We develop a multimode quantum model of optical-axis misalignment in a simplified representation of the differential mode of an Advanced LIGO interferometer. The system is described as two coupled optical resonators corresponding to the signal extraction cavity and the arm cavity. Analytical expressions for the mode-mixing coefficients are derived, establishing a direct connection between geometrical perturbations of optical elements and multimode optical dynamics. Using the developed formalism, we investigate the influence of optical-axis misalignment on quantum-noise-limited sensitivity and injected squeezed states. We show that misalignment between the signal extraction cavity and the arm cavity leads to significant sensitivity degradation, frequency-dependent rotation of the squeezing ellipse, and a reduction of the observable squeezing in the fundamental spatial mode. At the same time, the injected squeezing is not destroyed but redistributed among coupled spatial modes. The resulting mode coupling generates quantum correlations between the fundamental and higher-order modes and leads to spatial-mode entanglement verified using the positive partial transpose criterion. Our results demonstrate that optical-axis misalignment should be treated as a coherent multimode quantum process rather than as a simple optical loss mechanism.
We develop a multimode quantum model of optical-axis misalignment in a simplified representation of the differential mode of an Advanced LIGO interferometer. The system is described as two coupled optical resonators corresponding to the signal extraction cavity and the arm cavity. Analytical expressions for the mode-mixing coefficients are derived, establishing a direct connection between geometrical perturbations of optical elements and multimode optical dynamics. Using the developed formalism, we investigate the influence of optical-axis misalignment on quantum-noise-limited sensitivity and injected squeezed states. We show that misalignment between the signal extraction cavity and the arm cavity leads to significant sensitivity degradation, frequency-dependent rotation of the squeezing ellipse, and a reduction of the observable squeezing in the fundamental spatial mode. At the same time, the injected squeezing is not destroyed but redistributed among coupled spatial modes. The resulting mode coupling generates quantum correlations between the fundamental and higher-order modes and leads to spatial-mode entanglement verified using the positive partial transpose criterion. Our results demonstrate that optical-axis misalignment should be treated as a coherent multimode quantum process rather than as a simple optical loss mechanism.
Squeezed states of light have been successfully employed in interferometric gravitational-wave detectors to reduce quantum noise, thus becoming one of the most promising options for extending the astrophysical reach of the generation of detectors currently under construction worldwide. In these advanced instruments, quantum noise will limit sensitivity over the entire detection band. Therefore, to obtain the greatest benefit from squeezing, the injected squeezed state must be filtered using a long-storage-time optical resonator, or ``filter cavity,'' so as to realize a frequency-dependent rotation of the squeezed quadrature. While the ultimate performance of a filter cavity is determined by its storage time, several practical decoherence and degradation mechanisms limit the experimentally achievable quantum noise reduction. In this paper we develop an analytical model to explore these mechanisms in detail. As an example, we apply our results to the 16 m filter cavity design currently under consideration for the Advanced LIGO interferometers.
To date, frequency-dependent squeezed light has been used to reduce quantum noise in interferometric gravitational-wave detectors by 6.1 dB (a factor of two). Future upgrades and detectors aim to both reduce quantum noise by 10 dB (a factor of three) and to increase the circulating power in the interferometer arm cavities. Achieving these goals will be extremely challenging due, in part, to the degradations to the squeezed state caused by mode mismatch between the internal interferometer optical cavities and between the auxiliary external cavities. It is therefore imperative to gain a detailed understanding of all sources of mismatch and to obtain experience in mitigating their effects in the current detectors in order to improve astrophysical sensitivity now and in the future. Two types of internal mismatch are identified which are due to the thermal aberrations generated when the test mass optics absorb a small fraction of the circulating arm power. It is found that the dynamics responsible for the degradations caused by the mismatch between the quadratic part of the wavefront of two modes has a characteristic low-pass frequency dependence while the dynamics of the mismatch due to all higher order thermal aberrations has a high-pass behavior. As a consequence, the two types of mismatch are predominantly responsible for different squeezing degradations---some of which are significant for the current detectors and some of which will only be important for future detectors with longer arms. The behavior of these two types of internal mismatch are described, and the implications for detector design, operation, and characterization are discussed.
Gravitational-wave detectors use state-of-the-art quantum technologies to reduce the noise induced by vacuum fluctuations, via injection of squeezed states of light. Future detectors, such as Einstein Telescope, may require the use of two filter cavities or a three-mirror coupled filter cavity to achieve a complex rotation of the squeezing ellipse, in order to reduce the quantum noise over the whole detector bandwidth. In this work, we compare the theoretical feasibility and performances of these two optical layouts and their resilience with respect to different degradation sources (optical losses, mismatching, locking precision), analytically and numerically. We extend previous analysis on squeezing degradation and find that the coupled cavity scheme provides similar or better performances than the two-cavity option, in terms of resilience with respect to imperfections and optical losses. We further highlight the role of mode-mismatch phases in limiting squeezing. Finally, we propose a possible two-step implementation scheme for Einstein Telescope using a single filter cavity that can be possibly upgraded into a coupled filter cavity.
