by Michael Goldman
figures by Michael Gerhardt

LIGO’s observation of gravitational waves was perhaps the most stunning physics discovery of the past several years. Two black holes, each 20 to 30 times as massive as the sun, collided in an event of unimaginable violence and shook the very fabric of the space around them. About 1.4 billion years later, in February of this year, the LIGO (Laser Interferometer Gravitational-Wave Observatory) collaboration announced that they had measured these ripples in space, called gravitational waves, shaking two pairs of mirrors by 1/1000 the diameter of a proton, or about one billionth of one billionth of a meter. (A few minutes after that, the website of the journal that published their result promptly collapsed under the extraordinary glut of traffic.) The discovery was immediately hailed as a seminal achievement of astrophysics and a jaw-dropping experimental tour-de-force.

Opening up new views on the universe with gravitational waves

The discovery of gravitational waves was groundbreaking in part because it opened an entirely new method of looking at the universe. In effect, we had only ever looked at the universe; now, LIGO enables us to listen as well. We first looked up with our eyes, then collected that light with ever-improving telescopes, then branched out into higher-frequency x-rays and lower-frequency radio waves. All of these observational techniques, though, relied on the same electromagnetic radiation. The gravitational waves that LIGO detected are fundamentally different because they are ripples in space itself rather than waves of electric and magnetic fields. This enables us to study objects, like neutron stars and black holes, that are massive and astrophysically interesting but don’t emit measureable light, opening up entirely new fields in astronomy.

For a sense of scale, LIGO’s mirrors, whose motion the researchers measured with stunning precision, each have a mass of 40 kg (88 lbs.), roughly equivalent to the weight of a typical 12-year-old boy, and are separated from each other by 4 km (2 ½ miles). However, one aspect of the discovery that did not receive as much widespread attention was the painstaking attention that researchers have had to pay not to the very large parts of the experiment but to the very small. LIGO has already achieved such breathtaking sensitivity that researchers must now contend with the foundations of quantum mechanics, the branch of physics that governs the atomic world, in order to push the experiment farther.

Bumping up against a fundamental principle of quantum mechanics

LIGO is now contending with one of the most fundamental ideas in quantum mechanics, the Heisenberg uncertainty principle. Let’s first approach this principle through analogy: imagine yourself whistling and snapping your fingers. Your whistle has a well-defined pitch but does not occur at a single well-defined time; you can whistle a perfect middle C but the sound has to extend over some period of time in order for you to tell what note it is. On the other hand, your snap occurs at a well-defined time but does not have a well-defined pitch; you know exactly when the snap happens but the sound itself consists of many different pitches at once. In general, a sound cannot both occur at a well-defined instant in time and have a single, well-defined pitch.

Figure 1: According to the Heisenberg uncertainty principle, if a particle like an atom or electron has a well-defined position, then it must have an ill-defined velocity, and vice versa.

The Heisenberg uncertainty principle essentially says that the same concept applies to microscopic particles like atoms and electrons. The more precisely we know where a particle is (analogous to the time when a sound occurs), the more uncertain we are about how fast the particle is moving, or its momentum (analogous to the sound’s pitch). In other words, there is always some uncertainty in our knowledge of the particle’s position and some uncertainty in our knowledge of the particle’s momentum. More quantitatively, the Heisenberg uncertainty principle says that if we take these two uncertainties and multiply them together, then the result must always be greater than some fundamental minimum value.

It’s important to note that the Heisenberg uncertainty principle is a fundamental limitation, not a technical one. It’s not that a snap happens too quickly for our ears to judge its pitch accurately. Rather, the mathematics of sound dictate that a sound, like a snap, that occurs in a very short period of time must inevitably be composed of a number of different pitches. Similarly, we can’t hope that a better microscope will someday enable us to measure both a particle’s position and its momentum with perfect precision; the mathematics of quantum mechanics simply tell us that a particle that is located at a well-defined point in space must, as odd as it sounds, be moving at a range of different speeds simultaneously.

Figure 2: The Heisenberg uncertainty principle also applies to light waves. If the light’s oscillating electric field has a well-defined amplitude, then its phase (when the field crosses through zero) must be ill defined, and vice versa.

This principle applies not only to particles like atoms and electrons but also–and here we see the importance to LIGO–to light waves. We can think of light as a wave of oscillating electric and magnetic fields, which have an amplitude (the maximum strengths of the fields) and a phase (the times when the field strengths pass through zero, measured relative to some external reference). Just as there must always be some uncertainty in the position and momentum of an electron, there must also be some uncertainty in the amplitude and phase of a light wave.

