Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors

We consider enhancing the sensitivity of future gravitational-wave detectors by using double optical spring. When the power, detuning and bandwidth of the two carriers are chosen appropriately, the effect of the double optical spring can be described as a “negative inertia,” which cancels the positive inertia of the test masses and thus increases their response to gravitational waves. This allows us to surpass the free-mass standard quantum limit (SQL) over a broad frequency band, through signal amplification, rather than noise cancellation, which has been the case for all broadband SQL-beating schemes so far considered for gravitational-wave detectors. The merit of such signal amplification schemes lies in the fact that they are less susceptible to optical losses than noise-cancellation schemes. We show that it is feasible to demonstrate such an effect with the Gingin High Optical Power Test Facility, and it can eventually be implemented in future advanced GW detectors.

Figure 1

A schematic plot showing the experimental realization of double optical spring, as demonstrated experimentally [32]. The other carrier light is obtained by shifting the laser frequency with an acoustic-opto-modulator (AOM).

Figure 2

A schematic plot showing a linear quantum measurement device. In the context of GW detection, the external force $F_{\mathrm{ext}}$ is the GW tidal force. The meter is the optical field that measures the test-mass position $x$, and at the same time, exerts a radiation-pressure force (back action $F_{\mathrm{BA}}$).

Figure 3

Plots, showing the sum optimized noise spectral density $S_F^{\mathrm{opt}}=2\hslash |{\chi }^{-1}|+S_F^{\mathrm{add}}$ (blue solid line) normalized with respect to that of the free-mass SQL $[S_F^{\mathrm{SQL}}{]}_{\mathrm{freemass}}=2\hslash m{\Omega }^2$. The shaded area shows where the sensitivity surpasses the free-mass SQL. The dashed line shows the SQL $2\hslash |{\chi }^{-1}|$ with the new dynamics, and dotted line shows the spectral density $S_F^{\mathrm{add}}$ of the additional back action noise due to optical loss. The top row uses the specifications that are close to those of the Gingin facility with intracavity power of 100 kW. The bottom row is similar to the AdvLIGO specifications: $L=4\mathrm{km}$, $m=40\mathrm{kg}$ and a total intracavity power of 2 MW for two carriers. Left column: optical losses per bounce $A^2={10}^{-4}$, right column: $A^2={10}^{-5}$.