Emily Parnell, a fourth-year student of computer engineering, presented her theoretical study in photonics at the 2022 Frontiers in Optics-Laser Sciences, a flagship conference convened by Optica, formerly the Optical Society of America.

Parnell’s first-authored paper reports on research underway in the photonics lab led by Xu Yi, assistant professor of electrical and computer engineering who holds a courtesy appointment in physics. Funding from a National Science Foundation Research Experience Undergraduate site, aligned with an NSF RAISE EQuIP program grant to UVA, supports Parnell’s study.

Parnell’s study contributes to Yi’s research in the physics and applications of photonic devices that detect and shape light for a wide range of uses including communications and computing. As Nature Communications reported in August 2021, Yi’s research group has created a scalable quantum computing platform that drastically reduces the number of devices needed to achieve quantum efficiency on a photonic chip the size of a penny.

Here’s how it works. Yi’s group created a quantum source in an optical microresonator, a ring-shaped, millimeter-sized structure that envelopes the photons and generates a microcomb, a device that efficiently converts photons from single to multiple wavelengths. Light circulates around the ring to build up optical power. This power buildup enhances chances for photons to interact, which produces quantum entanglement between fields of light in the microcomb.

Parnell explained that as the microresonator squeezes the light, it generates pairs of side-band frequencies that can be correlated to enable precision measurements for quantum communication and information storage for quantum computing. In an ideal state, the sideband frequencies are spaced at an equal distance, so that chip designers can daisy chain the pairs for a more versatile and useful photonic device. In Yi’s prototype, the sideband frequencies are irregularly spaced. Parnell’s study answers the question of why the sideband frequencies do not perfectly align.

“I looked at this one effect called dispersion,” Parnell said. Dispersion arises from the fact that different frequencies of light move through a medium at different speeds, a value called the refractive index of light. In the equations commonly used to describe what happens in the microresonator, called coupling equations, dispersion is simply added as a catchall term, which can be filled with a measurement from an experiment.

However, there is value in expressing this term as a Taylor series (explicitly describing how it depends on frequency at this stage, instead of using a number). Using these modified coupling equations, which incorporate the higher-order terms of dispersion, Parnell was able to derive a more nuanced equation for the squeezing spectrum.

Parnell then wrote a script to plot her squeezing spectrum equation and compared it to plots of experimental data produced by graduate students in Yi’s group, Mandana Jahanbozorgi and Zijiao Yang, who co-authored the paper presented at Frontiers in Optics-Laser Sciences.

“It's not very illuminating to look at the squeezing at the single frequency where you want the photon to go,” Parnell said. “Instead, you can look at the squeezing spectrum, so, several frequencies within the neighborhood of our target frequency. Doing this, you observe a bell curve of light frequencies that are more or less squeezed.”

Breaking the dispersion effects into even order and odd order terms, Parnell predicted that even order terms would reduce the amount of squeezing and odd order terms would cause the center of the bell curve to shift into a higher or lower frequency.

“When we plugged in the parameters from the experiments conducted by Professor Yi’s graduate students, my equation and the actual data measurements matched pretty nicely,” Parnell said. “If we can describe the shifting modes, we can design a more finely tuned resonator. Ideally you want a resonator with no dispersion, or the ability to control dispersion to ensure everything is evenly spaced.”

Parnell’s passion for math drivers her academic study and research interests. She took Yi’s class in quantum for engineers. “(It was) the coolest thing ever,” Parnell said. Seeing Parnell’s enthusiasm, Yi invited her to join his lab. Parnell began working with Yi and his group members in January 2021, at first conducting literature reviews to broaden and deepen her knowledge, then tackling the challenge of the squeezing spectrum in the Fall 2021 term. She spent the past summer collaborating with her co-authors to finalize and submit their conference paper.

Parnell shares Yi’s interest in physics; after graduation, Parnell intends to earn a Ph.D. degree in physics or applied physics. Lessons learned from Yi’s lab will contribute to her future academic success.

“A big thing about research, whatever you’re trying to do, there’s not a very clearly defined answer for it,” Parnell said. “When I went about solving for the squeezing spectrum, looking at it on paper, it’s a complete mess. It’s not clear at first what the whole thing means. I can simplify things by writing the equation for an ideal situation. I can also play around with the terms to understand which factors are associated, then focus on those associations that affect the whole system. It was very satisfying to script the entire plot.”

Parnell also appreciated the opportunity to present her study to conference attendees. “Writing the paper was good practice in taking something that I did and expressing that to others,” Parnell said. “You can understand things in a very mathy way, but you have to figure out how to translate that into words that are meaningful to other people, including other people in your field. It was good to practice making that translation.”