Quantum Limit for Laser Interferometric Gravitational-Wave Detectors from Optical Dissipation

We derive a quantum limit to the sensitivity of laser interferometric gravitational-wave detectors from optical-loss-induced dissipation, analogous to the sensitivity limit from the mechanical dissipation. It applies universally to different interferometer configurations and cannot be surpassed unless the optical properties of the interferometer are improved. This result provides an answer to the long-standing question of how far we can push the detector sensitivity given the state-of-the-art optics.

Popular Summary

Gravitational-wave detectors have ushered in a new era of physics and astronomy as they record spacetime ripples from collisions among black holes and neutron stars in other galaxies. Despite the enormous size of these detectors, their sensitivity is limited by quantum fluctuations of light. Researchers have studied how to overcome this limitation by modifying the detector configuration, but one outstanding question remains: What is the ultimate sensitivity limit regardless of configuration? We answer this question by deriving a sensitivity limit from the dissipation associated with optical loss, which applies universally to different configurations.

We start with a general interferometer configuration that includes different techniques to modify quantum fluctuations in the light. We then convert it to a simplified scheme while keeping the interferometer’s key features, and we maximize the sensitivity over the configuration-dependent parameters. We obtain an ultimate sensitivity limit that depends only on shared optical properties.

While focused on gravitational-wave detectors, our result applies to other quantum-limited optical devices. Furthermore, this limit is analogous to the one from thermal noise due to mechanical dissipation. This not only highlights the fundamental role of optical loss but also motivates the future study of both the optical and mechanical dissipation under a unified framework.

Figure 1

Illustration of the general QND scheme with optical filters added to the typical configuration of advanced GW detectors—a dual-recycled Michelson interferometer. (ETM: end test mass; SRM: signal-recycling mirror.)

Figure 2

This plot shows the quantum-noise (QN) sensitivity limits resulting from optical loss in an interferometer as given in Eq. (3) (blue, green, red, and dashed-black curves). For illustration, we assume a set of parameters similar to those of Advanced LIGO (aLIGO) and show the aLIGO QN for reference (upper light grey curve). To demonstrate the limited nature of the QCRB, the QN of aLIGO with a highly squeezed input state is shown (solid purple curve) along with the corresponding QCRB (dot-dashed purple curve). Notice how the QN of the highly squeezed interferometer is limited by optical losses, while the QCRB is significantly less constraining. Since the QCRB does not take into account losses, it can be made arbitrarily low by further increasing the squeezing of the input state, i.e., reducing the uncertainty in the phase quadrature, and thereby increasing $S_{PP}$ in Eq. (2) beyond the 30-dB level used for this example. Note also that the highly squeezed interferometer QN is above the loss limit (dashed black curve) at low frequencies ($\lesssim 20\mathrm{Hz}$) due to the fixed read-out quadrature and at high frequencies ($\gtrsim 400\mathrm{Hz}$) due to uncompensated dispersion.

Figure 3

(a) A simplified schematic of the general scheme shown in Fig. 1 when only focusing on the differential mode that contains the GW signal. The optical losses at different places are illustrated. (b) A further simplified diagram by mapping the SRC into an effective mirror, and optical losses into internal and external components. Here, ${\mathbf{M}}_{\mathrm{rot}}$ accounts for a general rotation of the amplitude and phase quadratures; ${\mathbf{M}}_{\mathrm{sqz}}$ describes the general squeezing effect.

Figure 4

(a) The noise amplitude, given the measurement of output phase quadrature (dashed line) and the optimal quadrature (solid line) in the two cases: tuned SRC (blue) and detuned SRC (red), respectively. (b) The corresponding signal response for these two cases. We also show the half of the signal response with a phase measurement in the tuned case as a reference (dashed black curve). (c) The sensitivity curve, which is a ratio of the noise amplitude in (a) and the signal response in (b). We assume the interferometer parameters are the same as the aLIGO design, but we choose the detector bandwidth to be 240 Hz and the detuning to be 600 Hz for illustration. The optical spring frequency is marked using the vertical grid line around 35 Hz.