So, first review a little bit, and then I will discuss a very crazy scheme for improving

heterosensitivity.

And then I will show that the scheme is crazy but may not be impossible.

And then I will discuss this part of the way you realize the greatest scheme using optimal

mechanics.

So this is the plan.

So I do have a plan.

So after, what we discussed is the simple, in detail, the very simple element, just a

movable mirror, and then we said if you have an input field and output field, there is

an input optimization that says that you have this kind of behavior.

So if I write in a matrix formula, it's more compact and it sort of shows you the linear

transformation into this field.

So this is in a free-to-the-way, and this is the square root of the spectrum into a

standard quantum limit.

And this kappa is given by the frequency, the power, the mass.

So this is what we said.

We discussed several aspects of it.

We said, okay, the kappa is frequency dependent.

And then if you detect this quadrature, if your input state is a vacuum, we're subject

to the standard quantum limit.

But then you can squeeze a combination of these two.

Or you can detect a combination of these two.

And then what you will find out is that the previous sensitivity with the limited by the

standard quantum limit is one over a meter squared and then constant here, like this.

If you do a frequency dependent squeezing, you will be able to just do improved sensitivity

everywhere.

If you do this detection of the back action evading quadrature, what happens is you just

cancel back action as if this is zero.

You can't cancel it out with the variable quadrature.

So in principle, you get a flat curve.

But then you can combine that with squeezing the A2 quadrature, and then you will have

the red line.

So that is the mathematical behavior here.

And then you can take this as a building block and then you can analyze more complicated

in the front end.

So this kind of situation is not good because you need a very huge optical power to reach

a sharp noise-limited sensitivity.

So what people do, in fact, Ron River came up with some of these ingredients and people

proposed that you have fiber-procabular cavities.

So you have a fiber-sensitive traveler, and then you have a so-called power-selecting

cavity here.

So the power inside this region is amplified from here.

And then you have an arm cavity, which increases the number of bounces the light travels in

the cavity.

So you will have a gain in power and you have a gain in the optical response.

So what to do with this is that you take this ingredient and then you take two more ingredients

of your field propagation.

One ingredient is you can have A and B, C and E, input field and output field coming from

here, and you use the input-output relation for the reflection and transmission.

And then that's the typical relation.