I matched pictures online with my pom-poms. I decided that they are annual peony poppies. Whether the name is correct or not, they are annuals. They usually have one flower at a time on a tall (2-3 ft) stem. I've had some with successive blooms. They'll probably look best in groups.

Thanks!
A friend of mine has double red ones and I wondered if they would look like those. They come up every year but I am sure they just reseed themselves. They sound like what you have mentioned.