Quantum expander for gravitational-wave observatories

Abstract

The quantum uncertainty of laser light limits the sensitivity of gravitational-wave observatories. Over the past 30 years, techniques for squeezing the quantum uncertainty, as well as for enhancing gravitational-wave signals with optical resonators have been invented. Resonators, however, have finite linewidths, and the high signal frequencies that are produced during the highly scientifically interesting ring-down of astrophysical compact-binary mergers still cannot be resolved. Here, we propose a purely optical approach for expanding the detection bandwidth. It uses quantum uncertainty squeezing inside one of the optical resonators, compensating for the finite resonators' linewidths while keeping the low-frequency sensitivity unchanged. This quantum expander is intended to enhance the sensitivity of future gravitational-wave detectors, and we suggest the use of this new tool in other cavity-enhanced metrological experiments.

Keywords: Nonlinear optics; Optical metrology; Quantum optics.

Fig. 1. Conceptual representation of the GW observatory with our quantum expander.

The relative change in the distance between the central beam splitter and the test masses due to a gravitational wave is measured on the signal port with photodiode PD. Optical cavities in the arms are used to enhance the light power and the signal. Additional mirrors independently enhance the signal (signal extraction mirror, SE mirror) and power (power recycling mirror, PRM). We add a nonlinear χ⁽²⁾ crystal into the SE cavity, formed by the SE mirror and input mirrors, which creates an internally squeezed light field to enhance the high-frequency sensitivity and expand the detection bandwidth.

Fig. 2. Concept of the quantum expander.

a Model system of two coupled cavities, arm and signal extraction, with a nonlinear crystal inside the SE cavity; b resonance enhancement of the SE mode (solid red) at frequencies close to ω_s and suppression at low frequencies, with two longitudinal resonances of the arm cavity (dashed black) separated by a free spectral range (ω_FSR); c suppression of the shot noise at high frequency by the quantum expander (red) compared to the vacuum level (black), in comparison to the scaling of the signal transfer function (TF) due to the cavity linewidth with the quantum expander (green) and without it (black), where the signal is suppressed by 6 dB due to the parametric process; d noise-to-signal ratio for the detector with the quantum expander (red) and without it (black). In c, the quantum expander noise squeezing has exactly the same scaling as signal reduction due to the cavity bandwidth, so the bandwidth of the noise-to-signal ratio is expanded, as seen in d.

Fig. 3. Effect of the quantum expander on the detector’s sensitivity to gravitational-wave strain S_h(f), in combination with the variational readout.

The bandwidth of the semiclassical gravitational wave observatory (GWO, blue dashed line) is expanded by the squeezing operation inside the detector at high frequencies (solid red line, red shading). The effect deteriorates once quantum decoherence due to optical loss is introduced (different shades of red for the quantum expander, gray dot-dashed line for the semiclassical GWO). At low frequencies, quantum noise remains unaffected by quantum expansion, which enables the use of the variational readout (green shading) for evading the quantum radiation-pressure noise (QRPN). The efficiency of the variational readout is also affected by the optical loss, which leads to the loss of correlations between the two quadratures of the light field, resulting in a reduction in the sensitivity at low frequencies, as shown by dashed red lines. The boundary where the QRPN becomes equal to the shot noise at different light powers, known as the standard quantum limit (SQL), is plotted in black dots. The parameters used for plotting are based on the benchmark parameter set for the 3rd generation of GWOs: optical wavelength λ = 1550 nm; light power inside the arm cavity P_c = 4 MW; arm cavity length L_arm = 20 km; SE cavity length L_SE = 56 m; mirror mass m = 200 kg; input mirror power transmission T_ITM = 0.07; and SE mirror power transmission T_SE = 0.35.

Fig. 4. Histogram for the SNR of the loudest event for 100 realizations in the Monte-Carlo simulation.

Blue bins represent the SNR of our baseline GWO. Orange and red bins are associated with quantum expanders with a total loss of ~3 and 0.5%, respectively. The black dashed line indicates a detection threshold (SNR = 5). We used the equation of state in refs. ^,, and the binary merger rate is taken to be R = 1.54 Mpc⁻³Myr⁻¹. The mass distribution for each neutron star in the binary is taken to be Gaussian and centered around 1.33 $M_{\odot }$.