Upstairs in the data center, there is a Memory Transference Station. Interact with it and you will be able to pick up one of four Essence Traps. To use an essence trap, throw it down in the same way you would C4, and once an enemy walks over it, you can attempt to capture them by double-tapping the interact button. Enemies must be at a very low level of health to be captured, and after capture, you will have a limited time to insert them into the Memory Transference Station before the trap is destroyed.
You will need to capture three specific Mimics on the map that will give the correct memories. These Mimics must spawn from fake loot on the ground, and typically spawn in Dr. Peck's quarters near spawn, outside the weapons lab and garage, and above Mission Control. You will know you have captured the correct Mimic when Weaver tells you you have the done so after inserting the trap into the Memory Station.
Note: Only one correct Mimic will spawn per round.