The first-ever “space–time crystal” has been created in the US by Hanqing Zhao and Ivan Smalyukh at the University of Colorado Boulder. The system is patterned in both space and time and comprises a rigid lattice of topological solitons that are sustained by steady oscillations in the orientations of liquid crystal molecules.
In an ordinary crystal atomic or molecular structures repeat at periodic intervals in space. In 2012, however, Frank Wilczek suggested that systems might also exist with quantum states that repeat at perfectly periodic intervals in time – even as they remain in their lowest-energy state.
First observed experimentally in 2017, these time crystals are puzzling to physicists because they spontaneously break time–translation symmetry, which states that the laws of physics are the same no matter when you observe them. In contrast, a time crystal continuously oscillates over time, without consuming energy.
A space–time crystal is even more bizarre. In addition to breaking time–translation symmetry, such a system would also break spatial symmetry, just like the repeating molecular patterns of an ordinary crystal. Until now, however, a space–time crystal had not been observed directly.
Rod-like molecules
In their study, Zhao and Smalyukh created a space–time crystal in the nematic phase of a liquid crystal. In this phase the crystal’s rod-like molecules align parallel to each other and also flow like a liquid. Building on computer simulations, they confined the liquid crystal between two glass plates coated with a light-sensitive dye.
“We exploited strong light–matter interactions between dye-coated, light-reconfigurable surfaces, and the optical properties of the liquid crystal,” Smalyukh explains.
When the researchers illuminated the top plate with linearly polarized light at constant intensity, the dye molecules rotate to align perpendicular to the direction of polarization. This reorients nearby liquid crystal molecules, and the effect propagates deeper into the bulk. However, the influence weakens with depth, so that molecules farther from the top plate are progressively less aligned.
As light travels through this gradually twisting structure, its linear polarization is transformed, becoming elliptically polarized by the time it reaches the bottom plate. The dye molecules there become aligned with this new polarization, altering the liquid crystal alignment near the bottom plate. These changes propagate back upward, influencing molecules near the top plate again.
Feedback loop
This is a feedback loop, with the top and bottom plates continuously influencing each other via the polarized light passing through the liquid crystal.
“These light-powered dynamics in confined liquid crystals leads to the emergence of particle-like topological solitons and the space–time crystallinity,” Smalyukh says.
In this environment, particle-like topological solitons emerge as stable, localized twists in the liquid crystal’s orientation that do not decay over time. Like particles, the solitons move and interact with each other while remaining intact.
Once the feedback loop is established, these solitons emerge in a repeating lattice-like pattern. This arrangement not only persisted as the feedback loop continued, but is sustained by it. This is a clear sign that the system exhibits crystalline order in time and space simultaneously.
Accessible system
Having confirmed their conclusions with simulations, Zhao and Smalyukh are confident this is the first experimental demonstration of a space–time crystal. The discovery that such an exotic state can exist in a classical, room-temperature system may have important implications.
“This is the first time that such a phenomenon is observed emerging in a liquid crystalline soft matter system,” says Smalyukh. “Our study calls for a re-examining of various time-periodic phenomena to check if they meet the criteria of time-crystalline behaviour.”
Building on these results, the duo hope to broaden the scope of time crystal research beyond a purely theoretical and experimental curiosity. “This may help expand technological utility of liquid crystals, as well as expand the currently mostly fundamental focus of studies of time crystals to more applied aspects,” Smalyukh adds.
The research is described in Nature Materials.
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