What experiment shows this?
As you know, in the classical double-slit experiment, the screen is the only detector, and launching particles even one at a time through the slits produces the interference pattern.
However, if you add a second detector in one of the slits capable of measuring if a particle passes through that slit or not, the interference pattern on the screen disappears, regardless of how many particles you send through.
This is normally taken to mean that the slit detector collapses the wave function (in Copenhagen parlance); or that one particular state of the particle becomes entangled with the initial detector, which is already entangled with the screen, to there is no more constructive interference to be seen (in Many Worlds terms).
Here is a more complete explanation:
https://phys.org/news/2011-01-which-way-detector-mystery-dou...
The delayed choice quantum eraser is a much more complex experiment.
From what I've read, the existence of "collapse" of the wave-function is not established, and not even widely accepted as more than a useful computational tool by practicing physicists.