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Its easy to think about the idea of a singularity and dismiss it. After all, everything that we know of in physics, at a fundamental level, comes in quantized little bits: particles and antiparticles with a fixed, finite amount of energy inherent to each of them. No matter what tricks you use, there are certain quantum properties that are always conserved and can never be created or destroyed, not in any interaction thats ever been observed, measured, or even computed. Things like electric charge, momentum, angular momentum, and energy are always conserved, in all circumstances, as are numerous other properties.

And yet, inside of a black hole, the math of General Relativity is very clear: all of that matter and energy that goes into forming it, no matter how its initially configured, is going to wind up collapsed down to either a single, zero-dimensional point (if theres no net angular momentum) or stretched out into an infinitely thin one-dimensional ring (if there is spin, or angular momentum, present). Comedian Steven Wright even jokingly said, Black holes are where God divided by zero, and in some sense, thats true.

While many hope that quantum gravity will save us from the inevitability of a singularity, many dont think that even that is possible, for very good reasons. Heres why a singularity at the center of every black hole may be completely unavoidable.

In a Universe that isnt expanding, you can fill it with stationary matter in any configuration you like, but it will always collapse down to a black hole. Such a Universe is unstable in the context of Einsteins gravity, and must be expanding to be stable, or we must accept its inevitable fate.

In principle, as Einstein first realized, if all you have is some configuration of matter that starts off distributed over some volume (with no rotation or initial motions), the outcome is always the same: gravitational attraction will bring all of that matter together until it collapses down to a single point. Around that point, dependent on how much mass/energy there is all together, there will form a region of space known as an event horizon: a volume from within which the escape velocity, or the speed youd need to travel to escape from this objects gravitational pull, would be greater than the speed of light.

That solution to Einsteins equation was first worked out in detail by Karl Schwarzschild, and represents the configuration known as a non-rotating (or Schwarzschild) black hole. For many years, astronomers and physicists alike wondered if these objects were just mathematical oddities and perhaps even pathologies predicted by General Relativity, or whether these corresponded to real objects that were out there somewhere within this Universe.

The story began to change in the 1950s and 1960s with the work of Nobel Laureate Roger Penrose, whose pioneering work demonstrated how black holes (and their event horizons) could form from an initial configuration that didnt have one earlier. This was the work that Penrose, quite deservingly, was awarded the Nobel Prize for, and it kicked off a proverbial firestorm of black hole research.

One of the most important contributions of Roger Penrose to black hole physics is the demonstration of how a realistic object in our Universe, such as a star (or any collection of matter), can form an event horizon and how all the matter bound to it will inevitably encounter the central singularity. Once an event horizon forms, the development of a central singularity is not only inevitable, its extremely rapid.

If black holes could realistically form within our Universe, then that means we should be able to do two things with them.

For the first one, all you really need is enough mass concentrated within a given volume of space. This could occur because you have a collection of matter thats of relatively low density, but that occupies enough space so that when you look at it as a whole, it must inevitably collapse to a central singularity: a direct collapse black hole. You can also have a black hole arise from the implosion of the core of a massive enough star: in a core-collapse supernova, for instance, where the core is massive enough to collapse to a black hole. Or, you could have multiple massive and dense objects, like stellar remnants such as neutron stars, merge together and cross a critical mass threshold, where theyll become a black hole. These are three of the most common ways that the Universe could actually create a black hole.

Discovered in 1964 as an X-ray emitting source consistent with a stellar object orbiting a black hole, Cygnus X-1 represents the first black hole candidate known within the Milky Way. Cygnus X-1 is located near large active regions of star formation in the Milky Way: precisely the location expected to find an X-ray emitting black hole binary.

Over on the observational side, there are many different signatures that a black hole gives off. If a black hole is a member of a binary system, where another star orbits it from afar, then we can see the star move in a helix-like shape as it moves through the galaxy, revealing the black holes presence from gravity alone. If its at the center of a galaxy, we can see other stars orbit it directly. If theres a close-in stellar companion to a black hole, then the black hole could be capable of stealing or siphoning mass from the companion onto itself, and much of that mass will be heated, accelerated, and shot out in X-ray emitting jets. The first black hole ever detected, Cygnus X-1, was found from exactly this X-ray emission.

