Twisting of atoms through space and time

One of the most exciting applications of quantum computers will be to direct their gaze inward, to the very quantum rules that make them tick. Quantum computers could be used to simulate quantum physics itself, and perhaps even explore worlds not found anywhere in nature.

But even in the absence of a fully functional, large-scale quantum computer, physicists can use a quantum system they can easily control to simulate a more or less intuitive system. Ultracold atoms – atoms that are cooled to temperatures above absolute zero – are a leading platform for quantum simulations. These atoms can be controlled by Lasers and magnetic fields, and persuade them to perform a quantitative dance routine designed by the experimenter. It’s also fairly easy to look at their quantitative nature by using high-resolution imaging to extract information after – or during – they complete their steps.

Now, researchers at JQI and the NSF Quantum Leap Challenge Institute for Robust Quantum Simulation (RQS), led by former JQI postdoctoral fellow Mingwu Lu and graduate student Graham Reid, have trained their ultracold atoms to do a new dance, adding to the simulation’s growing suite of tools. Quantum. In a pair of studies, they bend their atoms out of shape, wrapping their quantum mechanical spin in both space and time before connecting them to create a kind of quantum pastry in space-time.

They plotted the squiggly space-time shape they created and report their findings in an article titled “Floquet Engineering Topological Dirac Bands” in the journal Physical review letters last summer. In a follow-up experiment, they watched their atoms transition between different zigzag shapes and found a rich structure inaccessible to fixed simple atoms. They published this result, titled “Dynamic-induced symmetry breaking and out-of-equilibrium topology in a two-dimensional quantum system”, in Physical review letters in September.

The rolls they studied are related to the mathematical field of topology — classifying objects according to the number of holes they contain. Donuts are topologically identical to hoops and coffee mugs since they each have a single hole. But donuts are different from eyeglass frames, which have two holes, or donuts, which have three.

This deceptively simple classification of shapes has been surprisingly influential in physics. I’ve demonstrated things like the quantitative Hall effect, which produces a precisely repeatable electrical resistance that is used to determine the resistance standard, and Topological insulatorswhich may one day serve as components for powerful quantum computers.

In physical environments — whether they’re solid pieces of metal or extremely cold atoms — the topology that physicists care about isn’t really about the shape of the actual matter. Rather, it is the form that quantum waves that travel within matter take. Oftentimes, physicists look at an intrinsic property of quantum particles called spin and how they spin when particles speed up or slow down inside a solid.

Most solids are crystals, consisting of a regular lattice extending in every direction in a repeating pattern of evenly spaced atoms. For electrons floating free within this lattice, hopping from one identical atom to another makes no difference — the landscape is exactly the same as far as the eye can see. A similar web emerges in the electron velocities landscape — things may change as the electron starts to accelerate, but at certain speeds the landscape will look as if it is not moving at all.

But position and velocity are just two properties of an electron. Another is rotation. Spin can behave more or less independently as position and velocity change, but when the position is shifted by a single site or the velocity is shifted by a single velocity “location,” the spin must remain unchanged—another reflection of the symmetry found in the crystal. But between two speed positions or “locations” everything goes well. The zigzag shape that the rotation draws before returning to where it started is what defines the structure.

In the realm of quantum simulations, very cold atoms can simulate the electrons in a crystal. The laser plays the role of a crystal, creating a repeating pattern of light populated by extremely cold atoms. Likewise, the position and velocity of atoms acquire a repeating pattern, and atomic spins trace the shapes that define the structure.

In their meandering experiment, Lu and his colleagues created a two-dimensional crystal, but not in the usual two dimensions of a paper. One dimension was in space, like direction along a thin thread, while the other was time. In this paper composed of space and time, the spin of their atoms has drawn a strange shape as a function of the atoms’ ● speed in the crystallization of time and space.

“Topologies are defined on surfaces,” says JQI Fellow Ian Spielman, principal investigator on the research and co-director of research at RQS. “One of the dimensions that defines a surface could be time. This has been known for a while in theory but is only now being tested experimentally.”

To create a surface that would blast through both space and time, the researchers shined two-way lasers and a radio-frequency magnetic field from above on a cloud of very cold atoms. laser f magnetic field Combined to form regions of higher and lower energy from which the atoms were pushed away or pulled towards them, like an egg carton for the atoms to live in. This carton had an odd shape: Instead of two rows of slots like a regular dozen you’d find in a grocery store, there was only one. Each slot in the carton consists of two sub-holes (see image below). This resulted in a repeating, crystal-like pattern along a line in space.

By adjusting how the lasers and magnetic fields align with each other, the team can shift the entire pattern to the side with a single sub-slit. But they didn’t change it just once. They shook the egg carton rhythmically back and forth between the two of them. This rhythmic vibration created a pattern repeat In time, similar to the recurring spatial pattern of nucleation in a crystal.

To do this, they had to ensure that their laser egg carton, as well as the timing of the blinking, were all right. “The hardest part was getting the timing right,” says Graham Reid, a graduate student in physics and one of the authors of the work. “This experience really relies on very precise timing of things that you don’t know ahead of time, so you just have to do a lot of tuning.”

However, after much fine-tuning, they experimentally depicted the rotation of the atoms in a space-time crystal. They drew a coil yarn As he traversed time and space on his way back to where he started. In this way, they directly measured the sinuous structure they had built.

To follow up on this work, they used the same laser pattern to perform a very different topology-related experiment. Instead of looking at topology in space and time, they focused on the spatial dimension only. This time, they prepared their atoms in different ways: all spin down, all spin up, or mix up.

These weren’t natural, relaxed states for the atoms in the laser pattern they created, and eventually, the atoms would settle into their natural states—their equilibrium states. But along the way, the researchers were able to capture freeze frames of several different topological shapes—some of which would never occur except for a moment. These findings revealed new mysteries that researchers are eager to investigate.

“There are two big questions that I think would be great to answer,” says Spellman. “The first is that the result of space-time topology has only really worked with precise timing. I wonder if there is a way to make that robust. Second, for unbalanced topologies, I’m interested in knowing what happens when we quickly switch between a variety of topological states.”

In addition to Spielman, who is also a fellow at the National Institute of Standards and Technology, Reid, and Lou, who is currently at Atom Computing, authors of the papers included Amilson Fritsch, a former JQI postdoctoral fellow now at the University of São Paulo São Carlos and Alina Pinheiro, a graduate student Graduate in Physics at JQI.