【量子光学】 Quantum Optics 2 Quiz 2.4(3)

Quantum Optics 2课程第三次测验

第1题 (不定项选择)

We consider a beam splitter with a quasi-classical wave-packet at the input 1 and vacuum at input 2. Each mode of the wave-packet is characterized by a complex number $\alpha_\ell$.
Using the formalism of the multimode creation operators $\hat{a}^\dagger_{multi}$, you can establish the expression of the complex number $\alpha_{3,multi}$ associated to the multimode radiation in the output 3. Select the right answer(s):

A) $\left|\alpha_{3,multi}\right|^2=r\left\langle N\right\rangle$

B) $\left|\alpha_{3,multi}\right|^2=r^2\left\langle N\right\rangle$

C) $\left|\alpha_{3,multi}\right|^2=r^2\Sigma_\ell\left|\alpha_\ell\right|^2$

D) $\left|\alpha_{3,multi}\right|^2=r\left|\alpha_{1,multi}\right|^2$

第2题 (不定项选择)

Based on the expression of $\alpha_{3,multi}$, express the probability distribution of photon number in the output 3. It is equal to:

A) $P(n_{3,multi})=e^{-r\left\langle N\right\rangle}\frac{\left(r\left\langle N\right\rangle\right)^{n_{3,multi}}}{n_{3,multi}!}$

B) $P(n_{3,multi})=e^{-r^2\left\langle N\right\rangle}\frac{\left(r^2\left\langle N\right\rangle\right)^{n_{3,multi}}}{n_{3,multi}!}$

C) $P(n_{3,multi})=e^{-r\left\langle N\right\rangle}\frac{\left(r\left\langle N\right\rangle\right)^{n_{3,multi}}}{\sqrt{n_{3,multi}!}}$

D) $P(n_{3,multi})=e^{-r^2\left\langle N\right\rangle}\frac{\left(r^2\left\langle N\right\rangle\right)^{n_{3,multi}}}{\sqrt{n_{3,multi}!}}$

第3题 (单选)

What type of distribution is it?

A) A Gaussian distribution.

B) A Poisson distribution.

C) An unknown distribution.

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