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Probing Macroscopic Quantum States with Gravitational-Wave Detectors

With state-of-the-art technologies, various types of sensors and detectors have achieved such high sensitivities that we will soon be able to probe the quantum jiggling of macroscopic objects. One notable example is the gravitational-wave (GW) detectors that sense the extremely tiny motion of the kilogram-scale test masses caused by gravitational waves. At present, a global network of GW detectors is now operating at their design sensitivities. In addition, tremendous efforts have been made in the GW community to further increase detector sensitivity. For the planned advanced detectors, the anticipated noise levels should be below the standard quantum limit. This will not only allow us to detect GWs from distant astronomical sources with high fidelity but also to shed light on investigations of quantum behavior of really macroscopic objects (~ 40 kg test masses). In previous work (see reference [1] below), we showed that the classical noise budget of advanced GW detectors allows for the creation of a nearly Heisenberg-limited quantum state of the test mass. More recently (see reference [2]), we showed that by applying an optimal measurement strategy, the same detector can also be used to probe this quantum state with accuracy below the Heisenberg limit.
In this Demonstration, we show the dependence of the accuracy on detector displacement sensitivity. The left panel is the spectral density of noise associated with displacement sensitivity for a typical advanced GW detector. The black line is the standard quantum limit of a 40 kg test mass. The orange line is the classical thermal noise caused by viscous damping. The red line is the sensing noise that quantifies the difference between the mirror center-of-mass motion and the surface motion which we actually probe. The blue curve is the total noise, which includes both classical and quantum contributions. The shaded region is the window where the classical noise goes below the standard quantum limit. Its size is crucial for both creation and detection of the macroscopic quantum state of the test mass. The right panel shows the accuracy in comparison with the Heisenberg limit. This basically gives the pixel size during the tomography process. If it is smaller than the Heisenberg limit, we will be able reconstruct the quantum state (i.e., the Wigner function) after multiple measurements of the marginal distributions of different combinations of the position and momentum (also known as quadratures).
There are three parameters you can tune: (1) the strength of the sensing noise; (2) the strength of the thermal noise; and (3) the phase squeezing factor, which is nonzero when a nonclassical squeezed light source is applied. This can significantly ease the requirement of high optical power in order to achieve a desired sensitivity at high frequencies.

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DETAILS

For more technical details, please refer to
[1] H. Mueller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, and Y. Chen, "Quantum State Preparation and Macroscopic Entanglement in Gravitational-Wave Detectors," arXiv:0903.0079, 2009.
[2] H. Miao, S. Danilishin, H. Muller-Ebhardt, H. Rehbein, K. Somiya, and Y. Chen, "Probing Macroscopic Quantum States with a Sub-Heisenberg Accuracy," arXiv:0905.3729, 2009.
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