Nondegenerate internal squeezing: An all-optical, loss-resistant quantum technique for gravitational-wave detection

The detection of kilohertz-band gravitational waves promises discoveries in astrophysics, exotic matter, and cosmology. To improve the kilohertz quantum noise–limited sensitivity of interferometric gravitational-wave detectors, we investigate nondegenerate internal squeezing: optical parametric oscillation inside the signal-recycling cavity with distinct signal-mode and idler-mode frequencies. We use an analytic Hamiltonian model to show that this stable, all-optical technique is tolerant to decoherence from optical detection loss and that it, with its optimal readout scheme, is feasible for broadband sensitivity enhancement.

Figure 1

(a) Simplified optical configuration of nondegenerate internal squeezing in a dual-recycled Fabry-Perot Michelson interferometer. Abbreviations are ETM: end test mass, ITM: input test mass, PRM: power-recycling mirror, and SRM: signal-recycling mirror. (b) Representation of how signal-mode readout sensitivity is improved by amplifying the signal more than the noise [48]. (c) Mode diagram showing that the system consists of three coupled optical modes $(\widehat{a},\widehat{b},\widehat{c})$ and that the gravitational-wave signal indirectly couples into the idler-mode.

Figure 2

Poles of the transfer functions as the squeezer parameter increases from zero (marked by a dot). Beyond the squeezing threshold (marked by a cross) one or more poles enter the unstable region above the real axis. (a) Lossless and (b) lossy cases using the parameters in Table 1. The $\mathrm{\Omega }=0$ pole from the free mass approximation is not shown.

Figure 3

Sensitivity versus frequency for signal-mode readout with different squeezer parameters. The ${\omega }_s=5\mathrm{kHz}$ feature in the baseline curve is the coupled-cavity pole. The baseline curve exceeds the standard quantum limit (SQL) [48] using frequency-dependent external squeezing which is compatible and used with internal squeezing. The parameters in Table 1 are used. The LIGO Voyager [13] quantum noise–limited design curve is also shown.

Figure 4

(a) Sensitivity versus frequency for signal-mode readout with different optical detection loss. (b) Peak sensitivity versus detection loss normalized to the peak sensitivity with 0 detection loss—higher values indicate greater sensitivity degradation. The parameters, including intracavity loss, in Table 1 are used with $\chi /{\chi }_{\mathrm{thr}}=0.95$.

Figure 5

Sensitivity versus frequency for alternative readout schemes. The parameters in Table 1 are used with $\chi /{\chi }_{\mathrm{thr}}=0.95$ except $T_{\mathrm{SRM},c}\approx 1.54\times {10}^{-4}$.