# Complex energies, quantum symmetries

What if energy could be the square root of a negative number?In a certain sense, physics is the study of the universe's symmetries. Physicists strive to understand how systems and symmetries change under various transformations.

Yogesh Joglekar, Ph.D. |

New research from IUPUI and Washington University in St. Louis realizes one of the first parity-time (PT) symmetric quantum systems, allowing scientists to observe how that kind of symmetry -- and the act of breaking of it -- leads to previously unexplored phenomena. The work is published Oct. 7 in the journal Nature Physics, with associate professors Yogesh Joglekar at IUPUI and Kater Murch at Washington University, as the corresponding authors.

Other experiments have demonstrated PT symmetry in classical systems such as coupled pendulums or optical devices, but this new work, along with experiments in China by Yang Wu et al., reported in Science this May, provides the first experimental realization of a PT-symmetric quantum system.

"For us, certainly, the biggest motivation is to explore the unknown territories of quantum physics," said Mahdi Naghiloo, lead author of the paper who recently earned his Ph.D. at Washington University. "We were curious to experimentally explore quantum systems when they are pushed into the complex world and look for powerful tools they may offer."

These and future PT symmetry experiments have potential applications to quantum computing.

'Quantum state tomography across the exceptional point in a single dissipative qubit' is published online today. The full research team included Mahdi Naghiloo, Maryam Abbasi, a Washington University graduate student, Joglekar, and Murch.

Watch a video explaining complex energies

**A new symmetry in quantum systems**

If you reflect a system in a mirror, that's called a parity transformation. This transformation sends a right hand to a left hand, and vice-versa. If you record a video of the system's evolution and play it backward, that's time reversal. If you perform both of these transformations simultaneously, and the system looks the same as it did before, then the system has PT symmetry.

Until recently, no one understood how to make a quantum system PT-symmetric.

Joglekar, a theoretical physicist, was interested in realizing PT systems across different platforms. He had worked with experimentalists to do so with electrical circuits, fluids, single photons and ultra-cold atoms. A fortuitous discussion between Murch and Joglekar in late 2017 provided the necessary insight. "Almost immediately, we sketched on the board exactly what the idea was. In 10 minutes, we had the whole idea for the experiment," Murch recalled.

The team used a superconducting circuit, called a qubit, to generate a three-state quantum system. The first excited state tends to decay to the ground state, and the two excited states have an oscillatory coupling. Using a technique called post-selection, the team considered only those trials where the qubit did not decay to the ground state, a choice that gives rise to effective PT symmetry. Controlling two parameters related to the energy of the system, they studied how the time-evolution behavior depended on those parameters.

"The key to this experiment was being able to control the environment so that just the excited state decays and the other states don't decay, and that was something that we could deliberately manufacture," Murch said. "At the same time, we can initialize it into a particular state and then we can do this process of quantum state tomography, where we're figuring out exactly what the quantum state is doing after some period of time."

**Potential applications to quantum computing**

The team's work is just the beginning of the experimental study of PT symmetry in quantum mechanics. Theory predicts strange geometric effects associated with encircling the exceptional point, which the lab is now trying to measure in experiments.

According to Murch, the "bane of a quantum engineer's existence" is decoherence, or the loss of quantum information. Early indications, based on quantum photonic simulations by Joglekar and Anthony Laing at the University of Bristol in England, suggest that in the Murch lab's set-up, the decay from the first excited state to the ground state might slow the process of decoherence, providing the possibility for more robust quantum computing.

The PT symmetry collaboration between Murch and Joglekar continues through the Fall 2019 semester while Joglekar spends a semester as a visiting professor at Washington University.

Joglekar emphasized the importance of collaboration between theorists like himself and experimentalists like Murch. "It's a very dynamic back-and-forth enterprise," he said. "And it should be like that, because you want, to in the end, understand nature. Nature doesn't care whether you call yourself a theorist or experimentalist."

Story by *Scott Hershberger**, Washington University in St. Louis, adapted for IUPUI*