Tabletop device might snare gravitational waves using tiny diamonds

Gravitational waves
Making waves: artist’s impression of gravitational waves being broadcast by a pair of black holes. (Courtesy: LIGO/T Pyle)

Rather than the kilometre-length observatories of today, future gravitational-wave detectors could be just a few metres long. That is the goal of physicists in the UK and the Netherlands, who have put forward a design for a matter-wave interferometer that would rely on the superposition of tiny objects such as diamond crystals rather than laser beams. They say that the device would be sensitive to low- and mid-frequency gravitational waves.

Gravitational waves were first observed directly in 2015, when the LIGO observatory in the US picked up the emission from a pair of merging black holes. These black holes broadcast a series of ripples through space-time that caused the pairs of perpendicular arms making up LIGO’s interferometers to undergo a series of miniscule expansions and contractions. Those tiny changes were registered as variations in the interference between laser beams sent along the arms.

Such laser-based observatories, however, are very large. A passing gravitational wave will typically induce fractional length changes on the order of 10-19 or less, meaning that the detector’s arms must be several kilometres long if the facility is to yield a reasonable signal above the many sources of background noise. In the case of LIGO, each arm extends for 4 km.

Tiny wavelength

The latest work proposes a far smaller type of observatory based on interfering beams of matter rather than light. The particles in question would have a mass of about 10-17 kg, corresponding to a de Broglie wavelength of 10-17 m. This is about 100 billion times smaller than the wavelength of laser light used in existing observatories and could be exploited in an interferometer measuring as little as 1 m in length.

The scheme has been put forward by Sougato Bose, Ryan Marshman and colleagues at University College London, together with researchers at the universities of Groningen and Warwick. It involves a Stern-Gerlach interferometer and nanometre-sized crystals containing embedded spins. Although several types of crystal could do the job, the researchers suggest diamond containing a nitrogen-vacancy centre spin – a system already used to make spin-qubit quantum computers.

The device has yet to be built, but it would involve trapping, uncharging and cooling the crystals before using microwaves to place their spins in a superposition of spin-0 and spin-1. Released from the trap and exposed to a suitable magnetic-field gradient, the two spin states would then separate out in space so that the spin-0 component travels forward horizontally while the spin-1 part follows a parabolic trajectory. After a certain distance, the two spin states would meet up again.

Spin-separated states

Bose and colleagues originally developed this type of interferometry to make very precise measurements of gravitational acceleration to study the quantum character of gravity. The idea is that the spin-separated states experience different accelerations as they follow different paths through the gravitational field. This results in a phase difference between them at the far end, which can be measured by counting the relative abundance of spin states over a given number of runs.

However, the researchers realized that the device could in principle be made sensitive enough to also detect gravitational waves. In this case, a wave changes the spatial separation of the two paths as it passes through the apparatus – resulting in a sinusoidal oscillation of the spin states’ phase difference.

Bose and colleagues say that their device would have a number of significant advantages compared to laser interferometers. Because the phase difference accumulates only while the crystals are traversing the interferometer, the output signal would be independent of any thermal, seismic or other noise that occurs before the particles are placed in a superposition. What is more, the absence of laser-based position measurements removes radiation pressure noise, while exact knowledge about the number of nanoparticles in the interferometer avoids shot noise.

Underground or in space

The researchers say that their interferometer – with perhaps several copies operating in parallel – would be most sensitive to relatively low-frequency gravitational waves. Located underground, they say it could cover part of the range to be targeted by the LISA space-based observatory – about 10-6  Hz-10 Hz. If operated in space, it should be able to cover all LISA’s proposed territory.

Shimon Kolkowitz of the University of Wisconsin-Madison in the US points out that many other proposals based on matter-wave interferometry use atoms to detect laser phase rather than gravitational waves themselves. The new approach is therefore more direct, he says, but also riskier. “[It is] based off of a technology that has yet to be realized and that will require major technical breakthroughs,” he says. “But it could be quite impactful.”

Bose says that he and his colleagues are confident they can overcome all the technical hurdles. In particular, they are looking to create a large magnetic-field gradient without having to generate a particularly high field – by sequentially turning on a series of flat carbon nanotubes in a stepped formation to approximate a particle’s parabolic trajectory. Looking to build a small-scale prototype within a decade, he “optimistically” estimates that the cost of reliable solid-state qubits and a large-scale atomic interferometer could each run into the tens of millions.

A paper describing the work will be published in the New Journal of Physics and is available as an accepted manuscript.

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