NOTE: To see the 2023 projects, click the buttons below. Please write your application in reference to these projects. The 2024 projects will likely be similar.
LIGO interferometers use frequency and amplitude-stabilized lasers that are reflected using test masses (large, cylindrical mirrors) to detect gravitational waves. Because the laser light is stored in optical cavities within the interferometer, the test masses heat up. This physically deforms the surface of the mirror. Physical deformation causes the test masses to not reflect the laser optimally and the interferometer will not function at its highest sensitivity. Ring heaters are coils that heat the outside of a test mass through resistance to counteract this effect and allow us to control the deformation of the test mass surface. Our objective is to modify the current ring heater design and develop improvements to be implemented in future ring heaters. We accomplish this by troubleshooting issues in the current design, comparing designs between versions, and modeling different designs in COMSOL. We have built spare ring heaters, identified causes of grounding issues and weaknesses in the current design, successfully modeled how differently-sized heating elements heat the test mass, and compared their effectiveness to the current design. With these results, we are now able to avoid grounding problems observed at other LIGO locations, as well as improve the ring heater design for future use.
The Response Function of the LIGO Interferometer is central to reconstructing the strain produced by incoming gravitational waves. A function of the interferometer's response to external stimuli, the Response Function is both analytically modeled and experimentally measured using excitations from the photon calibrator system at discrete frequencies. The uncertainty in each data point is propagated to the residual of the model and measurements, with both the uncertainty and residual being interpolated over a broadband frequency range. While valid, interpolation methods lack the accuracy to estimate measurement uncertainty at non-measured frequencies that fitting an analytical transfer function could provide. This project analyzes the results of fitting a series of transfer functions to the Response Function using Bayesian statistics as opposed to traditional transfer-function-fitting methods. We use data gathered from the OMC DCPD S2300004 whitening chassis at discrete frequency points, varying the signal-to-noise ratio as a proxy for varying the uncertainty in the measurements, and compare the results of each method.
In the current LIGO design, 1064 nm light propagates through a Michelson interferometer and reflects off test masses. In order to accurately measure minuscule changes in the lengths of LIGO's arms, it is crucial to reduce various types of noise in the system, such as frequency noise. The next generation of LIGO detectors will likely switch from fused silica mirrors to crystalline silicon and will use a wavelength of about 2 microns in the interferometer; mirrors made of crystalline silicon have demonstrated lower levels of mechanical loss than fused silica mirrors and have low absorption of 2-micron light. Access to low-cost sources of stable 2-micron light is crucial for researchers to develop the next generation of LIGO detectors. This work will address the stabilization of a 2050 nm laser, and will focus on reducing the frequency noise of the laser with a self-delayed heterodyne interferometry technique. This low-cost method has the potential to facilitate further testing and development of 2-micron light for gravitational-wave detection.
The length sensing and control (LSC) system of a gravitational wave interferometer is key to maintaining control of the detector and generating a linear response to the gravitational wave signal. In the LIGO 40m prototype and at the Advanced LIGO detectors, the controlled length degrees of freedom are outnumbered by the RF photodiode sensors sensitive to their motion. This generates an overdetermined system where virtual sensors, calculated from combinations of sensors, can be designed to reduce the noises contributed by the LSC system. This project studied sensor fusion techniques for the power recycling Michelson interferometer (PRMI) configuration of the LIGO 40m prototype interferometer. Measurements were made of transfer functions and closed loop noises of the 40m LSC system during a PRMI lock. These were used to evaluate several methods for sensor fusion with the eventual goal of implementing one of them at the 40m interferometer.
A central problem in control theory is that most of the field focuses on linear controllers, even though most of the systems we are aiming to control are nonlinear in nature. To circumvent this issue, control theory aims to approximate the behavior of the nonlinear system around the desired mode of operation by a linear function. This unfortunately creates a theoretical limit on the performance specification of the linear as it tries to control a nonlinear system with a linear control law. We aim to show that this limitation can be overcome with a nonlinear controller based on Reinforcement Learning (RL) methods. As a proof of our concept, we aim to implement the RL-based controller in a purely classical experiment: temperature stabilization of a test mass. Moreover, we explore the possible implications of such a nonlinear controller in the field of quantum mechanics and non-classical experiments, where nonlinearities can be encountered even in the vicinity of the desired setpoint/mode of action of the system, exacerbating the need for a controller that can manage such nonlinearities.
The proposed post-O5 LIGO Voyager upgrade as well as some proposed third-generation gravitational wave observatories center on a cryogenic silicon optics system for reduced thermal noise. This requires a shift of the laser wavelength further to the infrared using the comparatively noisy 2-micron technology to compensate for the high absorption of the current 1064nm laser in crystalline silicon. To meet the tight frequency noise requirements for desired sensitivities of these interferometers, we demonstrate a feed-forward frequency noise reduction system at 2050nm in fiber. Additionally, we characterize the sources of noise limiting the degree of noise reduction and the sensitivity of the interferometric measurement of the reduced frequency noise, allowing for the targeting of future improvements to the system.
