Saturday, 26 October 2024

Synthesizing New 3D Materials by Twisting


Overlapping two 3D lattices with a relative twist opens the door to synthesizing crystals with diverse symmetries that showcase nontrivial band structures and novel properties.
When two identical periodic lattices overlap in space, with one twisted at an angle relative to the other, they form moiré lattices. The best-known examples are formed from stacked and rotated 2D sheets. These structures can possess fascinating properties not seen in their component layers. Twisted bilayer graphene, for example, can exhibit superconductor and Mott insulator behavior. Ce Wang of Tongji University in China and his colleagues now propose how to construct a 3D moiré lattice using two cubic optical lattices hosting ultracold atoms. The researchers mathematically describe how two simple periodic structures, twisted relative to each other, can lead to 3D optical moiré patterns (Fig. 1). The result is a crystal-like structure with emergent properties that differ from those of the underlying simple lattices. The researchers show that adjusting the twisting axes and angles leads to various crystalline symmetries, enabling the exploration of diverse material properties.

In the past five years, researchers have experimentally demonstrated the moiré lattice concept in optical [4–7] and cold-atom [8] systems. These demonstrations show the possibility of extending the concept from 2D into 3D. One of the most intriguing aspects of 3D moiré patterns is their non-Abelian rotation: The order in which you rotate the lattice significantly affects the final structure. This property contrasts with 2D systems, in which rotating an object by one angle and then another yields the same result regardless of the order.


Non-Abelian rotation can be visualized by rotating a cube. Turning the cube 90° around one axis and then 45° around another axis results in a different orientation than if you had performed those rotations in the reverse order. Now, suppose you have two cubic lattices, one fixed and the other twisted about its axis. Combining the two—creating 3D moiré lattices—will obviously lead to different structures, depending on which rotation happens first. This complexity allows for a richer variety of crystalline arrangements and, consequently, of material properties. Exploiting this non-Abelianism, therefore, offers researchers a powerful tool to “synthesize” new materials by manipulating existing ones and to study how different crystalline symmetries interact with atoms, photons, and electrons.

Wang and colleagues’ mathematical demonstration of the range of 3D moiré crystal structures that can be realized offers a fascinating look into the outcomes that non-Abelian physics makes possible. Notable among these is a feature exclusive to 3D crystals: the presence of Weyl points. Weyl points are the intersections of linearly dispersing energy bands similar to the Dirac points that arise in 2D crystals. Synthesizing a material whose energy band structure contains Weyl points opens doors to exploring a variety of intriguing phenomena such as topologically protected surface states and chiral anomalies. In recent years, researchers have successfully designed various intricate 3D structures to generate Weyl points. Surprisingly, Wang and colleagues’ numerical work reveals that by simply twisting two cubic lattices, the resultant 3D moiré crystals host many Weyl points and nodal lines. This result shows that 3D moiré lattices represent an alternative route to creating topological materials and correspondingly exotic states.

Wang and colleagues propose to implement 3D moiré lattices in the context of ultracold atoms, where these arrangements have the potential to enhance the exploration of diverse crystalline symmetries and their associated nontrivial band structures. However, the concept can be extended to other fields such as optics and acoustics, where it might bring many other new possibilities. One intriguing avenue for further investigation is the study of 3D moiré crystals under nonperiodic, or incommensurate, phases—that is, in crystals that do not possess the property of translational invariance. Note that Wang’s current study only considers the periodic, or commensurate, phase. An immediate question concerning 3D nonperiodic moiré crystals is whether localized wave packets, confined within the 3D space, exist. The existence of such wave packets in 2D is already well established. In a 3D system, because three twisting angles can be tuned separately, one can imagine localizing a wave in one plane while controlling its propagation in another specific, tunable direction. This could offer a unique approach to wave localization (creating a totally novel cavity) and subsequent access to it (novel waveguiding).

Additionally, it would be interesting to explore how nonlinear phenomena that might occur in a lattice with a 3D moiré structure differ from their 2D counterparts. For example, optical Kerr nonlinearity or two-body interactions in Bose-Einstein condensates could bring about new properties like the formation of higher-dimensional solitons controlled by the twisting. Breakthroughs, both experimental and theoretical, in these intriguing directions involving 3D moiré lattices are anticipated in the near future.




