动量表象中自由演化的一维高斯波包的相干性

Coherence of a freely evolving one-dimensional Gaussian wave packet in momentum representation

相干度可用于定量计算各种量子态的相干性.自由演化的高斯波包会出现"波包弥散",其相干度可能会随时间变化.不同表象中,同一个态的相干度是不同的.本文在动量表象中,应用l1-范数、量子相对熵、方差和标准差4种度量方法分别计算一维高斯波包的相干度.计算结果表明:l1-范数和量子相对熵得到的整个波包的相干度都是定值,与时间无关;方差和标准差得到的结果分别与所选维数的比值,也都趋于定值.这表明波包虽然会弥散,但其在动量表象中的相干度保持不变.因此,这4种相干度的定义都描述了量子态的整体相干度是不变的,但不能对若干子波干涉的相干度细节进行描述.

The degree of coherence can be used to quantitatively calculate the coherence of various quantum states. The freely evolving Gaussian wave packet will“wave packet dispersion”,and its degree of coherence may change with time. In different representations,the degree of coherence of the same state is different. In momentum representation,the coherence of one-dimensional Gaussian wave packet is calculated by using four measurement methods:l1-norm,quantum relative entropy,variance and standard deviation,respectively. The results show that the degree of coherence of the whole wave packet obtained by l1-norm or quantum relative entropy is constant and independent of time,and the ratio of variance or standard deviation to the selected dimension tends to a constant value. This indicates that although the wave packet will disperse,the degree of coherence in momentum representation remains unchanged. Therefore,the definitions of all these four degrees of coherence describe the overall degree of coherence of the quantum state being invariant,but cannot describe the details of the degree of coherence of some wavelet interference.