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Design and Sensitivity



Hannover 10m interferometer for the sub-SQL measurement



Baseline: 10m

Laser wavelength: 1064nm (IR)

Test mass weight: 100g


What is the purpose of the experiment?

We are going to measure the position of a mirror with extremely high precision. Quantum Mechanics tells us that there is a limit in the measurement accuracy, which is called Standard Quantum Limit (SQL).

Nobody has seen this limit in the human history yet. We would like to see this.


Why is it important to see the SQL?

Unlike a photon or an electron, a macroscopic object like each one of us is regarded as a classical object. The macroscopic object has been exposed in the messy environment and has lost the quantum property. However, if we can do the measurement with the precision at the level of the SQL, it will recover the quantum property. We will then be able to see the quantum behavior of the macroscopic object and may find out a fundamental difference of the quantum world and the classical world.


Another motivation is the development of so-called Quantum Non-demolition techniques (QND)

. The SQL is indeed a limit for "standard" measurement. There have been number of ideas to overcome the limit. Once the sensitivity of the 10 m reaches the SQL, we can experimentally demonstrate these ideas. Some of the QND techniques will be implemented in gravitational-wave detectors to improve the sensitivity in the near future, so our experiment will play an important role as their R&D.


Is it possible to see the SQL?

Yes, indeed. As is shown in the figure below, we will see the SQL more than a factor of 3 above the classical-noise level at the 10-m experiment. Note that the SQL is the envelope of the crossing point of shot noise (red curve, flat region) and quantum radiation pressure noise (red curve, f^-2 region). We will change the input power and will see this point follows the SQL.




What are the limiting classical-noise sources?

There are three limiting noise sources in the current design.


(i) Thermal fluctuation of the wire to suspend the mass (orange solid curve in the figure). This noise increases faster than the SQL as the mass becomes lighter. The mass is set near the optimal so that we can see the SQL above other noise but suspension thermal noise does not limit the sensitivity.


(ii) Thermal fluctuation of the coating on the mirror (green solid curve in the figure). This noise decreases as the beam radius on the mirror increases. We set the beam radius as large as possible with the following issues taken into account; first, the diffraction loss should be less than a few ppm (1 ppm = 1e-6), and second, the surface inaccuracy would not cause the cavity instability. We also use a trick to reduce coating thermal noise, which we shall explain in the next paragraph.


(iii) Radiation pressure noise by the intensity fluctuation of the laser (blue dotted curve in the figure). Laser intensity is stabilized to the shot-noise level of 100-mW light (limited by the acceptable power on one photo-detector). This is larger than the vacuum fluctuation that causes quantum radiation pressure. However, classical radiation pressure noise appears as the common-mode motion of the interferometer, while we are interested in the differential motion, so it will be suppressed by a so-called common-mode-rejection (CMR) factor and will be smaller than the SQL.


So, what's the trick to reduce coating thermal noise?




The interferometer is based on the Michelson interferometer with a Fabry-Perot cavity in each arm; this is a typical configuration of a gravitational-wave detector. The Michelson interferometer is locked in such a way that the entire laser light goes back toward the light source with the common-mode signal and the differential signal comes to the other port. The arm cavity is locked to resonate the laser light, accumulating the power inside. In addition, we replace the end test mass of the arm cavity to another cavity, and this is the trick to reduce coating thermal noise.


While the reflectivity of an input test mass is about 99%, the reflectivity of the end test mass should be nearly 100%. It means that we need thicker coatings on the end test mass. Coating thermal noise is proportional to the square-root of the thickness of the coatings. In order to decrease coating thermal noise, we should reduce the thickness of the coatings on the end test mass, but we want to keep the power inside the arm cavity as high. So we reduce the coatings and compensate the reduction of the reflectivity by adding one more mirror after the end test mass. In other words, we replace the end test mass to a pair of mirrors that are locked anti-resonant. Noise of the end-end test mass is not sensed as much as the input-end test mass because there is not much light coming through the anti-resonant cavity.


This helps to reduce the thickness of the end test mass even lower than that of the input test mass. We could also replace the input test mass to another anti-resonant cavity. It is still an option, but it will increase the complexity of the system.



Please refer the following papers if you want to know more about the research.


* H.J.Kimble et al, Phys. Rev. D

, 65, 022002 (2002)

This paper is very well written and is good to learn the SQL and QND.


* H.Mueller-Ebhardt et al, quant-ph

, 0903.0079

This paper explains how we can prepare the quantum state of a macroscopic object by measurement.


* F.Y.Khalili, Phys. Lett. A

, 334, 67 (2005)

The author of this paper invented the idea of replacing the end test mass to an anti-resonant cavity and this paper explains the idea.





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