In practice how do we prepare a desired quantum state?

kof9595995

Let say we want to prepare a particular superposition state with a specified wavefunction, how can we accomplish that? I tried google but nothing useful showed up. Thanks.

arkajad

You just prepare your state with the specified wave function. You can then, if you want to, decompose it in thousands of ways as or complicated superpositions. The fact that it is a superposition is not coded in the wave function itself. It is coded in the way you want to analyze what happens.

kof9595995

Sorry I'm lost, can you elaborate more? For example I give you a lot of electrons and write you down a wavefunction, how do you make the electrons associated to the wavefunction I wrote you?

arkajad

Well, some tasks will be easy, some difficult, some impossible. It is like with stones. I give you a stone and ask you to put it at the position of Alpha Centauri. Normally, you see what is available in your lab and try to invent a laboratory procedure that will approximately realize your wave wave function, for instance by inventing a clever Hamiltonian.

But probably you wanted to formulate your question in a different way, something like that:

"Suppose I have two laboratory procedures that prepare my electrons in pure states |a> and |b> respectively. Can I use them in a clever way to prepare my electrons in |a>+|b>?"

Sometimes the answer will be easy (like in a double slit experiment), sometimes it will be impossible due to our limitations of manipulating the universe in which we live. We learn by examples. The same with gravitational fields. In general we can't prepare a gravitational field that corresponds to a given solution of Einstein field equations!