Current gravitational wave detectors, such as LIGO, Virgo and KAGRA, are laser interferometers. This technique consists of injecting a laser beam through an input port, which is then separated into two arms several kilometers long by a semi-reflecting mirror. At the end of each arm, a mirror reflects the beam back to the semi-reflecting mirror. The two beams then interfere and the power of the resulting beam, measured at the detection port, contains information about the relative length of the two arms. When a gravitational wave passes through the detector, this relative length varies in time. Several noise sources degrade the quality of the recorded signal, which affects the number of gravitational waves that can be observed. Currently, this sensitivity is limited at high-frequency by the quantum noise.An electromagnetic wave described by quantum mechanics has a classical amplitude and quantum fluctuations in amplitude and phase. A state with a null classical amplitude is called a vacuum state, but still has these quantum fluctuations. Thus, in the detector, although no light beam is introduced through the detection port, the vacuum state is present. It is then the quantum fluctuations of this vacuum state that are responsible for the quantum noise of the interferometer. In particular, the phase and amplitude fluctuations are respectively responsible for the quantum noise at high and low frequencies; the separation between these two regions occurs at about 100 Hz.The work presented in this thesis focuses on the injection of squeezed vacuum states into the Virgo detector via the detection port in order to lower the quantum noise. These states are characterized by the fact that their phase (amplitude) fluctuations are reduced, which allows reducing the quantum noise at high (low) frequency. As the Virgo detector is currently limited only by high-frequency quantum noise, only phase squeezed vacuum states were used during the last observation period O3. It was first necessary to ensure that these squeezed vacuum states had the proper geometric and phase parameters with respect to the interferometer beam such that they were not degraded. Control loops allowed these parameters to be maintained at their nominal values during O3, a year long period. The decrease in high-frequency quantum noise, but also the increase in low-frequency quantum noise, have been measured for the first time with the Virgo detector. These observations were in agreement with the measurements of the losses that affect the squeezed vacuum states.From O4 , quantum noise will also be limiting at low frequency. It will then be possible to use squeezed vacuum states having their amplitude fluctuations reduced at low frequency and their phase fluctuations reduced at high frequency. Thus, the total quantum noise can be reduced. Such states can be generated using an optical cavity called a filter cavity. The second part of the work presented in this thesis consisted in defining the optical parameters of the filter cavity that will be installed on Virgo for O4. To do this, it was first necessary to study the sources of degradation of the squeezed states of the vacuum. This then allowed defining the length of the filtering cavity and the set of parameters of the mirrors that compose it. Finally, the implementation of this filter cavity within the Virgo infrastructure was studied. This has shown that the use of compressed states will effectively reduce quantum noise over the entire sensitivity spectrum of Virgo.
The first detection of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory (LIGO) in 2015 launched the era of gravitational-wave astronomy. The quest for gravitational-wave signals from objects that are fainter or farther away impels technological advances to realize ever more sensitive detectors. Since 2019, one advanced technique, the injection of squeezed states of light, is being used to improve the shot-noise limit to the sensitivity of the Advanced LIGO detectors, at frequencies above ∼50 Hz. Below this frequency, quantum backaction, in the form of radiation pressure induced motion of the mirrors, degrades the sensitivity. To simultaneously reduce shot noise at high frequencies and quantum radiation pressure noise at low frequencies requires a quantum noise filter cavity with low optical losses to rotate the squeezed quadrature as a function of frequency. We report on the observation of frequency-dependent squeezed quadrature rotation with rotation frequency of 30 Hz, using a 16-m-long filter cavity. A novel control scheme is developed for this frequency-dependent squeezed vacuum source, and the results presented here demonstrate that a low-loss filter cavity can achieve the squeezed quadrature rotation necessary for the next planned upgrade to Advanced LIGO, known as "A+."
Optical decoherence degrades quantum correlations in squeezed states of light, severely limiting the quantum-nondemolition (QND) sensitivity of gravitational-wave detectors. Here, we propose the path-degenerate quantum interferometry scheme that obviates the need for entire optical subsystems---including additional filter cavities, auxiliary parametric amplifiers, and Faraday isolators---thereby drastically reducing spatial mode mismatches while inherently integrating variational output, a long-standing theoretical proposal to further deepen the QND regime. We experimentally demonstrate a core aspect of this scheme, achieving a shot-noise-preserving signal enhancement that directly counteracts the detrimental effects of readout loss. By delivering an improved signal-to-quantum-noise ratio solely through the consolidation and reduction of currently considered optical subsystems, our approach offers a highly optimized route toward enhanced quantum-noise reduction in upcoming LIGO upgrades and next-generation gravitational-wave observatories.