You can go to the dinner for the weekend lunch back.

So please say what you want for this weekend before tonight.

Otherwise, it will just be a lunch back for lunch and dinner.

OK?

Good.

So I wanted to quickly recount a story I told you

in the last lecture about thinking about what

we call the full quantum limit on continuous weak position

protection.

Connect that to some of the things

that I told you about and the way

we apply this kind of general formalism

to just a simple, driven, auto-mechanical pattern.

And then hopefully, I want to quickly go on

to something that's a little bit going

beyond this full quantum limit, a different kind of back

action evasion.

It's a way of measuring something

about a mechanical resonator that isn't limited by back

action at all.

And if you could do this kind of back action evasion,

it's different from the kind of back action evasion

that Jan Beethoven told us about.

If you could do this kind of back action evasion,

you could use the measure to prepare a quantum state

of the mechanics.

You could use the measurement to produce a quantum squeeze

state of mechanical motion.

So I'll try to give you an idea of how that comes about.

And also, some of the technical formalism

we need to use to describe that kind of process.

And that's the whole idea of conditional master equations.

So those will be ambitious goals.

We'll see how far he gets in the next half.

OK, so quick recap.

Here's our auto-mechanical cavities.

The position couples to the number

of photons in the cavity, very generally the number of photons

that some detector quantity f.

That's how the detector or cavity

works without the motion.

And then what do we do?

We're driving the cavity.

We're going to look at the output electron

cavity, in particular, one quadrature

is going to know about the motion of the mechanics.

Let's call that quadrature i and get it for a generic detector.

That's the detector quantity that we actually

look at to learn something about the mechanical motion.

So if I think about the total fluctuations