Sorry, but it can be done (if not true black then close enough) but you need to be able to apply some exposure compensation in camera and then be prepared to do a bit of work in post. Not hard once you get used to the challenge posed.
Yes - up to a point at least - it
can be done, relying heavily on post-production.
it isn't actually me who's saying that it
can't be done, I'm just standing on the shoulders of giants such as Isaac Newton (who in turn stood on the shoulders of other giants) because the laws of physics are immutable.
Like everyone else of my age, I was lucky enough to need to understand these immutable laws and to have to apply them to lighting; and then, when Photoshop arrived we used it to turn good images into outstanding ones, rather than to rescue bad ones.
Simply put, as I said earlier and as
@CharleyL also pointed out, we need to
1. Have enough distance between the front subject (the background is the rear subject which requires its own, separate lighting) so that whatever quantity of light reaches the rear subject doesn't survive to record on the camera, having been reduced in intensity by the Inverse Square Law to the point that it no longer exists in a practical sense.
2. Create precise lighting that enhances the front subject. You did a good job here, lighting from above and behind so that a minimum of light reached the rear subject, and it worked to a large extent, but by no means all subjects can be backlit in this way.
The same principle applies, of course, to white background shots. When I was doing fashion shots on transparency film I would light the white background with (usually) 4 flash heads, to get the exposure as even as possible and, using another law of physics (that the angle of reflection always equals the angle of incidence) I would be sure that no light reflected directly onto the rear of the subject. But the minimum space needed was 3 metres (but 4 was much better) and I refused any job where less space was available. This was necessary with film because there was no choice, with no editing possible. And, when we moved to digital we carried on just the same. The reasons for this were:
1. The slides would be viewed by the client on a(n actual) lightbox and the clients expected the background to be white, it wasn't good enough to say "Well, when you choose the shots you want we'll make the background white"
2. With hundreds or thousands of shots it simply wasn't viable to get the backgrounds white in PP, especially as the models had hair . . .
I repeat. Light tents were brought to market because they sold - extremely well - to people who believed that the over-processed images shown in their eBay listings could actually be created in camera, and that the light tent would solve all of the buyers lighting problems. And then the LED light cubes replaced them, but they are even worse than the light tents, but even easier for the user.
But, if you actually enjoy spending a lot of time on PP, then that's fine.