Increasing future gravitational-wave detectors’ sensitivity by means of amplitude filter cavities and quantum entanglement

The future laser interferometric gravitational-wave detectors’ sensitivity can be improved using squeezed light. In particular, recently a scheme which uses the optical field with frequency-dependent squeeze factor, prepared by means of a relatively short ($\sim 30\mathrm{m}$) amplitude filter cavity, was proposed [Thomas Corbitt, Nergis Mavalvala, and Stan Whitcomb, Phys. Rev. D 70, 022002 (2004).]. Here we consider an improved version of this scheme, which allows one to further reduce the quantum noise by exploiting the quantum entanglement between the optical fields at the filter cavity two ports.

Figure 1

Squeezed vacuum is reflected from the resonance-tuned filter cavity and is fed into the gravitational-wave detector dark port using the polarization beam splitter (PBS) and the Faraday rotator (FR).

Figure 2

Typical shape of the function $K(\Omega )$ of the original CMW scheme (dashed line) and of the CMW scheme with the additional detector (solid line) and with $\zeta =0$ (a), $\zeta ={\zeta }_{\mathrm{optimal}}$ (b), and $\zeta =\pi /2$ (c).

Figure 3

Square root of the sum quantum noise spectral density of the conventional unsqueezed interferometer (dashed line); the original CMW scheme (a); the CMW scheme with the additional homodyne detector (b). In all three cases, $W=840\mathrm{kW}$, $\gamma =2\pi \times 100{\mathrm{s}}^{-1}$, and $\eta =1$.

Figure 4

Square root of the sum quantum noise spectral density of the CMW scheme with the additional homodyne detector for different values of the optical power: (a) $W_0{e}^{-2r}\approx 84\mathrm{kW}$, (b) $W_0{e}^{-r}\approx 266\mathrm{kW}$, (c) $W_0=840\mathrm{kW}$ (solid lines), in comparison with the conventional unsqueezed interferometer at $W=840\mathrm{kW}$ (dashed line). In all cases, $\gamma =2\pi \times 100{\mathrm{s}}^{-1}$ and $\eta =1$.

Figure 5

Square root of the sum quantum noise spectral density of the CMW scheme with the additional homodyne detector for different values of the optical power: (a) $W_0{e}^{-2r}=84\mathrm{kW}$, (b) $W_0{e}^{-r}\approx 266\mathrm{kW}$, (c) $W_0=840\mathrm{kW}$. In all three cases, $\gamma =2\pi \times 100{\mathrm{s}}^{-1}$. Solid line: $\eta =0.9$; dashed line: $\eta =1$. (d) The sum quantum noise of the advanced LIGO; (e) the sum technical noise of the advanced LIGO.

Figure 6

Square root of the sum quantum noise spectral density of the CMW scheme with the additional homodyne detector for different values of the optical power and the interferometer bandwidth: (a) $W_0{e}^{-2r}=84\mathrm{kW}$, ${\gamma }_0=2\pi \times 100{\mathrm{s}}^{-1}$; (b) $W_0{e}^{-r}\approx 266\mathrm{kW}$, ${\gamma }_0{e}^r\approx 2\pi \times 314{\mathrm{s}}^{-1}$; (c) $W_0=840\mathrm{kW}$, ${\gamma }_0{e}^{2r}=2\pi \times 1000{\mathrm{s}}^{-1}$. Solid line: $\eta =0.9$; dashed line: $\eta =1$. (d) The sum quantum noise of the advanced LIGO; (e) the sum technical noise of the advanced LIGO.

Figure 7

Lossy amplitude filter cavity.