If you don’t want to install anything, try looking for locks that are targeted towards travels who want to make their hotel rooms more secure. Years back my apartment had a lock like this:

While some come with a cylinder to unlock it from the outside, it’s not necessary to use it. It can only be locked (and unlocked) from the inside when the apartment is occupied. They’re not very expensive and only require 6 or so screws to install. Maybe talk to your landlord and see if he would be willing to let you buy and install it. It’s cheap enough to leave behind when you leave.

I'm having a problem picturing how the doors are set, size of the gap etc. but Addalock worked pretty well for me when I was renting.