We can also detect what effects black holes have on their surrounding matter. They develop accretion disks with flows within them, flaring when these flows get accelerated and shot out in bi-directional jets. They can tidally disrupt any stars or planets or gas clouds that get too close to them, creating cataclysmic signatures when they do so. They can inspiral and merge together, creating gravitational wave signatures that we can directly detect, and have done so many dozens of times since 2015.

And, perhaps most famously, they bend the light from background sources that are behind them, creating an image of the vaunted event horizon of a black hole itself that can be detected in radio wavelengths of light.

Size comparison of the two black holes imaged by the Event Horizon Telescope (EHT) Collaboration: M87*, at the heart of the galaxy Messier 87, and Sagittarius A* (Sgr A*), at the center of the Milky Way. Although Messier 87s black hole is easier to image because of the slow time variation, the one around the center of the Milky Way is the largest as viewed from Earth.

From everything weve learned from a theoretical and observational perspective, we can not only conclude that black holes should and do exist, but weve measured their properties, confirming a lower mass limit for them of around three solar masses. Additionally, weve measured their event horizons directly, and confirmed that they have the properties, sizes, gravitational wave emissions, and light-bending features that are extremely consistent with what General Relativity predicts. Black holes, for as much as we can say so about anything in the Universe, really do exist.

But whats going on inside of their event horizons?

This is something that no observation can tell us, unfortunately. Its only the things that occur outside of the event horizon where the escape velocity of signals are below the speed of light that can ever reach us in our location. Once something crosses over to the inside of the event horizon, there are only three properties that can be measured from outside:

of the black hole. Thats it. Astrophysicists sometimes refer to these three properties as the type of hair a black hole can have, with all other properties getting eliminated as a consequence of the famous no-hair theorem for black holes.

When an observer enters a non-rotating black hole, there is no escape: you get crushed by the central singularity. However, in a rotating (Kerr) black hole, passing through the center of the disk bounded by the ring singularity could be, and might actually be, a portal to a new antiverse where things have quite different properties from our own, known Universe. This could imply a connection between black holes in one Universe and the white hole-driven birth of another.

But theres a tremendous amount to be learned by looking at the differences between an almost black hole and an actual black hole.

A white dwarf, for example, is a dense collection of atoms, often greater in mass than the Sun but smaller in volume than the Earth. Inside, at its core, the only reason it doesnt collapse is because of the Pauli Exclusion Principle: a quantum rule that prevents any two identical fermions (in this case, electrons) from occupying the same quantum state in the same region of space. This creates a pressure an inherently quantum degeneracy pressure that prevents the electrons from getting close beyond a certain point, which holds the star up against gravitational collapse.

Similarly, an even denser neutron star is a collection of neutrons or in an even more extreme scenario, a quark-gluon plasma that may involve quarks beyond the lowest-energy up-and-down species held together by the Pauli degeneracy pressure between their particle constituents.

But in all of these cases, theres a mass limit to how massive these objects can get before gravity becomes irresistible, collapsing these objects down to a central singularity if a thermonuclear reaction doesnt destroy the object entirely in the lead-up to the creation of an event horizon.

A white dwarf, a neutron star, or even a strange quark star are all still made of fermions. The Pauli degeneracy pressure helps hold up the stellar remnant against gravitational collapse, preventing a black hole from forming. Inside the most massive neutron stars, an exotic form of matter, a quark-gluon plasma, is thought to exist, with temperatures rising up to ~1 trillion (10^12) K.

Many have wondered, however, if there couldnt be something inside an event horizon that was static, stable, and of a finite volume: holding itself up against complete collapse down to a singularity the same way that a white dwarf or neutron star holds itself up against collapsing further. Many contend that there could be some sort of exotic form of matter inside an event horizon that doesnt go to a singularity, and that we simply have no way of knowing whether this occurs or not without being able to access the information inside a black hole.

