Quasi-particles seminar

keywords: Von neumann projective measurement, weak value/weak measurement, quantum non-demolition.

$|{\psi }_0⟩\stackrel{\text{External Drive}}{\to }|{\psi }_f⟩$

Von Neumann’s scheme: there are physical observables that cannot be associated to a Hermitian Operator. Energies at $t_0$ and $t_f$ can, but not their difference

Goal

How to obtain the average value of a measurement without destroying the coherence? Idea: Couple the detector with the system:

$H_{SD}=\lambda (t)H_S(t)\otimes p$

$|{\varphi }_D⟩=\frac{|p⟩+|-p⟩}{\sqrt{2}}$

The interaction generates a phase shift $|{ϵ}_i⟩|p⟩=e^{i\lambda t}|{ϵ}_i⟩|p⟩$. This way the coupling does not change the dynamics / interference by the initial measurement