2017/11/10 by Kouji Nakamura, Nakamura, Kouji, Masa-Katsu Fujimoto +1
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Quantum Physics (quant-ph) #gr-qc #quant-ph
paper · pdf · doi:10.48550/arxiv.1711.03713
34 pages 3 figures, full paper version of [arXiv:1709.01697]; 29 pages 3 figure, Explanations are made to be compact, Appendix B was removed, and references are added (v2); 31 pages, Explanations and references are added (v3)
arxiv created 2018/08/07 · arxiv updated 2018/08/08
In the context of the readout scheme for gravitational-wave detectors, the "double balanced homodyne detection" proposed in [K.~Nakamura and M.-K.~Fujimoto, arXiv:1709.01697.] is discussed in detail. This double balanced homodyne detection enables us to measure the expectation values of the photon creation and annihilation operators. Although it has been said that the operator bθ:=cosθb1+sinθb2 can be measured through the homodyne detection in literature, we first show that the expectation value of the operator bθ cannot be measured as the linear combination of the upper- and lower-sidebands from the output of the balanced homodyne detection. Here, the operators b1 and b2 are the amplitude and phase quadrature in the two-photon formulation, respectively. On the other hand, it is shown that the above double balanced homodyne detection enables us to measure the expectation value of the operator bθ if we can appropriately prepare the complex amplitude of the coherent state from the local oscillator. It is also shown that the interferometer set up of the eight-port homodyne detection realizes our idea of the double balanced homodyne detection. We also evaluate the noise-spectral density of the gravitational-wave detectors when our double balanced homodyne detection is applied as their readout scheme. Some requirements for the coherent state from the local oscillator to realize the double balanced homodyne detection are also discussed.