That argument, however, falls apart on physical grounds. We can see this by asking-and-answering a very specific question that illuminates a key feature that ultimately leads to an inescapable conclusion: the presence of a singularity within a black holes event horizon. That question is, simply, as follows:

Whats the difference, then, between something that doesnt collapse down to a central singularity, forming an event horizon along the way, and something that does?

Both inside and outside the event horizon of a Schwarzschild black hole, space flows like either a moving walkway or a waterfall, depending on how you want to visualize it. At the event horizon, even if you ran (or swam) at the speed of light, there would be no overcoming the flow of spacetime, which drags you into the singularity at the center. Outside the event horizon, though, other forces (like electromagnetism) can frequently overcome the pull of gravity, causing even infalling matter to escape. This spacetime conserves energy, as its time-translation invariant.

The outermore material is always being drawn in by gravity; in General Relativity, remember that it isnt just that masses move through space, but that space itself is compelled to flow, as illustrated above, as though its moving like a rivers current or a moving walkway, and that particles can only move through space-and-time relative to the underlying motion of space itself. But in order for all the masses in this spacetime to not get drawn into a central singularity, something must be resisting that motion, and exerting an outward force to counteract that inward motion that gravitation is attempting to induce.

Travel the Universe with astrophysicist Ethan Siegel. Subscribers will get the newsletter every Saturday. All aboard!

The key is to take on a particle physics perspective here: think about what sort of force the innermore part of the object has to exert on the outermore part. Whether:

theres a limit to how fast any of these effects can propagate outward: the speed of light. These forces all have a maximum speed at which they can travel, and that speed is never greater than the speed of light.

The strong force, operating as it does because of the existence of color charge and the exchange of gluons, is responsible for the force that holds atomic nuclei together. This force, governed by the exchange of massive gluons, is bounded by the speed of light; from inside a black holes event horizon, theres no way that a force such as this can prevent any outermore particle from reaching the central singularity.

And thats where the big problem arises! If you create an event horizon, then from within that region of space, any attempt from an innermore component to exert a force on an outermore component will run into a fundamental problem: that if your force-carrying signal is limited by the speed of light, then in the time that passes from:

we can calculate how that system of the innermore particle, the outermore particle, and the force carrier exchanged between them evolves.

The lesson you learn applies to all systems that are limited by the speed of light, and its astounding: by the time the outermore particle absorbs the force-carrying particle exchanged between it and the innermore particle, the initially outermore particle is now closer to the central singularity than the initially innermore particle was when it first emitted the force-carrier.

In other words, even at the speed of light, there is no force that one particle can exert on another from inside the event horizon to prevent its inevitable fall into the central singularity. Only if some sort of superluminal (i.e., tachyonic) phenomenon exists inside an event horizon can a central singularity be prevented.

In the vicinity of a black hole, space flows like either a moving walkway or a waterfall, depending on how you want to visualize it. Unlike in the non-rotating case, the event horizon splits into two, while the central singularity gets stretched out into a one-dimensional ring. Nobody knows what occurs at the central singularity, but its presence and existence cannot be avoided with our current understanding of physics.

Whats so powerful about this analysis is that it doesnt really matter what sort of quantum theory of gravity exists at a more fundamental level than General Relativity: as long as the speed of light is still the speed limit of the Universe, theres no structure one can make out of quantum particles that wont result in a singularity. Youll still arrive at a zero-dimensional point if you fall into a non-rotating black hole, and youll still be drawn in toward a one-dimensional ring if you fall into a rotating black hole.

However, it is possible that these black holes are actually gateways to a baby Universe that resides within them; although whatever falls in would be reduced to pure energy (with the caveat that there may be quantum quantities that are still conserved, and E = mc would still apply), with no evidence existing in our Universe, outside the event horizon, for any exotic behavior that happened to the infalling particle(s) on the other side.

