Can you quit your job after you have a new one?

I've been treated like crap in my current job and when you leave you have to work your two weeks notice.

I'm hoping to find a new job, once they do my phone references and I've signed the contract and everything is official, can I say to my current employer I quit?

I don't want to stay there any minute longer.

Can you quit your job after you have a new one?
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