Abstract-Dynamical Birefringence: Electron-Hole Recollisions as Probes of Berry Curvature

Hunter B. Banks, Qile Wu, Darren C. Valovcin, Shawn Mack, Arthur C. Gossard, Loren Pfeiffer, Ren-Bao Liu, and Mark S. Sherwin

https://journals.aps.org/prx/abstract/10.1103/PhysRevX.7.041042

The direct measurement of Berry phases is still a great challenge in condensed-matter systems. The bottleneck has been the ability to adiabatically drive an electron coherently across a large portion of the Brillouin zone in a solid where the scattering is strong and complicated. We break through this bottleneck and show that high-order sideband generation (HSG) in semiconductors is intimately affected by Berry phases. Electron-hole recollisions and HSG occur when a near-band-gap laser beam excites a semiconductor that is driven by sufficiently strong terahertz-frequency electric fields. We carry out experimental and theoretical studies of HSG from three $\mathrm{GaAs}/\mathrm{AlGaAs}$ quantum wells. The observed HSG spectra contain sidebands up to the 90th order, to our knowledge the highest-order optical nonlinearity reported in solids. The highest-order sidebands are associated with electron-hole pairs driven coherently across roughly 10% of the Brillouin zone around the $\Gamma$ point. The principal experimental claim is a dynamical birefringence: the intensity and polarization of the sidebands depend on the relative polarization of the exciting near-infrared (NIR) and the THz electric fields, as well as on the relative orientation of the laser fields with the crystal. We explain dynamical birefringence by generalizing the three-step model for high-order harmonic generation. The hole accumulates Berry phases due to variation of its internal state as the quasimomentum changes under the THz field. Dynamical birefringence arises from quantum interference between time-reversed pairs of electron-hole recollision pathways. We propose a method to use dynamical birefringence to measure Berry curvature in solids.

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Physicists Take Steps Towards Measuring Unmeasurable Berry Curvature

IN BRIEF

Berry curvature, a property of quantum mechanics, has never been directly observed. Thanks to new experimentation, observation may one day be possible.

https://futurism.com/physicists-measuring-berry-curvature/

BERRY CURVATURE

For years, physicists have worked towards the ability to directly measure Berry curvature. Often discussed as a “holy grail,” this observation has seemed impossible to make until now.

Berry curvature is associated with “Berry phase,” also known as a geometric phase, which is a phase angle. It “describes the global phase evolution of a complex vector as it is carried around a path in its vector space,” according to Rutgers.

Berry curvature isn’t widely popular or well-known, but it is a major unifying principle in both quantum and classical physics. This quantum mechanical property governs the dynamics of the motion of charges in semiconducting solids.

THE HOLY GRAIL

UC Santa Barbara physicists appear to have, in a world’s first, opened up the possibility of directly observing Berry curvature in solid matter. Published in the journal Physical Review X, their new paper uses a previous UCSB paper, in which the researchers aimed high- and low-frequency lasers at a gallium arsenide semiconductor to create an electron-hole recollision, as a stepping stone.

In conducting research for the new paper, physicists from CSB’s Sherwin Group worked with fellow scientists from China, Princeton University, and the U.S. Naval Research Laboratory. With the goal of improving the previous experiment, they discovered dynamical birefringence, a new phenomenon that can be used to explore Berry curvature.

“When we originally did the experiment, we could only detect one sideband at a time and the samples were very fragile and more difficult to work with,” said Mark Sherwin, physics professor and director of UCSB’s Institute for Terahertz Science and Technology.

An artist’s representation of Berry curvature, as illustrated by twisting ribbons. Image Credit: Brian Long

By installing a highly sensitive camera to simultaneously capture all the sidebands, improving how samples were mounted, and increasing the strength of the applied terahertz electric field, this team opened up the possibility of observing the property. Because the team could see more sidebands, they could discover more about the semiconductor. “We’re planning to turn dynamical birefringence into a direct measurement of Berry curvature,” Sherwin said.

This experimentation could lead to applications in electronic and optical devices, quantum computing, and more. “Once you can measure something that’s a basic property of a solid, then, when you’re designing new materials, you can optimize the Berry curvature for a particular device,” said Sherwin.