You can get window locks installed so that the window can only open a small amount or not at all. Pull down roman shades backed in white would be great, or natural roller blinds. Plantation shutters are expensive and usually custom, so a big expense for a rental.

Agree - window locks will lock the window and not block the light like shutters would.

If you went with window locks and are concerned about the light getting into the bedroom consider cellular shades. These will also add a barrier for any sound that might project up from the room below. They are available in numerous colors and would only need to be closed for privacy.

Is there another form of egress from the room? In other words, is there a window to the outside as well in this room?