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Partially coherent electron transport in terahertz quantum cascade lasers based on a Markovian master equation for the density matrix

机译:基于密度矩阵的马尔可夫主方程的太赫兹量子级联激光器中的部分相干电子传输

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We derive a Markovian master equation for the single-electron density matrix, applicable to quantum cascade lasers (QCLs). The equation conserves the positivity of the density matrix, includes off-diagonal elements (coherences) as well as in-plane dynamics, and accounts for electron scattering with phonons and impurities. We use the model to simulate a terahertz-frequency QCL, and compare the results with both experiment and simulation via nonequilibrium Green's functions (NEGF). We obtain very good agreement with both experiment and NEGF when the QCL is biased for optimal lasing. For the considered device, we show that the magnitude of coherences can be a significant fraction of the diagonal matrix elements, which demonstrates their importance when describing THz QCLs. We show that the in-plane energy distribution can deviate far from a heated Maxwellian distribution, which suggests that the assumption of thermalized subbands in simplified density-matrix models is inadequate. We also show that the current density and subband occupations relax toward their steady-state values on very different time scales.
机译:我们推导了适用于量子级联激光器(QCL)的单电子密度矩阵的Markovian主方程。该方程式保留了密度矩阵的正性,包括非对角元素(相干)以及平面内动力学,并解释了声子和杂质对电子的散射。我们使用该模型来模拟太赫兹频率QCL,并通过非平衡格林函数(NEGF)将结果与实验和仿真进行比较。当QCL偏向最佳激光时,我们与实验和NEGF都获得了很好的一致性。对于考虑的设备,我们表明相干性的大小可能是对角矩阵元素的很大一部分,这说明了它们在描述THz QCL时的重要性。我们显示面内能量分布可能偏离加热的麦克斯韦分布,这表明简化密度矩阵模型中热化子带的假设是不充分的。我们还表明,电流密度和子带占用在非常不同的时标上朝着其稳态值松弛。

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