##### Physics

# Viewpoint: A Quasicrystal for Quantum Simulations

Luis Santos, Institute for Theoretical Physics, Leibniz College Hannover, Hanover, Germany

March 20, 2019• Physics 12, 31

Experimentalists notice a Bose-Einstein condensate on a 2D quasicrystal optical lattice, opening the trail for simulations of a wide range of quantum many-body phenomena in these fractal constructions.

Solids have historically been divided into two opposing varieties: crystals, the place the atoms type a long-range periodic sample, and amorphous supplies, the place no long-range order of the atoms happens in any respect. Someplace in between are quasicrystals, which lack periodicity but nonetheless show a type of long-range order. To know this order-disorder frontier, researchers have studied each electrons in quasicrystalline solids, in addition to atoms and photons in “artificial” quasicrystalline lattices. A bunch led by Ulrich Schneider on the College of Cambridge, UK, has now launched a brand new system into the combination—a Bose-Einstein condensate (BEC) of atoms in a 2D quasicrystalline optical lattice [1]. Optical lattices are defect-free and could also be engineered extra simply than precise crystals, probably permitting well-controlled simulations of quantum many-body phenomena in a variety of latest quasicrystal environments.

Determine 1: Schneider’s group realized a 2D quasicrystalline optical lattice and probed it utilizing a Bose-Einstein condensate of potassium atoms. Because the atoms scatter from the lattice, they fall into states (dots) whose distribution in momentum house is self-similar. The dots type a sequence of octagons that may be scaled onto one other by an integer a number of of the silver imply, 1+2.Schneider’s group realized a 2D quasicrystalline optical lattice and probed it utilizing a Bose-Einstein condensate of potassium atoms. Because the atoms scatter from the lattice, they fall into states (dots) whose distribution in momentum house is self-simil… Present extra

Determine 1: Schneider’s group realized a 2D quasicrystalline optical lattice and probed it utilizing a Bose-Einstein condensate of potassium atoms. Because the atoms scatter from the lattice, they fall into states (dots) whose distribution in momentum house is self-similar. The dots type a sequence of octagons that may be scaled onto one other by an integer a number of of the silver imply, 1+2.×

Mathematically, a periodic construction can have solely two-, three-, four-, or sixfold rotational symmetry. However in 1984, Dan Shechtman and collaborators reported their discovery of tenfold rotational symmetry within the electron-diffraction sample from aluminum-manganese alloys [2]. Though this uncommon rotational symmetry couldn’t have come from a crystal, it implied that the atoms within the alloy had been ordered in a roundabout way. The researchers dubbed the solids quasicrystals, and it was later proven that these unusual solids can produce diffraction patterns with different “disallowed” rotational symmetries, together with fivefold and eightfold. Shechtman’s pioneering work was acknowledged with the 2011 Nobel Prize in Chemistry [3].

Quasicrystals have many different options that aren’t present in standard solids. They’re inherently self-similar, like fractals, that means that patterns of their construction recur as one zooms out and in. This self-similarity will be seen in diffraction patterns, which exhibit peaks at arbitrarily small momenta. As well as, not like the periodic (Bloch wave) states that exist incrystals, digital states in quasicrystalline solids have a peculiar fractal construction. Quasicrystals can be understood because the projection of a higher-dimensional “dad or mum” crystal onto a lower-dimensional house. Finding out these supplies subsequently gives a window into higher-dimensional phenomena [4]. Thirty-five years after their discovery, quasicrystals proceed to fascinate researchers [5], they usually have been realized in lots of varieties, reminiscent of photonic constructions [6] and twisted bilayer graphene [7].

Another platform for finding out quasicrystalline conduct is an atomic gasoline confined in an optical lattice [8]. Made by interfering two or extra laser beams, the standard optical lattice is completely periodic. Quasiperiodic lattices will be made by superimposing two lattices whose periodicities are “incommensurate”—that means their ratio isn’t a rational quantity. Each 1D and, extra not too long ago, 2D quasiperiodic lattices have been produced on this manner, however such lattices didn’t exhibit the forbidden rotational symmetries of a real quasicrystal [9]. A 1997 research succeeded in observing these options with an atom gasoline in a quasicrystalline optical lattice [10]. However the proximity of the laser frequency to an inside atomic resonance resulted in robust atom-light scattering, which prevented the simulation of quantum many-body conduct.

Of their new work [1], Schneider and collaborators opened a window into this physics. For one, they realized a 2D quasicrystal optical lattice tuned removed from any inside atomic resonance, decreasing problematic atom-light scattering results. Additionally they probed this lattice with a BEC, wherein all the atoms are in the identical quantum state. They produced the lattice utilizing a planar association of 4 intersecting 1D optical lattices, with an angle of 45° between every lattice. By tuning the relative energy of every laser, the group might swap between 1D and 2D periodic potentials, they usually might create 2D quasicrystals with eightfold rotational symmetry. Within the experiment, the optical lattice was flashed “on” for a number of microseconds in the identical spot as a preformed BEC of potassium atoms. Over the course of this pulse, the researchers noticed a sequence of momentum states rising within the BEC because the atoms scattered photons from one of many beams of the lattice into one other. Organized in a plot, these states fashioned a self-similar sample analogous to the diffraction patterns measured by Shechtman et al. 35 years in the past [2]. The brand new sample could possibly be described as an infinite sequence of progressively bigger octagons (Fig. 1).

Schneider’s group additionally confirmed that the time evolution of the BEC on the quasicrystal is sort of distinct from that on a periodic lattice. Within the quasicrystal, the fractal sample of momentum states emerges because the atoms transfer to successively decrease and extra intently spaced momentum states by means of a sequence of small, photon-induced velocity kicks. The successive inhabitants of those smaller momentum states constitutes a quantum stroll within the quasicrystal’s momentum house. However in a periodic lattice, these smaller momentum states are inaccessible.

Within the current work, Schneider and colleagues interpret their 2D quasicrystal as an incommensurate projection of a 4D cubic lattice onto a 2D airplane. The 4D character of this “dad or mum” lattice is mirrored within the properties of the BEC quantum stroll, which demonstrates the potential of quasicrystalline optical lattices for simulating larger dimensions. Attention-grabbing prospects embody the exploration of the quantum Corridor impact and different topological properties in 4D, the place unique new phenomena are anticipated.

The place else may these experiments lead? One avenue may be the research of a weakly interacting BEC in a quasicrystal, a system whose dynamics is anticipated to current hybrid options of dysfunction and periodicity. One other route can be the investigation of strongly correlated conduct—like that described by Hubbard and spin fashions—in a quasicrystalline atmosphere. With sufficiently deep potentials, one would notice these fashions with regionally variable parameters and discover such behaviors as antiferromagnetism, Mott transitions, and Bose glass phases within the peculiar setting of a quasicrystal. As well as, the brand new platform may also present other ways of finding out the results of quasiperiodicity on transport, reminiscent of anomalous diffusion and many-body localization.

This analysis is printed in Bodily Evaluation Letters.

## References

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## In regards to the Creator

Luis Santos is a full professor on the Leibniz College Hannover, Germany. He obtained his Ph.D. in 1998 on the College of Salamanca, Spain. His analysis focuses on the idea of ultracold quantum gases. His present pursuits embody dipolar and spinor gases, strongly correlated gases in optical lattices, artificial magnetism, and disordered quantum techniques.

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