Optical contacting is a type of bonding that can be achieved when flat, polished surfaces are brought into close contact. When used as a replacement for fused silica, optically contacted silicon has the potential to increase the sensitivity of LIGO Voyager to gravitational waves. This project is aimed at determining the quality factor of optically contacted silicon bonds in order to quantify their potential to reduce the noise in LIGO Voyager. By maximizing the energy contribution from the bond and oscillating a silicon cantilever, the quality factor of the bond can be estimated. The eventual goal is to create an ideal optically contacted bond which minimizes damping and energy loss.
The LIGO interferometers need to robustly lock its various degrees of freedom to be sensitive to Gravitational Waves. The LIGO 40m prototype uses an auxiliary (AUX) laser as a reference to lock the main laser to the arm cavity and stabilize it. The AUX laser is stabilized by locking it to the arm cavity using the Pound-Drever-Hall (PDH) technique. The stability of the AUX laser is crucial for the stability of the main laser. Mechanical resonances of the AUX laser's piezoelectric (PZT) actuator and the rigid nature of the currently implemented analogue PDH controller limits the performance of the system, hindering noise suppression especially at low frequencies. This project aims to develop a digital controller to replace the currently implemented AUX laser locking system. A digital controller will be more robust and easily customizable. Specifically, the features to be implemented include better controller performance in the 10Hz-20kHz range, where the AUX laser noise has greater contribution, supplying an increase in bandwidth over the current analogue system, enable fast lock reacquisition when lock is broken and adding resonant gain filters at specific resonant bands to facilitate calibration of the interferometer.
Gravitational wave detectors, like LIGO, require high-quality test mass mirrors to accurately measure the minute changes caused by gravitational waves. While fused silica has been the preferred material for test masses, the upcoming cryogenic upgrades of gravitational wave detectors require materials with exceptional properties at low temperatures and compatibility with 1550-nm laser. Crystalline silicon has emerged as a potential alternative to fused silica due to its mechanical, optical, and thermal characteristics. However, birefringence in silicon can negatively impact detector performance by reducing the signal-to-noise ratio. This project aims to investigate birefringence in crystalline silicon through laser depolarization techniques. The experimental setup involves a 1550 nm laser, polarizers, a half-wave plate, and photodiodes. Lock-in amplifiers and low-pass filters are employed to enhance sensitivity and reduce noise in the measurement system. The project aims to achieve measurements of birefringence fluctuations at the order of 10-15/rtHz at 100 Hz. The results will provide valuable insights into the suitability of crystalline silicon for future gravitational wave detectors and contribute to our understanding of material properties at extreme conditions.
All second-generation gravitational wave detectors use laser radiation pressure to calibrate the detector output signals. A significant source of uncertainty for these Photon Calibrator (Pcal) systems, one usually installed at each interferometer end station, is unintended rotation of the suspended mirrors. Comparing the two Pcal system calibrations enables reducing calibration uncertainty. At the LIGO Hanford Observatory (LHO), this X/Y comparison has been calculated continuously since May 2023 and has been stable within 0.05 %. This stability can be leveraged to quantify interferometer and Pcal beam position offsets. Reducing Pcal beam position errors minimizes unintended rotation. Moving the position of one Pcal beam by 2.5 mm at the LHO X-end station is expected to the change the X/Y comparison by as much as 0.0054, more than ten times the observed X/Y comparison variations. A second measurement with the Pcal beam displaced orthogonally can be used to quantify both the magnitude and direction of the interferometer beam position offset. Making similar measurements after known displacements of the interferometer beam can be used to quantify center of force offsets for the Pcal beams. This method would provide a means for minimizing one of the largest sources of uncertainty for the Photon Calibrator systems.
The descriptions below consist of a list of broad areas of interest within each project topic.
LIGO data is both non-Gaussian and non-stationary. Fourier transformed LIGO data contains strong features at particular frequencies which can pollute searches for gravitational waves from long-duration sources like spinning neutron stars and a stochastic gravitational wave background. LIGO data also contains short bursts of noise called 'glitches' that can confuse searches for transient gravitational waves including black hole and neutron star mergers. This project will investigate sources of detector noise, quantify their impact on the astrophysical searches, and explore methods for improving astrophysical search performance.
Interest in / experience with python and/or signal processing is recommended.
One of the primary goals in GW astronomy is to identify weak signals in very noisy detector data. The inspiral and merger (coalescence) of compact stars (neutron stars and black holes) produce a GW signal that is well modeled using numerical simulations of General Relativity to predict the signal waveform. We search for these signals using matched filtering. Matched filter searches on LIGO data use hundreds of thousands of waveforms models that span different object masses and spins. To date, dozens of such signals have been detected in this way.
