How did medieval empires manage to make loyal slave soldiers?

We heard about Safavid Ghulam, Egyptian Mamluks, Indian Habshi, and Ottoman Yeniceri: slaves forced to become soldiers and in some case were castrated. Now, while they were infamous for their tendency to revolt, the fact they were even willing to fight for their new masters with a very high degree of bravery and loyalty was impressive enough.

So, that brought us to a question: how did these states manage to make loyal soldiers out of people whom the states bought/captured? Whose family the state very likely killed/raped/etc.?