When I hang out in nightclubs, I seem to have two discrete states with a very abrupt transition between them: an "off" state where I'm almost invisible to girls, and an "on" state where they suddenly hang on me in twos and threes.

In PUA lingo, this state is referred to as simply "state", since it's of course the state that PUAs want to be in. ;-)

PUA theorists vary as to what this "state" consists of, but they do say a few things in common about it and about how to produce it. Many have commented on this aspect you describe:

I also know that it's easier to reach the "on" state after a random girl smiles at me: it becomes a little easier to make the next random girl smile at me, and (with luck) it escalates like runaway AI

Some thinking goes along the lines that the key elements are "nonreactivity" (ie., not being concerned about what other people think of you) and "self-amusement" (i.e. doing things for your own enjoyment and amusement, rather than to achieve some particular outcome).

At the same time, the comments of many gurus suggest that they themselves do not have total or absolute control over this state: they sometimes talk about the need to get early good responses in order to get more later, just like you... but they have rituals and processes both to prime the pump in the first place, or to recover their state when it falters.

Usually, these rituals are both silly and masculine: chest thumping, jumping up and down and whooping, marching through a club with friends while chanting something nonsensical (aka "lording the club"), offering strangers high-fives, opening with ridiculous, but self-amusing lines in a deliberate attempt to invite rejection, etc.

The stated purpose of these rituals is to aid a transition to the desired state, rather than for the direct purposes of a display of confidence, but it's possible that part of the point is to convince one's self that the current environment is a safe one for confident self-expression and masculine display... in which case the smiles of females might function similarly.

I've tried a couple of these things to improve general outgoingness and sociability (or to get psyched up for writing or speaking performances), with some limited usefulness. But I have not tested any of them as a way to attract women, so your mileage may vary.