Students interested in searching for compact binaries can study the origin, evolution, and morphology of these signals to learn as much as possible about their implications for astrophysics and cosmology.
Gravitational waves carry information about the astrophysical sources that create them, which can be measured with precision by comparing observed data to models and simulations. In particular, source masses, angular momenta, location on the sky, and distance from Earth (among other things) all affect the amplitude or phase evolution of an observed GW signal.
Students who work on parameter estimation will be at the interface between theory and experiment, analyzing LIGO data and developing methods to improve our knowledge of the explosive sources of gravitational waves.
Interest in / knowledge of Python, signal processing, and statistics is recommended.
Rapidly spinning neutron stars in our galaxy will produce gravitational waves that are essentially at one frequency, with very long duration - essentially continuous waves. In order to produce GWs, these sources cannot be perfectly spherical, instead they must have some asphericity. This roughly amounts to something like a 1 mm high mountain sitting on the surface of a neutron star, the shape and height of which can teach us about how matter behaves at super-nuclear densities. Students will have the opportunity to look for potential LIGO signals that correlate with known pulsars in frequency and sky location, as well as sources corresponding to neutron stars not observed with light-based telescopes.
Interest in / experience with programming, signal processing, and Bayesian statistics is recommended.
In the new era of gravitational wave astronomy, our primary goal is to measure source parameters and draw astrophysical inferences from observed signals, as accurately as possible. To do this effectively, we require an accurate estimate of the calibrated strain, due to gravitational waves passing through our detectors. This is especially important for testing General Relativity using well modeled waveforms. Students who work in LIGO calibration will combine precision controls engineering with computationally efficient signal processing to provide such data in real time.
Interest in / experience with signal processing and Python is recommended; stunents will also learn some techniques from controls engineering.
Some of the GW signals that LIGO detects, such as the binary neutron star merger GW170817, will have gamma-ray, X-ray, optical/infrared, radio, or neutrino counterparts. In many ways this can be thought of as witnessing the same event with several different senses. But for many compact binary source types, LIGO is the one to catch them first, locate the source in the sky, and inform astronomers where to point their telescopes. Students who get involved in multi-messenger astronomy will analyze data and develop software to learn as much as possible from joint observations with other telescopes scattered across the world and in space.
Interest in / knowledge of Python, signal processing, image processing, and Bayesian statistics is recommended.
Breakthroughs in physics are often made at extremes, and the weakest of all interactions -- gravity -- is no exception. General relativity is the prevailing theory of gravity, which describes gravitation as curvature in space and time rather than as a force. Since the early 20th century, tests of general relativity were all done using measurements of Solar System objects where gravitation is relatively weak. However, with every LIGO observation of extremely compact sources such as neutron stars and black holes comes a unique opportunity to test general relativity using extreme spacetime curvature, pushing the theory to its limits. Students who work on such projects will test this foundational principle of modern physics using the cutting-edge LIGO experiment.
Numerical relativity is a powerful tool for simulating the gravitational wave signatures of binary black hole mergers, as well as the recoil response of the system after merger. One key direction in current research is using simulations, population models, and observations of black holes to understand more about the evolution of black hole progenitor stars and binary black hole systems. Another direction is contributing to the body of waveforms that searches for modeled gravitational waves signals in LIGO data can draw on by improving the accuracy of phenomenological models and/or the efficiency of numerical simulations.
Interest in / experience with signal processing and Bayesian statistics are recommended; students will also learn a great deal about general relativity.
Some anticipated sources of gravitational waves are not well modeled, and therefore do not have predictable waveforms. Examples are: galactic core-collapse supernovae, magnetar bursts, hypothetical cosmic string cusps, and compact binary mergers that are not well described by General Relativity (or by the waveforms predicted by General Relativity that may leave out crucial effects such as eccentric orbits). For such sources we use model-agnostic transient (or 'burst') gravitational wave searches. Burst searches are particularly useful to explore perhaps the most exciting potential gravitational wave signal of all: the unknown. As these searches are more susceptible to noise sources, current work explores methods to better differentiate astrophysical signals from detector noise.
Interest in / experience with programming in a terminal and/or via a remote connection is recommended.
It is very likely that echoes of the Big Bang are currently reverberating around the Universe in the form of gravitational waves, which form a stochastic cosmological background (by analogy with the cosmic microwave background). In addition, there will be a stochastic astrophysical "foreground" formed by the superposition of many weak signals from compact binary mergers, core collapse supernovae, and all other astrophysical sources in the universe. A key science goal for Advanced LIGO is to detect this background by searching for long-lasting coherent power between multiple gravitational wave detectors.
Interest in / experience with programming and statistics is recommended.
Caltech LIGO Summer Undergraduate Research Program has been in existence since 1997. Below are project titles and abstracts from recent years: