First-step experiment for sensitivity improvement of DECIGO: Sensitivity optimization for simulated quantum noise by completing the square

Decihertz Interferometer Gravitational Wave Observatory (DECIGO) is a future mission for a space-borne laser interferometer. DECIGO has 1000-km-long arm cavities mainly to detect the primordial gravitational waves (PGWs) at lower frequencies around 0.1 Hz. Observations in the electromagnetic spectrum have lowered the bounds on the upper limit of PGWs energy density (${\mathrm{\Omega }}_{\mathrm{gw}}\sim {10}^{-15}\to {10}^{-16}$). As a result, DECIGO’s target sensitivity, which is mainly limited by quantum noise, needs further improvement. To maximize the feasibility of detection while constrained by DECIGO’s large diffraction loss, a quantum locking technique with an optical spring was theoretically proposed to improve the signal-to-noise ratio of the PGWs. In this paper, we experimentally verify one key element used in the theory: sensitivity optimization by completing the square of multiple detector outputs. This experiment is operated on a simplified tabletop optical setup with classical noise simulating quantum noise. We succeed in getting the best of the sensitivities with two different laser powers by the square completion method.

Figure 1

Schematic geometry of a single arm in DECIGO with quantum locking. Each mirror in the arm cavity (red) is shared with a subcavity (green) located inside a satellite. The output signal from each subcavity is individually fed back to the respective shared mirror.

Figure 2

Quantum-noise sensitivities for two different laser powers. The quantum noise contains a trade-off relation between the shot noise and the RP noise. The tangent line to the two quantum-noise curves shows the SQL.

Figure 3

Simulated sensitivities for the optimal combined signal ${\tilde{V}}_{\mathrm{opt}}$ in the three cases: high, low, and typical loop gain. (a) Includes the optimized sensitivities and two sensitivities of the single arm cavity with high/low laser power. The applied loop gain is shown in (b). For better visibility of the optimized sensitivities in (a), we slightly displace the blue trace upward and the green trace downward from the yellow curve.

Figure 4

Simplified layout with the modeled quantum noise for the three cases. The essence of the optical setup (a), the same as Fig. 1, is broken down into two cases: (b) the single cavity case with the high/low laser power and (c) the dual cavity case. A mirror, which is assumed to have infinite mass, is colored dark gray. Arrows from the signal generators show the injection points.

Figure 5

(a) Experimental setup overview and (b) detailed control signal flow diagram for the two cavities with the classical noise injections and the measuring points. The two identically designed Fabry-Perot cavities share an end mirror and are individually controlled by separate feedback signals. The main/subcavities are individually operated in the high-/low-power single cavity case, while both cavities are operated in the dual cavity case. The dashed blue arrow in (b) only exists in the dual cavity case. AOM, acousto-optic modulator; EOM, electro-optic modulator; FA, filter amplifier; FI, Faraday isolator; HBS, half beam splitter; PBS, polarizing beam splitter; rf, radio frequency; $\lambda /2$, half-wave plate; $\lambda /4$, quarter-wave plate.

Figure 6

Corrected calibration functions at the observation frequency range from 700 Hz to 10 kHz. The functions for the main cavity (a) and for the subcavity (b) depict similar trends with different mechanical resonances.

Figure 7

Measured sensitivities compared with simulated sensitivities. (a) Includes the measured sensitivities in the three cases, the modeled quantum-noise components in the single cavity cases, and excess background noise of the cavities. The three main curves in (a) are plotted alone in (b). (c) Simulated sensitivities to compare the experimental results with (b). (a) and (c) share a color scheme for the same noise components.

Figure 8

Frequency dependence of the optimized combination coefficient ${\chi }_{\mathrm{opt}}$. The mechanical resonances of the mirror-holding structures appear in ${\chi }_{\mathrm{opt}}$ at the observation frequency range from 700 Hz to 10 kHz.

Figure 9

Measured loop gain for the two cavities. The blue/red curves show the loop gain for the main/subcavity, respectively.