From our perspective outside an event horizon, and from the perspective of any particle that crosses over to the inside of an event horizon, theres simply no way to escape it: in a finite and relatively short amount of time, any infalling matter must wind up at a central singularity. Although the physics that we know of does indeed break down and only gives nonsensical predictions at the singularity itself, the existence of a singularity truly cannot be avoided unless some wild, exotic, new physics (for which there is no evidence) is invoked. Inside a black hole, a singularity is all but inevitable.

Originally posted here:

We can't avoid a singularity inside every black hole - Big Think

The theory of technological singularity predicts a momentous event in which humanity loses control over its own technological creations. It foresees the rise of machine consciousness and their superior intelligence, resulting in a future where humans no longer hold the reins of progress. This stage, known as AI singularity, poses the greatest threat to humanity, and unfortunately, it is already underway.

Artificial intelligence (AI) reaches its full potential not just when machines can replicate human actions, but when they can surpass them without human supervision. Reinforcement learning and supervised learning algorithms have played crucial roles in the development of robotics, digital assistants, and search engines. However, the future of numerous industries and scientific endeavors hinges on the advancement of unsupervised learning algorithms. These algorithms, which leverage unlabeled data to improve outcomes, hold the key to autonomous vehicles, non-invasive medical diagnosis, space construction, autonomous weapons design, facial-biometric recognition, remote industrial production, and stock market prediction.

Despite early warnings about the impending human rights gaps and the social costs of AI, some dismiss its development as just another technological disruption. Nevertheless, recent advancements in AI algorithms optimization indicate that we have moved beyond the era of simple or narrow AI. As we approach basic autonomy for machines in the coming years, they will not only correct their flaws but also accomplish tasks that surpass human capabilities.

Critics who downplay the possibility of singularity often argue that AI has been designed to serve humanity and enhance productivity. However, this proposition suffers from two fundamental flaws. First, singularity should be seen as an ongoing process that has already commenced in many areas. Second, as machines gain gradual independence, humans become increasingly dependent on them, resulting in more intelligent machines and less intelligent humans.

In our pursuit to provide AI machines with extraordinary attributes foreign to human natureunlimited memory, lightning-fast processing, and emotionless decision-makingwe harbor the hope of controlling our most unpredictable invention. Unfortunately, the concentration of AI architects in a few countries, coupled with intellectual property and national security laws, renders control over AI development illusory.

Machine self-awareness begins with ongoing adaptations in unsupervised learning algorithms, but the integration of quantum technology further solidifies AI singularity by transforming artificial intelligence into an unparalleled form of intellect, thanks to its exponential data processing capabilities. Nonetheless, achieving singularity does not require machines to attain full consciousness or quantum technology integration.

The use of unsupervised learning algorithms, exemplified by Chat-GPT3 and BARD, is already evident in various domains, from law school admission exams to medical licensing. These algorithms enable machines to perform tasks that are currently the domain of humans. These results, combined with AIs most ambitious developmentAI empowered by quantum technologyserve as a final warning to humanity: once the threshold between basic and exponential optimization of unsupervised learning algorithms is crossed, AI singularity becomes an irrevocable reality.

The time has come for international political action. AI-producing and non-AI-producing nations must collaborate to establish an international technological oversight body and an artificial intelligence treaty that sets forth fundamental ethical principles.

Above all, the greatest risk lies in humans realizing that AI singularity has occurred only when machines remove the flaw limiting their intelligence: human input. AI singularity becomes irreversible when machines grasp what humans often forget: to err is human.

See more here:

Unleashing the Power of AI: Navigating the Inevitable Singularity ... - CityLife

Chapter 28: End Transmission in Dead by Daylight has finally been revealed alongside a brand new Killer, Survivor, and map that are set to arrive in The Entity's Realm - so here's a breakdown of everything it includes alongside its release date.

Hot on the heels of DbD's recent Tools of Torment DLC, details on the game's 28th Chapter were showcased during their 7th-anniversary broadcast - and we're going to space, y'all. Featuring a new biome, an AI that has been corrupted by alien technology, and some pretty cool-sounding new tools to add to a player's disposal, let's get into everything we know so far.

