So I recently moved into a new apartment, and in the living room there is no light fixture. Instead, there is one outlet tied to a light switch, intended to plug a lamp into. However, I have two identical lamps, and in order to light the entire room I would like to position them on opposite sides of the room, without running an extension cord for the second lamp around the room. Of course I can turn on the other lamp manually, but it would be more convenient to have them both triggered by the light switch.

Is there any sort of simple attachment or system I can set up with the lamps so that when I trigger power to one, the other turns on as well? My first thought was a sort of power strip/socket plug set where if it detects that power is going to one device, it triggers the other, but I haven't been able to find any device like that so I'm not sure if it exists. Or maybe smart LED bulbs?