Detecting Gravitational Waves. Can Quantum Mechanics Help?

Secrets can be very hard to keep. The thought of having to wait five months to be able to talk about what is arguably the biggest scientific discovery in a century is incomprehensible. But for every member of the LIGO Scientific Collaboration (LSC), it was absolutely essential that nobody let the cat out the bag (or should that be box?). The time between the first hints that the LIGO detectors had measured gravitational waves in September 2015 and the official press announcement in February 2016 was filled with the most thorough due diligence procedures imaginable, including checking the whereabouts of every member of the collaboration at the time of the event to rule out the possibility of a falsified signal. And there is no external experiment that can be asked to verify the results so the internal review process employed by the LSC must adhere to the strictest regulations. But, after five gruelling months of telecons, meetings, emails and sleepless nights, they finally had the privilege of announcing to the world that they had done it. They had detected gravitational waves.

But this is only the beginning. Of course it’s gratifying to ‘prove Einstein right’ but gravitational waves are only a small piece in that puzzle – the General Theory of Relativity has already correctly predicted  gravitational lensing, perihelion precession, gravitational redshift, the Shapiro effect, the Equivalence Principle and frame-dragging to name a few. Each of these has been achieved once the necessary technology for required measurements finally caught up with the prediction. And while the extent of practical application varies (GPS is always a favourite example of the necessity of GR), the contribution to astronomy of directly detecting gravitational waves cannot be overstated.

Perhaps now is a good time to admit my allegiances, so you can forgive the bias in this post. Before moving into the world of quantum optics, I studied gamma ray bursts and gravitational wave standard sirens as cosmological distance indicators for my thesis and then spent over two years working in the LSC developing the search for gravitational waves from the ringdown signal produced by merging black holes. So aside from an innate passion for all things GR-related, it was incredibly exciting and a huge privilege to work with so many people that have dedicated their entire careers to the search for gravitational waves. And now that they have been detected, we have an entirely new way in which to observe the Universe. So, how does it work?

Instead of considering gravity as a force, Einstein introduced the idea of matter shaping spacetime and in turn this warping dictates how matter, and indeed light, moves through spacetime (Figure 1).

Massive bodies warp spacetime

Figure 1. Massive bodies warp spacetime.
Image Credit: T. Pyle/Caltech/MIT/LIGO Lab

This relationship between the matter and resulting curvature is encoded in the field equations. When matter is accelerated, such as a star collapsing asymmetrically or a binary black hole system inspiralling and colliding, radiation is emitted in the form of gravitational waves (Figure 2).

Accelerating bodies radiate gravitational waves.

Figure 2. Accelerating bodies radiate gravitational waves. Image Credit: R. Hurt/Caltech-JPL

Einstein showed that gravitational radiation is quadrupolar in nature and obeys a wave equation in a manner similar to electromagnetic radiation, with the speed of propagation equal to the speed of light. These gravitational waves will stretch and compress spacetime as they pass, which suggests a plausible method of detection – we simply require a ruler of known length and a mechanism to monitor any change. Initial experiments employed Weber bar detectors: a passing gravitational wave could excite the resonant frequency of the bar. Unfortunately, it turns out that spacetime is incredibly stiff and a far more sensitive meter is required.

Hanford, WA and Livingston, LA are home to the Advanced LIGO detectors – Michelson interferometers with 4km long arms, which have recently undergone a five year upgrade to improve their sensitivity by up to a factor of 10 compared to the Initial and Enhanced LIGO detectors that previously operated at the same sites. In addition to this, the 600m GEO600 detector in Hanover, Germany is used for technology testing and development and the 3km Advanced Virgo detector near Pisa, Italy completes the current network. They work on the principle that a passing gravitational wave will stretch and squeeze spacetime, changing the distance between the two test masses that are delicately suspended at the end of the arms, thus producing an interference pattern (Figure 3). This signal is then compared to templates that are calculated theoretically and numerically in order to best-fit the source parameters. Two or more detectors must agree in order for a signal to be verified, with the time delay between the detections confirming the travel time of the signal. Ideally, three or more detectors online concurrently would provide an accurate sky location. The binary black hole merger announced in February serendipitously occurred during an engineering run of the two US-based detectors but Advanced Virgo was not yet operational. It is therefore not possible to fully constrain the sky location for that event.

A passing gravitational wave (plus and cross polarisations) stretches and squeezes the interferometer arms.

Figure 3. A passing gravitational wave (plus and cross polarisations) stretches and squeezes the interferometer arms.

Proving that it is possible to detect gravitational waves is obviously cause for great celebration. However, this is also the first ever direct detection of black holes. Until now, their presence has only been inferred by electromagnetic observations of accretion discs and gravitational interactions such as the orbits of stars around the galactic centre. Gravitational waves will provide a completely new way to observe the Universe, allowing us to not only confirm models of exotic objects such as neutron stars and black holes but also to watch in real time as they interact and evolve. Additionally, because gravitational waves pass through matter, the observations are not obscured by intervening galaxies or dust clouds. One of the big challenges is to probe the relic gravitational radiation from the Big Bang itself. Unfortunately, as with all things in science, there are limits to be overcome. Different sources emit gravitational radiation at different frequencies and, as with electromagnetic telescopes, a range of detectors are required. The current ground-based detectors are most sensitive around 100Hz and will be able to best target compact binary inspirals and supernovae events. Lower frequencies start to become limited by gravity-gradient noise and therefore space-based detectors are the natural solution. The LISA Pathfinder mission is currently orbiting Lagrangian point L1 in a bid to test the technology required for a million-km scale, 3-arm interferometer that will probe the milliHertz end of the spectrum, detecting the local neighbourhood population of binary white dwarfs, neutron stars and galactic black holes. However, there is a more fundamental challenge than just bandwidth considerations.

 GWG, University of Birmingham

Figure 4: Noise sources in Advanced LIGO detectors.
Image Credit: GWG, University of Birmingham

The current ground-based detectors are so sensitive that they can measure relative strains of the order of 10-22. This has been achieved in part by reducing the noise caused by the test-mass suspensions and coatings and has been so effective that the detectors are essentially quantum noise limited (Figure 4). Do we therefore need to consider quantum metrology? The object (mirror) and light (meter) are coupled by a linear interaction Hamiltonian and the standard quantum limit (SQL) is governed by the mechanical susceptibility of the object to the force exerted (the kicks from the photons on the mirrors). There is a huge interest in the bid to beat the SQL but current investigations yield no better than a factor of 3 improvement in the wide band (which is required as the frequency of the gravitational wave is unknown). Do we simply have to accept that this is a fundamental limit? What contribution can the world of quantum mechanics make to the nascent field of gravitational wave astronomy? If this is something that interests you, more information can be found in “Quantum Measurement Theory in Gravitational Wave Detectors”, Danilishin & Khalili, Living Rev. Rel. (2012).

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