提出引入s激子激发的必要性。通过对比不同激发方式下系统发射特性的不同,发现在s激子-p激子激发机制下系统提前进入激发区域和自淬灭区域。
4.建立了不同结构输入-输出关系理论,比如双量子点-微腔-波导结构、双腔-量子点-波导系统等。在格林函数理论基础上,解析定义了微腔和波导之间的耦合速率。研究了这两种结构的光子输运特性。对于双量子点结构,波导弱激发时量子点-微腔耦合因子会引起透射谱峰谷的明显位移,波导强激发时共振位置透过率受到量子点-微腔耦合因子调制。对于双腔结构,双腔共振时透射谱出现单峰结构,双腔非共振情况下透射谱呈现三峰结构,次峰强度紧密依赖于双腔距离。
Quantum dot-microcavity system has extensive application in integrated optical device, such as single quantum dot laser and single photon source. How to handle the interaction between light and matter in this structure is crucial. To address it, one usually has recourse to the master equation technique, which bases on the quantization of light field. The research work within this dissertation uses this technique to investigate the interaction between light and matter in coupled quantum dot-cavity system. Through analyzing structural parameters, single exciton emission and single photon emission is obtained in the quantum dot-cavity system with shallow confinement potential. Lasing properties of a non-resonant quantum dot-cavity system with deep confinement poten-tial is investigated and a low laser threshold is achieved. Moreover, we study the photon transport of quantum dot-cavity system coupled with waveguide.
The main research works are as follows:
1. Based on the laser model, we investigate the lasing properties of quantum dot-cavity system with shallow confinement potential. The dependence of lasing on cavity decay rate, cavity pump rate and exciton pump rate is amply investigated. The calculation reveals that the whole system achieves lasing easier when the cavity pump rate is smaller. By directly solving the master equation, we derive the spontaneous emission rate, stimulated emission and absorption rate from the density matrix elements. The difference between three different definitions of lasing threshold is investigated by varying coupling rate and cavity decay rate.
2. We propose a structure with a quantum dot integrated with coupled photonic res-onators to investigate single photon emission. Due to photon blockade effect be-tween the coupled photonic resonators, single photon emission is generated with second order correlation on the magnitude of10-2. The effect of structural param- eters on single photon emission is studied. It reveals that, the coupled photonic resonators detune with the excitation frequency asymmetrically, second order cor-relation is more close to0. In addition, the calculation reveals that the decay rate of the cavity coupled with quantum dot has a drastic influence on single photon emission.
3. Based on the two electrons multi-configuration quantum dot model, we propose a non-resonant quantum dot-cavity model. The detuning between s-exciton and cavity in some way offsets the energy loss caused by the biexciton transition. The influence of detuning on lasing is detailedly investigated. The result reveals that the detuning directly influences the generation of lasing. When the detuning is4.36meV, the laser threshold achieves its optimum Pth=0.197/ps. At this time, the effect of exchange energy is totally offset by the detuning, where the dressed quantum dot is resonant with the cavity. Due to the capture mechanism and the negligible energy space of s and p-exciton, s-exciton pump is introduced. Through comparing the three different excitations, the whole system goes into the lasing and self-quenching regime in advance under s-and p-exciton pump, which fits the experiment better.
4. Based on the Input-output theory of coupled cavity-waveguide system, we de-rive the Input-output relation of different structures, such as two quantum dots-cavity system coupled with waveguide. By gradually increased coupling strength, the photon transport is investigated under weak and strong excitation. For weak excitation case, the dips of the transmission appear at the position of√g12+g22which shifts outward with increased coupling rate. At strong excitation, the on-resonance transmissivity is modulated by the quantum dot-cavity coupling rate.
5. We derive the Input-output relation of cavities-quantum dot-waveguide system. By means of the Green's function, the coupling rate between cavity and waveg-uide is analytically defined. With the aid of Heisenberg equation of system op-erators, the analytic transmission is derived under weak excitation limit. The dependence of transmission on the distance and detuning between two cavities is studied. The results reveal that, the transmission is singlet when the left cav-ity resonant with right cavity, and the transmission behaves three-peak structure when the left cavity detuned with right cavity. This method can be applied to treat coupled photonic resonators.
Highlights of the dissertation are in the following:
1. We establish a laser model for two level quantum dot-cavity system and study the influence of system parameters on lasing. By directly solving the master equa-tion, we relate the spontaneous emission rate, stimulated emission and absorp-tion rate with the density matrix elements. On the basis of dipole approximation and Markov approximation, this derivation doesn't need addition approximation-s. Through violently solving the master equation, we can get the three emission rates. Using the two level quantum dot-cavity system, we comparing the three definitions of lasing threshold.
2. A structure with quantum dot-cavity coupled with another single mode microcav-ity is designed. We systematically investigate the influence of the relative param-eters on the single photon emission. Using the photon blockade effect between two cavities, the system behaves better single photon emission.
3. A non-resonant quantum dot-cavity system is established. By compensating for the energy loss of biexciton transition with the detuning between s-exciton and cavity, a lower laser threshold is achieved. Furthermore, s-exciton pump is intro-duced. By investigating the emission properties under different excitation mech-anism, we find that the system goes into lasing and self-quenching regime in ad-vance under s-and p-exciton pump.
4. Based on the Input-output theory of coupled cavity-waveguide system, we derive the Input-output relation of different structures, such as two quantum dots-cavity-waveguide system and two cavities-quantum dots-waveguide system. By means of the Green's function, the coupling rate between cavity and waveguide is an-alytically defined. The photon transport is investigated in detail using different parameters. For the two quantum dots case, the dip of transmission is shifted outward with increased quantum dot-cavity coupling rate at weak excitation, at strong pump the on-resonance transmission is modulated by quantum dot-cavity coupling rate. While for two cavities, the transmission is singlet when the left cav-ity resonant with right cavity, and the transmission behaves three-peak structure when the left cavity detuned with right cavity.
引文
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