How Anthony Leggett pushed the boundaries of quantum physics

In my first year of graduate school, I briefly shared an office with a quiet, older graduate student. When we finally managed some chit-chat, I learned that he was “working on theory of glasses with Tony.” Two things became clear: cracking the physics of glasses was difficult, and I really ought to have known who Tony was. I met him soon enough. A polite British man in his 70s, he spoke with the cadence of a life-long teacher and an incontrovertible twinkle in his eyes. His full name was Anthony James Leggett: a Nobel laureate, a knight of the British Empire, winner of countless prizes, an expert on the ultracold denizens of the quantum world, and a theorist who co-developed an influential test for probing just where that world might end, a question he pursued for decades. He passed away on 8 March, survived not only by his family but by countless inspired researchers to whom he was, in his characteristically humble way, also just Tony.

Leggett was born in South London in 1938 and attended a Jesuit school where his father taught physics and chemistry, before pursuing a degree in classical literature, philosophy and ancient history at the University of Oxford. But the siren call of physics was louder than ancient texts and dead languages. He earned another degree, now in physics, and moved to the University of Illinois Urbana-Champaign (UIUC) for his postdoctoral training.

At the time, UIUC was rich with physicists studying new types of quantum matter and materials, many of which only revealed their exotic properties when made extremely cold. From his past work, Tony was already conversant in the physics of the ultracold, but the time at UIUC brought to his attention the problem of a rare form of helium called helium-3. In his Nobel prize lecture, he recounted the time physicists John Bardeen and Leo Kadanoff came into his office to tell him about an ultracold helium experiment happening in the basement. Leggett set out to capture facets of that experiment with mathematical equations but got sidetracked. He abandoned the calculation but would continue to have an on-again-off-again relationship with ultracold helium-3 for the next decade.

Serendipity stepped in to pull him back to the study of this strange matter. One day in 1972,  he was on vacation when rainy weather thwarted his plans to go hiking. So, he met with an experimentalist friend, Robert Richardson, instead. According to Leggett, what he heard that day changed his research career forever and led to his Nobel prize. Richardson described the results of a study of ultracold helium-3 where his team used an imaging method called NMR that baffled Leggett to such an extent that as soon as Richardson left, Leggett said he “sat down to try to construct a formal proof that given the generally accepted laws of quantum and statistical mechanics, the shift observed in the experiments simply could not occur”. In other words, he worried that by studying ultracold helium, Richardson and his colleagues may have stumbled upon a crack in quantum physics itself.

Within a few years, Leggett worked out that quantum physics was actually fine, but ultracold helium-3 really was unlike any ultracold system that had been studied before. Around this time, the ultracold realm was already throwing physicists for a loop. Make gases or even some solid materials cold enough, and they sometimes behave so strangely. For example, at a low enough temperature, the electrons in superconductors don’t repel each other as usual but pair up and carry electricity with perfect efficiency. In other cases, tens or hundreds of thousands of atoms subjected to extreme cold can all assume the same quantum state and effectively behave as one chunk of quantum stuff instead of as distinct individuals. This is how a superfluid forms, and why it has zero viscosity and can perform unexpected tricks, such as climbing the walls of a container. Was helium-3 a super-something as well? Leggett wanted to find out, and did so with rigour.

He developed a comprehensive theory of ultracold helium-3, a mathematical undertaking that revealed that it wasn’t just a single superfluid, but that its atoms could form several different types of superfluid. In describing this, he also discovered a novel form of symmetry breaking – a mathematical feature of the new ultracold theory that could explain the previously mysterious measurements from the lab.

Richardson had been awarded the Nobel prize for his helium-3 experiment in 1966, and Leggett’s Nobel, for the theory, came in 2003.

“I still remember the communal euphoria in 2003 on the day the Nobel prize was announced in the wee hours of the morning,” says Smitha Vishveshwara, who was my graduate advisor at UIUC. Tony moved to UIUC in 1983, and she came to work with him as a postdoctoral researcher in 2002. “He was such a caring, gentle, wise mentor, friend, colleague and inspiration for so many of us.” I can picture him sitting at one of the round tables in the institute for condensed matter physics theory at UIUC, which now bears his name, engrossed in thought but never too busy to answer a question.

And Tony was interested in so many more questions than just the mystery of superfluid helium-3. There was the study of glasses that that older graduate student told me about, but Tony was especially gripped by the idea that quantum theory may not apply to the whole world, and specifically that it may not work for large objects. Could all the weirdness of quantum physics – like a particle being mere clouds of possible properties when no one is looking at it – be restricted to tiny objects only?

Legget speculated about this in a 2003 interview following the Nobel prize ceremony, saying: “If we really do still believe [quantum physics] in the year 3000, then I think in some sense our attitude towards the physical world at the everyday level will be radically different from what it is today, because we will really have had to face up to this weirdness, which by that time I’m confident will have been amplified to the everyday level. I think it’s at least equally probable and perhaps more so, that…we will find that somewhere along the line quantum mechanics breaks down and some new theory, of which we can have at present no conception, will take over.” He said his personal hope was that exactly this would happen.

Finding the edge of quantum physics

Looking for this elusive line of quantum breakdown, he and Anupam Garg had formulated a mathematical test in 1985 that can be used to assess the quantumness of large objects. You can observe an object’s behaviour at different times, plug those observations into an equation now called the “Leggett-Garg inequality”, and discern whether the rules of quantum physics still have a grip on it or not. In recent years, Leggett-Garg experiments have been carried out on several systems, from particles of light to tiny crystals, and researchers are constantly pushing them to ever bigger scales.

Leggett’s questions about the relationship between the macroscopic world and quantum physics also seeded the experiments that were awarded the Nobel prize just this past year. “I heard him talk about this in the early ‘80s, and others did too. We took his proposal and turned it into a very good experiment,” says John Martinis at the quantum computing firm QoLab, who was awarded the Nobel for demonstrating that quantum effects can show up at scales as large as circuits made from layers of superconductors and insulators. Leggett already had an in-depth understanding of how such circuits could test the existence of macroscopic quantumness, which was great motivation for Martinis and his team to painstakingly build them in the lab, he says.

“I think it is fair to say that Tony could look at what everyone else dismissed as a minor glitch on a graph and recognise it as signalling something completely new,” wrote his former student David Waxman at Fudan University in China. “Tony was extraordinarily sensitive to what nature was trying to say.”

Leggett’s own advice to young physicists encouraged the same approach. “If there’s something in the conventional wisdom that you don’t understand, worry away at it for as long as it takes and don’t be deterred by the assurances of your fellow physicists that these questions are well understood,” he once advised. Then, he added that “no piece of honestly conducted research is ever wasted”, even if it ends up sitting in a drawer for decades before spurring some new idea.

I left UIUC in the spring of 2020, and even at that time you could still catch a glimpse of Tony in his office, working into his 80s. I truly believe that he never stopped listening to nature with that famous curiosity and care. I wish I could have looked at whatever studies were still waiting for their moment in his desk drawers.