用量子随机演算构造共振荧光Davies过程
Constructing the Davies process of Resonance Fluorescence with Quantum Stochastic Calculus
摘要：
起点是给定的2乘2矩阵上的完全正映射半群。这个半群描述了衰变二能级原子的不可逆演化。利用量子随机微积分的积分和核方法，我们将二能级原子耦合到一个环境中，在我们的情况下，该环境将被解释为电磁场。二能级原子的不可逆时间演化则源于原子和场的可逆时间演化。从数学上讲，我们构造了半群的马尔可夫膨胀。下一步是用激光驱动原子，并计算衰变的二能级原子发射到场中的光子数。对于每一个可能的光子计数序列，我们构造一个映射，给出由该序列推断的2能级原子的时间演化。我们用这种方法得到的映射族形成了所谓的戴维斯过程。戴维斯在他的书中描述了这些过程的结构，这将我们带入了量子轨道领域。在我们的模型中，我们计算跳跃运算符，并简要描述由此产生的计数过程。
英文摘要：
Starting point is a given semigroup of completely positive maps on the 2 times 2 matrices. This semigroup describes the irreversible evolution of a decaying 2-level atom. Using the integral-sum kernel approach to quantum stochastic calculus we couple the 2-level atom to an environment, which in our case will be interpreted as the electromagnetic field. The irreversible time evolution of the 2-level atom then stems from the reversible time evolution of atom and field together. Mathematically speaking, we have constructed a Markov dilation of the semigroup. The next step is to drive the atom by a laser and to count the photons emitted into the field by the decaying 2-level atom. For every possible sequence of photon counts we construct a map that gives the time evolution of the 2-level atom inferred by that sequence. The family of maps that we obtain in this way forms a so-called Davies process. In his book Davies describes the structure of these processes, which brings us into the field of quantum trajectories. Within our model we calculate the jump operators and we briefly describe the resulting counting process.
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