Subject + 睡着 + 了
The compound verb 睡着 (shuìzháo) means 'to fall asleep' and combines the verb 睡 (to sleep) with the resultative complement 着 (to achieve/succeed). It indicates that the action of sleeping has been successfully achieved, distinguishing it from merely trying to sleep.
孩子刚睡着,我们说话小声一点。
Háizi gāng shuìzháo, wǒmen shuōhuà xiǎo shēng yìdiǎn.
The child just fell asleep — let's keep our voices down.
昨晚我一躺下就睡着了。
Zuówǎn wǒ yī tǎng xià jiù shuìzháo le.
Last night I fell asleep as soon as I lay down.
他太累了,坐在沙发上就睡着了。
Tā tài lèi le, zuò zài shāfā shàng jiù shuìzháo le.
He was so tired that he fell asleep sitting on the sofa.