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Evidence of ‘Negative Time’ Found in Quantum Physics Experiment



Physicists showed that photons can seem to exit a material before entering it, revealing observational evidence of negative time. Quantum physicists are familiar with wonky, seemingly nonsensical phenomena: atoms and molecules sometimes act as particles, sometimes as waves; particles can be connected to one another by a “spooky action at a distance,” even over great distances; and quantum objects can detach themselves from their properties like the Cheshire Cat from Alice’s Adventures in Wonderland detaches itself from its grin. Now researchers led by Daniela Angulo of the University of Toronto have revealed another oddball quantum outcome: photons, wave-particles of light, can spend a negative amount of time zipping through a cloud of chilled atoms. In other words, photons can seem to exit a material before entering it.

The idea for this work emerged in 2017. At the time, Steinberg and a lab colleague, then doctoral student Josiah Sinclair, were interested in the interaction of light and matter, specifically a phenomenon called atomic excitation: when photons pass through a medium and get absorbed, electrons swirling around atoms in that medium jump to higher energy levels. When these excited electrons lapse to their original state, they release that absorbed energy as reemitted photons, introducing a time delay in the light’s observed transit time through the medium.


Sinclair’s team wanted to measure that time delay (which is sometimes technically called a “group delay”) and learn whether it depends on the fate of that photon: Was it scattered and absorbed inside the atomic cloud, or was it transmitted with no interaction whatsoever? “At the time, we weren’t sure what the answer was, and we felt like such a basic question about something so fundamental should be easy to answer,” Sinclair says. “But the more people we talked to, the more we realized that while everyone had their own intuition or guess, there was no expert consensus on what the right answer would be.” Because the nature of these delays can be so strange and counterintuitive, some researchers had written the phenomenon off as effectively meaningless for describing any physical property associated with light.


After three years of planning, his team developed an apparatus to test this question in the lab. Their experiments involved shooting photons through a cloud of ultracold rubidium atoms and measuring the resulting degree of atomic excitation. Two surprises emerged from the experiment: Sometimes photons would pass through unscathed, yet the rubidium atoms would still become excited—and for just as long as if they had absorbed those photons. Stranger still, when photons were absorbed, they would seem to be reemitted almost instantly, well before the rubidium atoms returned to their ground state—as if the photons, on average, were leaving the atoms quicker than expected.


The team then collaborated with Howard Wiseman, a theoretical and quantum physicist at Griffith University in Australia, to devise an explanation. The theoretical framework that emerged showed that the time these transmitted photons spent as an atomic excitation matched perfectly with the expected group delay acquired by the light—even for cases where it seemed as though the photons were reemitted before the atomic excitation had ebbed.


To understand the nonsensical finding, you can think of photons as the fuzzy quantum objects they are, in which any given photon’s absorption and reemission through an atomic excitation is not guaranteed to occur over a certain fixed amount of time; rather, it takes place across a smeared-out, probabilistic range of temporal values. As demonstrated by the team’s experiments, these values can encompass instances when an individual photon’s transit time is instantaneous—or, bizarrely, when it concludes before the atomic excitation has ceased, which gives a negative value.


“I can promise you that we were completely surprised by this prediction,” Sinclair says, referring to the matchup between the group delay and the time that the transmitted photons spent as atomic excitations. “And as soon as we were confident we hadn’t made a mistake, Steinberg and the rest of the team—I had moved on to do a postdoc at [the Massachusetts Institute of Technology] by this point—began planning to do a follow-up experiment to test this crazy prediction of negative dwell time and see if the theory would hold up.”
That follow-up experiment, the one led by Angulo that Steinberg touted on X, can be understood by considering the two ways a photon can be transmitted. In one, the photon wears blinders of sorts and ignores the atom entirely, leaving without even a nod. In the other, it interacts with the atom, boosting it to a higher energy level, before getting reemitted.


“When you see a transmitted photon, you can’t know which of these occurred,” Steinberg says, adding that because photons are quantum particles in the quantum realm, the two outcomes can be in superposition—both things can happen at the same time. “The measuring device ends up in a superposition of measuring zero and measuring some small positive value.” But correspondingly, Steinberg notes, that also means that sometimes “the measuring device ends up in a state that looks not like ‘zero’ plus ‘something positive’ but like ‘zero’ minus ‘something positive,’ resulting in what looks like the wrong sign, a negative value, for this excitation time.”

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