Since pretty much everything is decohered, why we can even made superpositions in the lab at all?

Question

We knew that one reason why most quantum mechanical experiments have to be done in a low temperature and isolated from environment condition is to preserve the coherence required for quantum states to be in superposition and entanglement, as the environment, via einselection, will entangle some of the states in the Hilbert space of the quantum system, turn them into pointer states and hence leaking the information about the phase relationship into the environment, making the coherence to be lost to noise, as well increases the entropy of the universe.

So, since almost every starting material we use in setting up a quantum experiment, from the photon emitters, to the magnets etc. are all perceived to be classical, when we create a superposition state in the lab (be it subjecting some atom to Rabi oscillation or some other means), are we actually introducing a new phase relationship to the observables of interests to the system thus allowing superpositions to happen, or are we somehow recovering some of the phase relationship that is leaked to the environment?

Another way to phrase this question, in creating a pure state in the lab, which starts off as very noisy and classical like described by a lot of particles in pointer states, are we actually lowering the entropy of the region where the pure state is created, and increase it elsewhere in accord to the second law of thermodynamics?

Answer 1

To get coherent states one has to set up the boundary conditions of a quantum mechanical setup, where the solution will be picked by the boundary conditions.

In the double slit experiment one electron at a time, we define the momentum of the electron impinging on the two slits, the width of each slit and the distance between them such as to be of the same order as the de Broglie wave, and lo, we get the interference pattern of the electron wave function to these boundary conditions.

The increased order in the pattern is compensated by increased disorder in the environment where the boundary conditions for the pattern are created: in the magnetic and electric fields that give the specific momentum to the electron.

Every quantum mechanical experiment is a solution of a specific wave function which is studied. Of course to set up the experiment a lot of disorder is generated, fulfilling the entropy law.