Northwestern looks to the heart of the universe with robust quantum sensors

Using Boulder Opal, our quantum control infrastructure software for R&D teams, researchers from Prof. Kovachy’s group at Northwestern University designed an atomic interferometer based on optimized pulses with performance levels unachievable using standard techniques. In this paper published on Physical Review A, the team describes how they used Boulder Opal’s flexible optimization tools to create high-quality pulses that show sustained performance even in the presence of the multiple experimental imperfections that affect their quantum interferometer.

“The breadth and flexibility of Boulder Opal allowed us to create our own optimization scenario and obtain pulses robust to the five most relevant experimental noise sources at the same time! This will be crucial in the development of atomic interferometers to detect dark matter and gravitational waves at currently unexplored frequencies.”

Zilin Chen, Postdoc at Northwestern University.

Detecting subtle effects using atoms

Detecting phenomena like dark matter or gravitational waves is notoriously hard due to the minuscule effects that they produce in laboratories on Earth. Take the LIGO experiments to detect gravitational waves, for example, they are designed to measure a huge mirror moving by one billionth of a billionth of a meter! To achieve such sensitivity, laser light is split into two beams that travel over two 4km long paths with mirrors at their ends. The light is reflected back and recombined to produce an interference pattern in a configuration called an interferometer.

A small relative change between the two paths, such as the one produced by the presence of a gravitational wave, shifts the so-called interference pattern of bright and dark light that can then be detected in the experiments.

To visualize this, consider how waves at the beach combine to grow or cancel one another. Any change in the shape of the shoreline leads to a different pattern of peaks and troughs.

Using atom interferometers to detect gravitational waves

In order to perform such challenging precision measurements, the research group led by Prof. Tim Kovachy at Northwestern University is exploring a different path. The team is using atom interferometers to detect the miniscule effects of gravitational waves.

These devices are just like the interferometers used in the LIGO experiment, except the role of light and matter is inverted! Instead of light waves being split and combined by bouncing off of mirrors, waves of matter are split and recombined using laser light! This device fundamentally exploits the wave-like nature of matter under the rules of quantum physics to measure very small differences in the paths taken by the two beams of atomic waves.   

In this case, a cloud of cold atoms receives a kick that quantum mechanically splits it in two (creating what’s called a superposition), with half of the atoms moving upwards and the other half downwards. This kick comes from a short pulse of laser light that changes the state of the atoms. After a while, the atoms are kicked back in the opposite direction and the two clouds merge together. When they recombine they produce a matter-wave interference pattern - peaks and troughs measurable by a special detector. As in the previous case, small changes in the paths traveled by the two halves induced by the quantity being measured translates into a detectable signal in the interference pattern.

Because quantum systems are extremely sensitive to small changes in their environment, atomic interferometers make exceptional candidates for precision sensors. Furthermore, since the measurement signal output by such sensors depends only on atomic properties that do not change over time, these devices also promise a much more reliable signal which isn’t subject to slow changes as conventional sensors age or experience varying environmental conditions. Better stability allows them to run longer, average together more data, and ultimately pick out smaller signals from the background noise.

Kicking atoms harder for more sensitivity

Gravitational waves are very weak signals. In order to detect them, one requires a well tuned sensor - one able to measure even tiny deviations. In the case of an atom interferometer, that often means setting up the device just the right way to make it as sensitive as possible. In any interferometer, this is achieved by making the device itself as big as possible.

The team at Northwestern is doing this in two ways. First, they’re making their interferometers big. Really big. The team is part of the MAGIS100 collaboration building an interferometer 100m tall!

But they’re also making sure the atom interferometer takes advantage of all of that distance by kicking the atoms really hard to separate them further. This is accomplished using a technique known as large momentum transfer (LMT), as they can consider the application of hundreds, or even thousands, of pulses (i.e. lots of little kicks) on their strontium atoms before they are measured.

While this works in theory, in practice small errors add up as the number of pulses increase, limiting the scalability of the LMT procedure. Noise and imperfections in the experiment build up gradually until the signal of interest is totally lost: noise in the amplitude of the driving field, inhomogeneities across the atoms, variations in the magnetic field, or noise in the laser polarizations, all conspire to prevent these devices from operating at peak performance.

Enabling robust interferometer design with the right software

Getting to peak performance in a quantum device is the domain of quantum control - our area of expertise!

The expert team at Northwestern apply optimal control to quantum devices - these are techniques designed to extract greater performance from quantum hardware by manipulating it in just the right way. There are many techniques stretching back decades designed to improve the performance of the light-matter interactions at the heart of an atom interferometer. But the Northwestern team set out to achieve more and turned to our team at Q-CTRL for help.

Facing a broad array of sources of noise and error, the team at Northwestern knew they couldn’t rely on existing techniques; their problem was much harder than anything ever treated before. It required consideration of more energy levels in the atoms - 20 instead of two. It required simultaneous suppression of five different noise sources. And it required the treatment of errors that change in time, instead of the usual static errors (for instance, miscalibrations).

The team at Northwestern is seeking to implement these new control solutions in an exciting experiment searching for dark matter using atom interferometry. Accordingly, they also wanted to ensure the pulses they designed could actually be implemented on real hardware without distortion due to fast changes in the signal - that is, to keep the control solutions from changing too rapidly and making them impossible to use, they now needed a new element of the optimization called a constraint. Constrained optimization is effectively impossible for most standard research tools.

Using Boulder Opal to design error-robust controls

Designing error-robust controls subject to complicated noise processes and constraints is a key part of Boulder Opal’s power. It comes from an intuitive graph-based framework to represent all the elements of challenging optimization problem as nodes in a graph - connect them the right way to represent relationships (e.g. node 1 is a cost and node 2 is a source of noise contributing to that cost), and even very complex calculations can be handled easily.

The team at Northwestern encoded their problem as a graph and applied Boulder Opal’s gradient based optimization engine. In particular they used a technique based on “Stochastic Optimization” in which an agent attempts to find a robust solution by calculating the impact of noise on the actual action of the quantum operation being optimized, sampling from a distribution. It’s a technique particularly well suited to handling potentially large sources of noise. They even pushed a bit further and employed efficient strategies for batching to speed up the calculation.

The results were incredible.

In a regime where optimal and robust control has seen limited application due to the technical difficulties of these calculations, they found solutions which suppressed all of their different sources of noise and performed up to 10x, better than any solutions that had been studied previously. These results became possible because of the power and flexibility afforded by Boulder Opal.

As the team looks forward, it’s clear that robust control solutions developed by Boulder Opal have a major role to play in pushing atom interferometry to the limits in the search for Dark Matter. We’re excited to support exceptional scientific missions such as this, and we look forward to supporting the Northwestern team along the way!

‍

Reference: Enhancing strontium clock atom interferometry using quantum optimal control, Phys. Rev. A 107, 063302