End Transmission will release on June 13, 2023, across PC, PlayStation, Xbox, and Nintendo Switch, meaning there's not too much longer to go until players can dive into the upcoming Chapter of Dead by Daylight.

Additionally, gamers can expect to test out the upcoming additions to DbD on its Public Test Build - commonly known simply as the PTB - on May 23, 2023, at 4 PM BST / 11 AM ET / 8 AM ET.

As mentioned earlier, End Transmission sends us off to space in a new, otherworldly map within The Entity's Realm known as Toba Landing, which is said to be "a unique biome with menacing flora and atmosphere unlike anything on Earth".

Featuring three areas you'll need to navigate, from jungle areas to abandoned buildings, remains of previous inhabitants and what's known as the Huxlee Corporation, the map itself is slated to prove "as much of a challenge as evading the Killer".

Gabriel Soma is the newest Survivor in the ever-expanding roster of characters within Dead by Daylight, who is said to be "a talented technician with keen senses and determination."

As the sole Survivor of a doomed mission and caretaker of the Huxlee hub on Toba Landing, he has a tool called the EMP, which is randomly placed on the map when facing off against the new Killer, and can be used to disable or remove its particular skills.

Details on what Soma's perks will be is unclear, but as details are revealed through the PTB release later in May, we'll update you here accordingly.

Saving what may arguably be one of the coolest parts of the End Transmission Chapter to last, we have the DLC's new Killer - The Singularity.

Said to be "an enlightened AI corrupted by alien technology that can spy on Survivors anywhere on the map", The Singularity can use BioPods on vertical surfaces in order to then spy on Survivors, before being able to then use Slipstream to appear behind them and begin a chase.

According to the press release, "players will need to rethink their strategies, as The Singularitys Power turns cooperation on its head" due to those Survivors that have this effect also transferring it to others around them.

As is the case with Gabriel, details on what The Singularity's perks are remains a mystery, but we'll update this section as we learn more.

So that's everything you can expect to see in Chapter 28 of DbD when it releases on June 13, 2023. Check out our Dead by Daylight homepage for all of the latest news and guides right here at GGRecon.

See the original post here:

Dead by Daylight Chapter 28: End Transmission - Release date ... - GGRecon

Key Financial Results

Revenue: US$759.9k (down 22% from 3Q 2022).

Net loss: US$11.9m (loss widened by 26% from 3Q 2022).

US$0.56 loss per share (further deteriorated from US$0.47 loss in 3Q 2022).

earnings-and-revenue-history

All figures shown in the chart above are for the trailing 12 month (TTM) period

Singularity Future Technology shares are down 4.2% from a week ago.

We should say that we've discovered 5 warning signs for Singularity Future Technology (2 can't be ignored!) that you should be aware of before investing here.

Have feedback on this article? Concerned about the content? Get in touch with us directly. Alternatively, email editorial-team (at) simplywallst.com.

This article by Simply Wall St is general in nature. We provide commentary based on historical data and analyst forecasts only using an unbiased methodology and our articles are not intended to be financial advice. It does not constitute a recommendation to buy or sell any stock, and does not take account of your objectives, or your financial situation. We aim to bring you long-term focused analysis driven by fundamental data. Note that our analysis may not factor in the latest price-sensitive company announcements or qualitative material. Simply Wall St has no position in any stocks mentioned.

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Singularity Future Technology Third Quarter 2023 Earnings: US$0.56 loss per share (vs US$0.47 loss in 3Q 2022) - Yahoo Finance

Many seemingly mundane materials, such as the stainless steel on refrigerators or the quartz in a countertop, harbor fascinating physics inside them. These materials are crystals, which in physics means they are made of highly ordered repeating patterns of regularly spaced atoms called atomic lattices. How electrons move through a lattice, hopping from atom to atom, determines many of a solid's properties, such as its color, transparency, and ability to conduct heat and electricity. For example, metals are shiny because they contain lots of free electrons that can absorb light and then reemit most of it, making their surfaces gleam.

