Function test

This is H1 title

Tested by zq on 2022/10/08.

2022/10/10: when the title contains spacebar, better use ‘-’ to connect between.

This is H2 title

Now we test in-line formula: $a^2+b^2=c^2$.

This is H3 title

Here we test math mode^[1]：

$$E = mc^2$$

This is H4 title

$\text{Does it work?} IDK.$ Outside math mode here.

Picture test

Note that in markdown file path, we use / while in html we use \.

Markdown

markdown format ![]() with spacebar in .png file name, folder contains spacebar as well.


markdown format ![]() with _ connected in .png file name, folder contains spacebar as well.


markdown format ![]() with spacebar in .png file name, folder doesn’t contain spacebar.


markdown format ![]() with _ connected in .png file name, folder doesn’t contain spacebar.

cannot zoom picture in markdown format. But we have a title under the picture.

HTML

html format <img src=" " /> with spacebar in .png file name.

hrml format <img src=" " /> with _ connected in .png file name.

always work! But no title.

Practice

Motivation

Pound-Drever-Hall (PDH) method: first used in microwave frequency stabilization, then expanded to optical field in LIGO project.

A naive idea to lock the laser is to lock the laser on the transmission signal of FP cavity.

Transmitted intensity profile for a cavity with two identical mirrors. The blue curve represents the transmission profile of a cavity without losses. Mirror losses are considered for the orange curve.

However, for photon in a high finesse cavity, the lifetime is pretty long ($\tau = \mathcal{F}L / \pi c$, ~10$\mu \mathrm{s}$), which means the transmission signal have a delay on laser frequency.^[2]

This is fatal, as any noise whose frequency is higher than $1/10\mu\mathrm{s} \sim 100\mathrm{kHz}$ cannot be cancelled.

The solution is to utilize the reflection signal.

1. alright let’s try some English instead of Chinese… 似乎并不是中文的锅=。= 似乎是$[$^1$]$后边需要有一个空格。:arrow_left:错误的，其实是因为英文冒号在markdown里有特殊含义。其他标点是可以正常work的。 ↩
2. about the 加粗问题: see https://ld246.com/article/1597581380183. ↩