Gravitational wave detectors consist of multiple resonant optical cavities. The laser field exiting one cavity is the input to the next. However, non-idealities in the surface geometry and positioning of the optics cause the laser mode exiting one cavity to imperfectly match the mode supported by the next, resulting in optical losses which degrade the sensitivity to gravitational waves. Higher order adaptive optics hold the potential to eliminate these losses by finely "canceling" imperfections in the laser beam wavefront. This project will model the resonant behavior of the optical cavities in LIGO, then design and test elements of a suitable optical actuator in the lab.
Python programming, finite-element analysis (e.g., COMSOL), and a knowledge of basic optics are recommended.
Seismic noise causes the LIGO mirrors to move and thereby, the position of the laser beams on the mirrors. The coupling of laser noise sources from the laser to the gravitational-wave readout is modulated by this beam motion. In this project, we will use the video cameras from a prototype interferometer on the Caltech campus that monitor the interferometer mirrors to determine the beam position as a function of time with high accuracy using a supervised learning approach with convolutional neural networks to reject image noise. This beam spot motion will then be used as an input to nonlinear regression algorithms to improve the LIGO sensitivity.
Knowledge of Python, image processing, and CNNs will be useful. recommended.
With the advent of gravitational-wave astronomy, techniques to extend the reach of the detectors are desired. In addition to the stellar mass black hole and neutron star mergers already detected, many more are below the surface of the noise, available for detection if the noise is reduced enough. This project applies machine learning algorithms to gravitational-wave detector data and auxiliary channels to reduce the noise due to instrumental artifacts (analogous to noise-canceling headphones). This framework is generic enough to subtract both linear and non-linear coupling mechanisms, and teach us about the mechanisms which limiting detector sensitivities. Using realistic assumptions about coupling mechanisms, we seek to reduce the noise floor to lead to sensitivity improvements for binary systems. The expectation is that this work can be generalized to other time series regression analyses in all areas of science.
Interest and knowledge of Python, Machine Learning methods, and FFT / signal processing are recommended.
Fast lock acquisition and high duty cycle operation of the LIGO interferometers relies on hundreds of feedback loops keeping the various subsystems under control. Improving the performance of these feedback loops, particularly extending linear control to non-linear control, could dramatically improve the ease of keeping the interferometers in observing mode. This project will explore the applications of novel machine learning techniques to design and implement non-linear feedback control on a prototype system (inverted pendulum on a cart), and extend it to some of the simpler subsystems of the 40m prototype interferometer.
Experience with mechanics, electronics, and python/machine learning/Neural-Network tools are desirable.
One limiting source of noise for gravitational wave detectors is thermal (Brownian) noise, and it is also a source of decoherence in a broad class of optomechanical measurement devices operating at or near their quantum limits. This project uses a recently developed testbed for measuring the internal friction of thin disk resonators to explore open problems in controlling and optimizing such systems, such as: (i) Testing candidate materials for low-loss coatings for LIGO optics, (ii) Optimal experimental design for measuring resonators with nonconventional topologies, (iii) New or improved methods for fast, non-contact temperature readout and control.
Experience with vacuum systems, cryogenics, FEM, and precision measurement would be useful for this project.
Seismic activity is one of the major noise sources for gravitational wave detectors. For understanding and eliminating seismic noises, it is effective to scrutinize the source and statistics of persistent and transient seismic activities. We form a seismic radiometer, employing the multiple seismometers located at the LIGO 40m prototype interferometer. Using the time-series data of the seismometer outputs, we evaluate the seismic heat map around the campus, which allows us to investigate anthropogenic activities and its statistics. We utilize known artificial vibration to precisely calibrate the response of the seismometers. We hope to build an interactive graphical display of this seismic heatmap on a web site as a final product of the project.
Interest and knowledge of Python and signal processing are recommended.
Low-noise and cryo-compatible sensors and actuators will be required to control the suspended mirrors of the next-generation gravitational wave interferometers. This project will involve design work, prototyping, and testing of a compact optical sensor and linear motor assembly in a cryogenic setting. Factors to be considered include the sensing noise, the actuator strength and its magnetic noise coupling, the range and tolerances required to accommodate ground motion and thermal expansion effects, and the thermal loading and temperature characteristics of the opto-electronics.
Thermal noise is a limiting noise source in many of the LIGO sensors. Cooling of photodiodes and optical components to cryogenic temperatures can reduce this noise greatly. A way to achieve refrigeration with minimal disturbance is by pumping a phononic transition of a solid with a red-detuned laser, thus achieving cooling by fluorescence.
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.
Projects that may be offered in Summer 2020:
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.
Projects that may be offerefd in Summer 2020:
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.
Projects that may be offered in Summer 2020:
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: