Caltech physicists finally measure a quantum energy ladder predicted 40 years ago
Researchers have experimentally observed energy patterns that physicists have predicted for about 40 years. By arranging laser-trapped atoms into a quantum simulator, they recreated two different quantum tipping points and watched the atoms fall into the exact energy ratios predicted by theory. The technique could now be used to explore mysterious quantum systems where scientists do not already know the answer.
When materials undergo major changes, such as water boiling or a magnet losing its magnetism, very different systems can sometimes start behaving according to the same mathematical rules.
"Physicists call this trait universality -- the messy, microscopic details wash out and only a few essential features survive," explains Jason Alicea, William K. Davis Professor of Theoretical Physics.
Physicists often describe this universal behavior using a mathematical framework known as conformal field theory.
Quantum simulators test fundamental physics
In a study published in Nature, researchers carried out the first experiments of their kind on two different conformal field theories using quantum simulators. These specialized systems are simpler than general purpose quantum computers and are designed to reproduce particular quantum behaviors.
The collaboration brought together the experimental group of Caltech's Manuel Endres, professor of physics, Alicea's theory group, and theorists at Université Paris-Saclay and the Technical University of Munich.
Using newly developed quantum simulator technology, the researchers made the first direct measurements of energy levels in synthetic quantum matter predicted by the Ising and tricritical Ising conformal field theories. (Ising refers to Ernst Ising, a physicist who, in the 1920s, solved an early model of magnetism.)
Both theories describe universal behavior that can appear when a quantum system with unusual properties such as entanglement and superposition reaches a critical point between two states, with one state being more ordered than the other.
A quantum tipping point near absolute zero
Unlike an ordinary phase transition such as water becoming steam, this transition is not caused by temperature. Instead, it arises entirely from quantum effects at temperatures close to absolute zero.
At this critical point, lasers can excite the system into a sequence of specific energy states. The researchers compare those levels to the rungs of a ladder.
"The energy levels predicted by these theories are important because they encode profound information about the theories themselves," Alicea says.
For about 40 years, physicists have used conformal field theories to calculate how far apart those energy rungs should be. The levels are expected to appear in precise ratios, but until this experiment, those predictions had never been directly measured.
"Our new tools borrow from quantum computing platforms," says Xiangkai Sun, a co-lead author of the new study and a graduate student working in the Endres lab. "Over the past 10 years, people have been learning to control these systems, and now we are at the point where we can use them to do fundamental physics research."
Trapping atoms with lasers
The experiment builds on technology that the Endres lab also uses for developing quantum computers. The system relies on arrays of neutral atoms held in place by tightly focused lasers known as optical tweezers.
A related neutral atom platform in the lab recently reached a major milestone by trapping 6,100 atoms in a single array.
Although optical tweezer arrays were developed largely for quantum computing, the researchers instead used the technology to investigate a fundamental question in physics.
They arranged strontium atoms in a line using optical tweezers. Additional lasers then pushed the atoms into highly excited energy levels known as Rydberg states. In these states, neighboring atoms interact very strongly.
Those interactions caused the chain of atoms to behave collectively rather than as separate individual particles. The researchers then adjusted the lasers until the entire system reached the critical tipping point they wanted to study.
Measuring a hidden energy ladder
To detect the predicted energy levels, the researchers developed a technique called many body modulation spectroscopy.
They gently disturbed the entire atomic chain by changing the lasers at a particular frequency and then measured how strongly the atoms responded. By scanning through many frequencies and looking for peaks in the response, the researchers could identify the different energy levels.
The basic idea is similar to running a wet finger around the rim of a wine glass. When the motion matches the glass's natural frequency, the glass resonates and produces a sound. At other frequencies, little happens.
"We repeated the experiment on chains of up to 35 atoms, and the rungs came out as predicted by the Ising conformal field theory: the spectra collapsed onto a single universal curve once rescaled for size," Sun says. "We then tuned to the tricritical point and measured the lowest levels of its distinct spectrum, which came out in the different ratios theory predicts."
Hidden patterns emerge from individual atoms
Because the scientists could control each atom separately, they were able to perform measurements that would be much more difficult with conventional materials.
The team classified the excitations by their symmetry, exposing a second set of energy rungs that was hidden in the initial measurement.
They also changed the behavior of the atoms at either end of the chain. Doing so rearranged the energy ladder, producing different patterns that matched predictions from the tricritical Ising theory.
"Even though we believed these theories to be true, it's important to have an experimental realization, something you can poke and prod," Alicea says. "To see those predictions borne out is a beautiful thing."
Pushing quantum simulations into new territory
The researchers now plan to expand the experiments to larger quantum systems. Rather than arranging atoms only in a line, they hope to study grids of atoms as well.
"In two dimensions, the conformal field theories are not as well understood, so this is an exciting opportunity," Sun says.
That could allow scientists to investigate quantum systems whose behavior cannot yet be calculated precisely, potentially including problems too difficult for classical computers.
"What excites me is that the technique doesn't require knowing the answer in advance. Here we could check our measurements against exact predictions," Endres says. "The next step is to point this at systems where nobody knows the response of the system quantitatively -- including regimes that classical computers can't reach."
The Nature study, "Observation of conformal field theory spectra in a quantum simulator," was funded by the US Department of Energy, including its Quantum Systems Accelerator and its Quantum Science Center; the National Science Foundation, including the Institute for Quantum Information and Matter at Caltech (IQIM); the Army Research Office; the Defense Advanced Research Projects Agency; the Air Force Office of Scientific Research; the Gordon and Betty Moore Foundation; and the Deutsche Forschungsgemeinschaft.
Other Caltech authors include Yuan Le, Stephen Naus, Richard Bing-Shiun Tsai, and Lewis Picard, who is now working at the Caltech-linked startup Oratomic. Additional authors are Sara Murciano of the Université Paris-Saclay (previously a postdoctoral scholar at Caltech) and Michael Knap of the Technical University of Munich and the Munich Center for Quantum Science and Technology.