How to understand vacuum squeezing in quantum optics?

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The part that's easy to understand is that amplitude and phase are non-commuting so the more precise you are on one, the more uncertainty in the other.

But how, in an application like LIGO, are the amplitude and phase uncertainties controlled?

I have looked for explanations and found partial ones that raise more questions. One question is how a frequency-halving crystal results in changes to uncertainty levels. The other is related to what sound like claims that it's the vacuum itself that is getting squeezed, and if I'm guessing right, that there's a beam of squeezed vacuum with no photons?

So clearly this is one of the quantum things impossible to understand with classical analogies.

What is a way to think about how LIGO light squeezing is implemented that makes sense, as much as anything quantum makes sense?

For a bonus, is there a way to understand how their "filter cavities" produce different squeezing for different gravitational wave frequencies?