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.
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.
Proposed near-future upgrades of the current advanced interferometric gravitational wave detectors include the usage of frequency dependent squeezed light to reduce the current sensitivity-limiting quantum noise. We quantify and describe the degradation effects that spatial mode-mismatches between optical resonators have on the squeezed field. These mode-mismatches can to first order be described by scattering of light into second-order Gaussian modes. As a demonstration of principle, we also show that squeezing the second-order Hermite-Gaussian modes HG02 and HG20, in addition to the fundamental mode, has the potential to increase the robustness to spatial mode-mismatches. This scheme, however, requires independently optimised squeeze angles for each squeezed spatial mode, which would be challenging to realise in practise.
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 ability to directly detect gravitational waves will open a completely new branch of astronomy to view the Universe, one that is inaccessible to electromagnetic-based astronomy. First generation ground-based interferometric gravitational-wave detectors have achieved strain sensitivities of order one part in ten to the twenty-one, at 100 Hz detection frequency. A new generation of detectors are under construction, designed to improve on the sensitivity of the first-generation detectors by a factor of 10. The quantum nature of light will broadly limit the sensitivity of these new instruments. This quantum noise will originate from the quantum vacuum fluctuations that enter the unused port of the interferometer. One of the most promising options for reducing the quantum noise impact and further increasing the sensitivity is applying quantum squeezed vacuum states. These squeezed states have lower noise in one quadrature than the vacuum state. By replacing the quantum vacuum fluctuations entering the interferometer with squeezed vacuum states, the quantum noise impact is reduced. This thesis firstly details the development of a squeezed light source that produces squeezed states applicable for enhancing interferometric gravitational-wave detectors. A doubly-resonant, travelling-wave bow-tie cavity squeezed light source is presented. For the first time, greater than 10 dB of quantum noise suppression across the gravitational-wave detection band is directly observed, and 11.6 dB of quantum noise suppression is observed above 200 Hz. This squeezing cavity design also has benefits with intrinsic isolation to backscattered light. Experiments that quantify this isolation are reported. The properties affecting squeezing magnitude and low-frequency squeezing measurement are discussed. In addition, a modified squeezing-ellipse-phase control technique for squeezed vacuum states is presented. This thesis secondly presents results from the LIGO Squeezed Light Injection Experiment, undertaken to test squeezed light injection into a 4 km interferometric gravitational-wave detector. The results of the experiment show the first measurement of squeezing-enhancement in a 4 km gravitational-wave detector, with 2.15 dB measured above 250 Hz. This represents the best sensitivity to gravitational waves yet achieved at these frequencies by any single gravitational-wave detector to date. An unknown area was whether the addition of a squeezer would introduce noise couplings that degrade the crucial low frequency sensitivity. The results demonstrate that injected squeezed states are compatible with low frequency gravitational-wave measurement. The characterisation of squeezing-injection optical losses and fluctuations of the squeezing angle are also reported. The knowledge and processes gained, from both the squeezed light source development work and the LIGO Squeezed Light Injection Experiment, will inform the design, planning and implementation of squeezed states in future gravitational-wave detectors.
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 thebeam 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.
Current interferometric gravitational wave detectors were designed to be limited, in much of their sensitive
band, by quantum noise in the form of shot noise (at high frequency) or quantum radiation pressure noise
(at low frequency). In the current observation run (O3), a squeezed light source has been used to
manipulate quantum noise and surpass the limits imposed by the circulating laser power by injecting nonclassical states of the electromagnetic field, called squeezed vacuum states, in the interferometer's dark
port. Recent O3 results show that this technique was able to reduce the shot noise contribution to the
noise spectral density by about one half. To surpass the so called standard quantum limit across the entire
sensitivity band, an even more complex variation of this technique will be implemented, which requires the
use of a so called “filter cavity” to reflect the squeezed quantum field and rotate the squeezing angle as a
function of frequency.
The performance of this techniques is however severely limited by light losses. One big contributor to
optical losses is the mismatch between the squeezed vacuum beam, the beam circulating into the
interferometer and, in the near future, the filter cavity fundamental transverse spatial mode.
To be able to monitor and actively correct mode mismatch, an accurate, online sensing technique is
needed. A possible solution consists in the introduction of an Electro-Optic Lens (EOL) that can induce
radio-frequency sidebands in the Laguerre-Gauss 10 (LG10) transverse mode of the beam. If the
modulation frequency is tuned in a way that one sideband is at the cavity LG10 frequency, then the
resonance breaks the symmetry of the two sidebands and converts phase modulation into amplitude
modulation, making it possible to retrieve an error signal directly from the cavity reflected electric field
with the same single-element photodetector used for the Pound Drever Hall (PDH) locking technique. This
error signal carries information about the magnitude and nature of the mismatch, providing all is needed to
inform a dedicated feedback loop with a suitable actuator to maintain the mismatch at or below the 1%
level.
The goal of this thesis is to demonstrate the technique on a dedicated bench-top experiment employing an
EOL prototype device. The EOL alignment and working point, as well as the cavity lock parameters were
optimized in an already existing setup. Simulations and theoretical calculations of the cavity reflected field
were performed to evaluate the system non-idealities: both Electro-Optic Modulator (for PDH technique)
and EOL modulations effects and interactions, as well as some system imperfections were considered. The
simulations confirm that this technique requires a stable cavity lock condition, and for this reason an
accurate study and optimization of the feedback loop parameters was done. In conclusion, a
characterization of the EOL error signal response to different mismatch conditions are presented.
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.