Nature Communications Publishes Dartmouth Collaboration on Controllable Non‑Hermitian Dynamics

In early August, results from a research collaboration between the Fitzpatrick lab at Thayer School of Engineering and Professor Viola's quantum theory group at the Physics and Astronomy Department were published in Nature Communications. The work, 'Demonstration of a tunable non-Hermitian nonlinear microwave dimer', presents a new method of precisely controlling harmonic oscillations of light to investigate phase non-reciprocity, and introduces a phenomenological model that quantitatively explains the observed behavior.

Two faculty supervised this collaboration; Mattias Fitzpatrick, an assistant professor at Thayer with an adjunct appointment in Physics, and Lorenza Viola, the James Frank Family Professor of Physics. The paper's first author, Juan S. Salcedo-Gallo, joined as the first graduate student in Fitzpatrick's group. The two lead theory authors, Michiel Burgelman and Vincent P. Flynn, are postdoctoral fellows working in Viola's group. 

Viola's group has long carried out research on open quantum systems and non-Hermitian physics. Notably, Flynn graduated in 2023 from the group with a PhD thesis on non-Hermiticity in bosonic systems that was published in the Springer Thesis series. The Fitzpatrick lab opened in early 2023, and this paper is its first publication. It is rare for a group's inaugural paper to appear in Nature Communications, and the achievement highlights both the lab's strong start and the value of cross‑discipline collaboration at Dartmouth.

"I think one of our biggest contributions to the field is the exploration of phase-non-reciprocity as a resource, along with the high level of tunability we achieved over all relevant parameters in the experimental setup. Our device combined phase-non-reciprocal, non-Hermitian, and nonlinear interactions in one platform, which is itself an important contribution"

- Juan Sebastian Salcedo-Gallo, first author

Early in their training, many physicists learn about ideal, isolated systems evolving in reversible ways. In reality, systems lose or gain energy, can be amplified, and even become unstable. Such open systems are often described as non‑Hermitian dynamical systems and lead to a rich variety of phenomena that aren't possible under the constraint of energy conservation. 

One particularly interesting non-Hermitian phenomenon is phase non‑reciprocity. In a pair of isolated cavities, any phase shift a photon picks up when hopping from one cavity to the other would be reversed when the photon travels back. An open, driven system allows photons to accumulate phase shifts even when reversing direction. Phase non-reciprocity encodes directional information, and being able to precisely control it has great potential for fields such as quantum information, sensing, optics, and condensed-matter physics. 

Many existing implementations of non-reciprocity rely on specialized materials, cryogenic temperatures, or complex and fixed circuits. This research project prioritized simple room‑temperature components to create a flexible, highly tunable platform. The team describes their device as one of the first potential building blocks for scalable, driven-dissipative synthetic photonic lattices.

Thayer microwave dimer.png

Diagrams and schematic of the microwave dimer built in the Fitzpatrick lab at Thayer.

Researchers in Fitzpatrick's lab built a tunable 'dimer' of two microwave cavities acting as harmonic oscillators. The dimer uses amplifiers to increase the number of photons hopping between cavities. A phase shifter was also used to precisely control the interference between photons along different paths. 

The team finely tuned both amplitude and directional phase of signals, and explored how that control combines with amplifier saturation - a common nonlinear effect - to produce complex output signals. The dimer produced a wealth of dynamical phenomena, including non‑reciprocal phase control, self‑sustained oscillations, and synchronization to external tones. 

Viola's group developed a new phenomenological model to explain the observations in all the parameter regimes relevant to the experiment. The model reproduced the experimental output both numerically and analytically, with what Salcedo‑Gallo calls "remarkable agreement." Viola's team also advised on which observables to measure and how to interpret the data through analytics and simulation. 

Although this work was conducted in the classical (room-temperature) regime, the group is now excited to investigate phase non-reciprocity in a regime where quantum effects can no longer be neglected. "We plan to push these ideas into the quantum realm by replacing room-temperature components with cryogenic ones and utilizing a dilution refrigerator setup in Fitzpatrick's lab" Fitzpatrick says. "By extending these ideas to the quantum domain, we hope to find novel ways to control and manipulate quantum information." "By scaling up to a large number of cavities, one may in principle also hope to study aspects of driven-dissipative many-body open quantum systems," Viola adds.  

Salcedo-Gallo has worked alongside Fitzpatrick to build the lab from the ground up–walls included. To hear them converse about the creation of the Fitz lab and the research that went into this paper, you can listen to their podcast on Spotify or Youtube. 

You can read the full publication in Nature Communications here.