Figure 3: The LIGO setup, where a partially reflective mirror splits and then recombines a laser beam, is called an interferometer. The two halves of the beam interfere destructively when the interferometer is balanced. When a gravitational wave passes the detector, it disturbs this balance and allows light to reach the detector.
Figure 3: The LIGO setup, where a partially reflective mirror splits and then recombines a laser beam, is called an interferometer. The two halves of the beam interfere destructively when the interferometer is balanced. When a gravitational wave passes the detector, it disturbs this balance and allows light to reach the detector.

How LIGO works

To see why this uncertainty, or noise, is a problem, let’s look at how LIGO measures gravitational waves. Essentially, they fire a laser, say from the west, at a partially reflective mirror, which reflects half the beam at a right angle toward the north and lets the other half pass through going east. These two halves travel to distant mirrors placed 4 km to the north and to the east, which together form a huge L shape. This arrangement of mirrors, known as an interferometer, is balanced so that when the two beam halves arrive back at the first mirror, they interfere so that no light passes through to reach a detector placed to the south. When a gravitational wave passes by the detector, it distorts the lengths of the two arms, breaking this delicate balance and allowing light to pass through to the detector.

This simple picture, where light at the detector heralds the arrival of a gravitational wave, is how the detector works in principle. In practice, however, the experiment is vulnerable to a bewildering variety of noise, like thermal motion of the atoms in the mirrors, earthquakes, traffic on nearby roads, and even people shooting at the detectors. LIGO can counteract many of these noise sources by isolating the mirrors and actively cancelling spurious vibrations, like how noise-cancelling headphones both muffle and actively cancel out the roar of a plane’s engines, and by trusting that the same loud truck or seismic vibration won’t show up simultaneously in data from the observatories in Louisiana and Washington state, as a gravitational wave would. The noise that they are most concerned about comes from the light itself.

When searching for gravitational waves with frequencies above 50 Hz (roughly the lowest pitch humans can hear), the dominant noise source is shot noise. Shot noise, which is related to the light’s phase noise, stems from the fact that, in addition to being an electromagnetic wave, light can be thought of as a collection of quantized particles, called photons, that randomly hit the detector like rain drops pinging on a metal roof. If you want to measure how much rain hits your house every second, then the fact that the rain falls not in a constant stream but in discrete drops, slightly more one second and slightly fewer the next, will introduce noise into your measurement. Below 50 Hz, however, radiation pressure noise dominates. Photons carry momentum, so the light pushes on the mirrors at the ends of the arms like wind pushing on a ship’s sail, an effect known as radiation pressure. Noise in the light’s amplitude causes fluctuations in this pressure, which can cause the mirrors to shake and mimic a gravity wave.

Squeezing the uncertainty out of LIGO’s light

The LIGO collaboration would seem to be stuck then, hemmed in by phase noise on one side and by amplitude noise on the other, with both fundamentally required by quantum mechanics. The Heisenberg uncertainty principle, however, only sets a lower limit on the product of the phase noise and amplitude noise, not on either one individually. Physicists can therefore reduce one type of noise at the expense of increasing the other type, creating what is known as squeezed light. Essentially, they can squeeze the uncertainty out of the component, either the light’s phase or amplitude, to which the experiment is sensitive and put it in the component to which the experiment is relatively insensitive.

This advanced quantum optics technique is especially tricky in LIGO’s case because the experiment is sensitive to phase noise at higher frequencies and to amplitude noise at lower frequencies. Recently, though, researchers at MIT precisely pulled off this balancing act in a series of demonstrations. First, by passing carefully controlled light through a crystal with certain optical properties, they created a state of light whose noise profile was precisely tuned to match LIGO’s exacting needs, simultaneously reducing the light’s amplitude noise at low frequencies and its phase noise at high frequencies. Using this state of light, researchers will be able to reduce the effects of both shot noise and radiation pressure noise on LIGO’s sensitivity, giving it a significant boost.

When this squeezed light technique is integrated into the main LIGO measurement sequence in an upcoming upgrade, it is expected to increase the volume of space that LIGO can probe by a factor of 2. Along with other improvements, LIGO’s sensing volume could be boosted by as much as a factor of 10, which would increase the number of astronomical events, like two black holes crashing together, that LIGO is able to observe by a corresponding factor of 10. LIGO made one observation of gravitational waves roughly every two months during its most recent measurement run, so such historic events might soon become weekly occurrences as LIGO expands its reach. It has been said that these first few observations of gravitational waves have opened a new window on the universe, enabling us for the first time to hear it rumble as well as see it shine. However, with physicists pushing the boundaries of quantum optics to make LIGO ever more sensitive, it seems that this window has only just been cracked open.

Michael Goldman is a Ph.D. student in atomic physics at Harvard University.

For more information

SITN’s write-up of the discovery
New York Times announcement
New Yorker profile of the LIGO project
Longer explanation of Heisenberg uncertainty principle
More detailed description of squeezed light

Cover image of LIGO Hanford from here

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