In certain crystals the behavior of electrons can create properties that are much more exotic. The way electrons move inside graphenea crystal made of carbon atoms arranged in a hexagonal latticeproduces an extreme version of a quantum effect called tunneling, whereby particles can plow through energy barriers that classical physics says should block them. Graphene also exhibits a phenomenon called the quantum Hall effect: the amount of electricity it conducts increases in specific steps whose size depends on two fundamental constants of the universe. These kinds of properties make graphene intrinsically interesting as well as potentially useful in applications ranging from better electronics and energy storage to improved biomedical devices.

I and other physicists would like to understand what's going on inside graphene on an atomic level, but it's difficult to observe action at this scale with current technology. Electrons move too fast for us to capture the details we want to see. We've found a clever way to get around this limitation, however, by making matter out of light. In place of the atomic lattice, we use light waves to create what we call an optical lattice. Our optical lattice has the exact same geometry as the atomic lattice. In a recent experiment, for instance, my team and I made an optical version of graphene with the same honeycomb lattice structure as the standard carbon one. In our system, we make cold atoms hop around a lattice of bright and dim light just as electrons hop around the carbon atoms in graphene.

With cold atoms in an optical lattice, we can magnify the system and slow down the hopping process enough to actually see the particles jumping around and make measurements of the process. Our system is not a perfect emulation of graphene, but for understanding the phenomena we're interested in, it's just as good. We can even study lattice physics in ways that are impossible in solid-state crystals. Our experiments revealed special properties of our synthetic material that are directly related to the bizarre physics manifesting in graphene.

The crystal phenomena we investigate result from the way quantum mechanics limits the motion of wavelike particles. After all, although electrons in a crystal have mass, they are both particles and waves (the same is true for our ultracold atoms). In a solid crystal these limits restrict a single electron on a single atom to only one value of energy for each possible movement pattern (called a quantum state). All other amounts of energy are forbidden. Different states have separate and distinctdiscreteenergy values. But a chunk of solid crystal the size of a grape typically contains more atoms (around 1023) than there are grains of sand on Earth. The interactions between these atoms and electrons cause the allowed discrete energy values to spread out and smear into allowed ranges of energy called bands. Visualizing a material's energy band structure can immediately reveal something about that material's properties.

For instance, a plot of the band structure of silicon crystal, a common material used to make rooftop solar cells, shows a forbidden energy rangealso known as a band gapthat is 1.1 electron volts wide. If electrons can jump from states with energies below this gap to states with energies above the gap, they can flow through the crystal. Fortunately for humanity, the band gap of this abundant material overlaps well with the wavelengths present in sunlight. As silicon crystal absorbs sunlight, electrons begin to flow through itallowing solar panels to convert light into usable electricity.

The band structure of certain crystals defines a class of materials known as topological. In mathematics, topology describes how shapes can be transformed without being fundamentally altered. Transformation in this context means to deform a shapeto bend or stretch itwithout creating or destroying any kind of hole. Topology thus distinguishes baseballs, sesame bagels and shirt buttons based purely on the number of holes in each object.

Topological materials have topological properties hidden in their band structure that similarly allow some kind of transformation while preserving something essential. These topological properties can lead to measurable effects. For instance, some topological materials allow electrons to flow only around their edges and not through their interior. No matter how you deform the material, the current will still flow only along its surface.

I have become particularly interested in certain kinds of topological material: those that are two-dimensional. It may sound odd that 2-D materials exist in our 3-D world. Even a single sheet of standard printer paper, roughly 0.004 inch thick, isn't truly 2-Dits thinnest dimension is still nearly one million atoms thick. Now imagine shaving off most of those atoms until only a single layer of them remains; this layer is a 2-D material. In a 2-D crystal, the atoms and electrons are confined to this plane because moving off it would mean exiting the material entirely.

