I hope I can explain these steps clearly enough.
STEP 1
On the Red layer, press Ctrl L to open the Levels dialog. Because it's the "Red" layer, we're going to leave the red channel untouched, and only adjust the green and blue channels. So go to the green channel first, and drag the white Output slider all the way to the left:
Then go to Blue, and also drag that white Output slider all the way to the left.
This will result in the whole photo looking red and black. Press OK.
Then change that layer's blend mode to "Screen".
STEP 2
Now go to the Green layer. Again, press Ctrl L to open the Levels dialog. This time we're leaving the green channel alone. Move the white Output slider all the way to the left on both the red and blue channels. Press OK, then change that layer to "Screen" blend mode as well.
STEP 3
Now go to the Blue layer and press Ctrl L. Move the white Output slider on the red and green channels (and leave blue alone). Press OK. For this one, don't change the layer blend mode to Screen, but leave it on Normal.
STEP 4
Now you should be able to move the top two layers to create your effect.
Let me know how you go.