You’ll automatically receive the Ether Lift Research scenario quest in Xenoblade Chronicles 3 Future Redeemed during Chapter 4. For this quest, head into Riku’s workshop to trigger a cutscene. Afterwards, make your way over to the Pioneer’s Camp rest spot in the Aurora Shelf. Once there, construct the Ether Slide to reach the cave across the way.
You’ll need Noise Bite x2, Black Shard x1 and Ether Cylinder x2 to construct the slide. After it’s been constructed, go ahead and slide on across. Once on the other side, a cutscene will trigger during which Rex will clear the entrance to the Sealed Cave. Make your way through this cave in search of the Photonium. One can be found down a ladder near a bunch of Igna.
The second one can be found on the far western side of the cave just past a Fog Rift.
The last Photonium can be found protected by the Level 37 Fograptor D’nari unique enemy.
Once you collect all the Photonium, the quest will complete. As a reward, you’ll receive 1880 EXP, 2980 Gold, Quantum Scarf and Platinum Belt.