Squeezing the Quantum Noise of LIGO below the Standard Quantum Limit

Abstract

The year 2015 marked the first detection of a gravitational wave signal from a pair of black holes located 410 megaparsecs (1.3 billion light-years) away. Their merger unleashed an immense amount of energy, with the peak emission rate surpassing the combined power of all luminous stars in the observable universe. Unlike stars, the merger of two black holes does not emit electromagnetic radiation like visible light but instead illuminates the universe with gravitational radiation. These waves traveled freely for over a billion years before being captured by the twin Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors. Upon reaching Earth, these waves caused a minuscule length change between the LIGO mirrors, on the order of 10^(−18) m, a thousand times smaller than a proton.

The unprecedented sensitivity of LIGO requires an extremely low noise level. The design of LIGO as an interferometer converts the gravitational-wave signal to an optical signal, which is measured on photodiodes along with other noises. One of the noise sources is the quantum noise due to the quantum vacuum fluctuations of the light itself. Besides the light, the mirror also has quantum-mechanical features and experiences quantum back-actions when we probe it with light. Knowing the position of the mirror very well would inevitably perturb its momentum, which prevents us from precisely making the next measurement of the position. This is fundamental physics dictated by Heisenberg’s uncertainty principle. In the case of continuous measurement like LIGO, the quantum back-action leads to an apparent sensitivity limit known as the Standard Quantum Limit (SQL). It tells us how precisely we can measure an object with light.

The SQL applies when using uncorrelated photons or coherent light to measure the object, such as a laser beam. However, introducing quantum correlations through squeezed light, a technique called squeezing (Chapter 2), can circumvent this limit. Squeezed vacuum, a non-classical light state, exploits quantum correlations between photon pairs to reduce vacuum fluctuations in one quadrature at the cost of another. By manipulating the quantum correlation between light and the mirror, the squeezed vacuum can potentially reduce quantum noise below the SQL, a concept explored in frequency-dependent squeezing. This thesis develops a first-principle model of quantum noise in LIGO (Chapter 3) and investigates how squeezing can mitigate it while considering practical factors like optical losses and mode-mismatch (Chapter 4). These theories are constructed with a bottom-up approach. Experimental details on generating and utilizing frequency-dependent squeezing for LIGO are also discussed (Chapter 5), culminating in the observation of LIGO’s quantum noise below the SQL (Chapter 6).

Besides squeezing, increasing optical power can also reduce quantum shot noise. Nevertheless, maintaining high power levels (fractions of megawatts) in LIGO is challenging due to experimental imperfections, such as unintended point absorbers on the mirror coating. This thesis analyzes the thermoelastic distortions caused by these absorbers, which limit achievable optical power in current and future gravitational-wave detectors (Chapter 7).