Vedika Khemani, assistant professor of physics at Stanford University, has been awarded a New Horizons in Physics Prize from the Breakthrough Prize Foundation. Khemani was recognized “for pioneering theoretical work formulating novel phases of non-equilibrium quantum matter, including time crystals.”

Vedika Khemani (Image credit: Rod Searcey)

Time crystals got their name for the fact that, like crystals, they are structurally arranged in a repeating pattern. But, while standard crystals – like diamonds or salt – have an arrangement that repeats in space, time crystals repeat across time forever. Importantly, they do so without any input of energy, like a clock that runs forever without batteries. Khemani’s work offered a theoretical formulation for the first time crystals, as well as a blueprint for their experimental creation. But she emphasizes that time crystals are only one of the exciting potential outcomes of out-of-equilibrium quantum physics, which is still a nascent field.

“None of the world is in equilibrium; just look out your window, right? We’re starting to see into these vastly larger spaces of how quantum systems evolve through experiments,” said Khemani, who is faculty in the School of Humanities and Sciences and a member of Q-Farm, Stanford’s broad interdisciplinary initiative in quantum science and engineering. “I’m very excited to see what kinds of new physics these new regimes will bring. Time crystals are one example of something new we could get, but I think it’s just the beginning.”

The $100,000 New Horizons Prize in Physics is given each year to up to three “promising junior researchers who have already produced important work,” according to the prize website. New Horizons prizes are one of three groups of Breakthrough Prizes in physics – the others are the $3 million Special Breakthrough Prize and the $3 million Breakthrough Prize. The Breakthrough Prizes also recognize researchers in mathematics and life sciences. Called the “Oscars of Science,” the prizes are celebrated at a gala award ceremony presented by superstars of movies, music, sports and tech entrepreneurship. Since the prizes began in 2012, 10 Stanford faculty and researchers have won Breakthrough Prizes.

Time crystal surprise

The concept of “time crystals” was first proposed in 2012 by physicist and Nobel laureate Frank Wilczek, but the idea was met with significant skepticism and comparisons to the impossible perpetual motion machine. In 2014, shortly after Wilczek’s proposal, it was shown by Masaki Oshikawa and Haruki Watanabe that fundamental laws of thermodynamics provably forbid the existence of time crystals. (Watanabe is a co-recipient of the New Horizons Prize.)

Thus, Khemani wasn’t thinking of time crystals at all as she went about her graduate work at Princeton University on non-equilibrium quantum physics. But in 2016, a reviewer for a preprint paper co-authored by Khemani pointed out that she and her colleagues had, without intending to, outlined a working model for time crystals.

“I think if we had set out to find the time crystal we would have run into the same kinds of objections as Wilczek,” said Khemani. “Instead, we were thinking about: How do we generalize the ideas of quantum phases of matter to systems that are out of equilibrium?”

Khemani and her doctoral advisor, Shivaji Sondhi, a professor of physics at Princeton University, were working on the problem of many-body localization. In a many-body localized system, particles get “stuck” in the state in which they started and can never relax to an equilibrium state. As such, these systems lie strictly outside the framework of equilibrium thermodynamics, which underpins our conventional understanding of all phases of matter.

Sondhi and Khemani worked with Achilleas Lazarides and Roderich Moessner at the Max Planck Institute to figure out how to think about phases of matter in many-body localized systems that are periodically driven in time, for instance by a laser. They found that, while equilibrium thermodynamics goes out the window, the possibility of formulating phases of matter need not. In addition to abstract theoretical formulations, they studied a concrete model: a periodically driven system of Ising spins. (The Ising model is often described as the “fruit fly of statistical physics” and has been extensively studied in equilibrium to understand fundamental phenomena, such as magnetism.)

These researchers found a number of phases in the out-of-equilibrium Ising model, including a novel one in which the system displays a stable, repetitive flip between patterns that repeat in time forever, at a period twice that of the driving period of the laser. (As required by the definition of time crystals, the laser does not impart energy into the system.) The phase Khemani and co-workers had found was, in fact, a time crystal – the out-of-equilibrium setting in which they were working allowed them to evade the constraints imposed by the laws of thermodynamics.

From theory to experiment

In the months that followed the preprint, important properties about the new phase were worked out by Khemani and her collaborators, notably Curt von Keyserlingk at the University of Birmingham, as well as a by Dominic Else, Bela Bauer and Chetan Nayak at Microsoft Station Q. (Else and collaborators also independently identified Khemani’s model as a time crystal, and Else is a co-recipient of the New Horizons Prize.) It was found that the phase displays a remarkable amount of robustness and stability. Then, various early experiments in 2017 showed promising precursors of the phase – although they were ultimately found to not realize a stable many-body time crystal.

Khemani describes work in the years that followed as creating a “checklist” of what actually makes a time crystal a time crystal, and the measurements needed to experimentally establish its existence, both under ideal and realistic conditions.

In 2020, Matteo Ippoliti, a postdoctoral scholar at Stanford working with Khemani, and others published a proposal for experimentally realizing a time crystal using the unique capabilities of Google’s Sycamore quantum computer. Following this proposal, this summer, Ippoliti and Khemani, collaborating with the large Google Quantum AI team, published a preprint paper detailing the experimental creation of the first-ever time crystal on Google’s device. That paper is now undergoing peer review.

Khemani sees great promise in these types of quantum experiments for many-body physics.

“While many of these efforts are broadly motivated by the quest to build quantum computers – which may only be achievable in the distant future, if at all – these devices are also, and immediately, useful when viewed as experimental platforms for probing new nonequilibrium regimes in many-body physics,” said Khemani.

As for the award recognizing all of this work, Khemani described how it reflects the bigger picture. “This is called the ‘New Horizons’ prize and I do think we are looking at new horizons in physics,” she said. “There are people at Stanford who think about black holes and big astronomical questions talking to people who are trying to build quantum computers, talking to many-body theorists, talking to quantum information scientists. It’s really exciting when you start getting so many different perspectives and so many different new ways of looking at problems.”

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