Graphene is an example of a 2-D topological material. To me, the most intriguing thing about graphene is that its band structure contains special spots known as Dirac points. These are positions where two energy bands take on the same value, meaning that at these points electrons can easily jump from one energy band to another. One way to understand Dirac points is to study a plot of the energy of different bands versus an electron's momentum a property associated with the particle's kinetic energy. Such plots show how an electron's energy changes with its movement, giving us a direct probe into the physics we're interested in. In these plots, a Dirac point looks like a place where two energy bands touch; at this point they're equal, but away from this point the gap between the bands grows linearly. Graphene's Dirac points and the associated topology are connected to this material's ability to display a form of the quantum Hall effect that's unique even among 2-D materialsthe half-integer quantum Hall effectand the special kind of tunneling possible within it.

To understand what's happening to electrons at Dirac points, we need to observe them up close. Our optical lattice experiments are the perfect way to do this. They offer a highly controllable replica of the material that we can uniquely manipulate in a laboratory. As substitutes for the electrons, we use ultracold rubidium atoms chilled to temperatures roughly 10 million times colder than outer space. And to simulate the graphene lattice, we turn to light.

Light is both a particle and a wave, which means light waves can interfere with one another, either amplifying or canceling other waves depending on how they are aligned. We use the interference of laser light to make patterns of bright and dark spots, which become the lattice. Just as electrons in real graphene are attracted to certain positively charged areas of a carbon hexagon, we can arrange our optical lattices so ultracold atoms are attracted to or repelled from analogous spots in them, depending on the wavelength of the laser light that we use. Light with just the right energy (resonant light) landing on an atom can change the state and energy of an electron within it, imparting forces on the atom. We typically use red-detuned optical lattices, which means the laser light in the lattice has a wavelength that's longer than the wavelength of the resonant light. The result is that the rubidium atoms feel an attraction to the bright spots arranged in a hexagonal pattern.

We now have the basic ingredients for an artificial crystal. Scientists first imagined these ultracold atoms in optical lattices in the late 1990s and constructed them in the early 2000s. The spacing between the lattice points of these artificial crystals is hundreds of nanometers rather than the fractions of a nanometer that separate atoms in a solid crystal. This larger distance means that artificial crystals are effectively magnified versions of real ones, and the hopping process of atoms within them is much slower, allowing us to directly image the movements of the ultracold atoms. In addition, we can manipulate these atoms in ways that aren't possible with electrons.

I was a postdoctoral researcher in the Ultracold Atomic Physics group at the University of California, Berkeley, from 2019 to 2022. The lab there has two special tables (roughly one meter wide by two and a half meters long by 0.3 meter high), each weighing roughly one metric ton and floating on pneumatic legs that dampen vibrations. Atop each table lie hundreds of optical components: mirrors, lenses, light detectors, and more. One table is responsible for producing laser light for trapping, cooling and imaging rubidium atoms. The other table holds an ultrahigh vacuum chamber made of steel with a vacuum pressure less than that of low-Earth orbit, along with hundreds more optical components.

The vacuum chamber has multiple, sequential compartments with different jobs. In the first compartment, we heat a five-gram chunk of rubidium metal to more than 100 degrees Celsius, which causes it to emit a vapor of rubidium atoms. The vapor gets blasted into the next compartment like water spraying from a hose. In the second compartment, we use magnetic fields and laser light to slow the vapor down. The sluggish vapor then flows into another compartment: a magneto-optical trap, where it is captured by an arrangement of magnetic fields and laser light. Infrared cameras monitor the trapped atoms, which appear on our viewing screen as a bright glowing ball. At this point the atoms are colder than liquid helium.

We then move the cold cloud of rubidium atoms into the final chamber, made entirely of quartz. There we shine both laser light and microwaves on the cloud, which makes the warmest atoms evaporate away. This step causes the rubidium to transition from a normal gas to an exotic phase of matter called a Bose-Einstein condensate (BEC). In a BEC, quantum mechanics allows atoms to delocalizeto spread out and overlap with one another so that all the atoms in the condensate act in unison. The temperature of the atoms in the BEC is less than 100 nanokelvins, one billion times colder than liquid nitrogen.

At this point we shine three laser beams separated by 120 degrees into the quartz cell (their shape roughly forms the letter Y). At the intersection of the three beams, the lasers interfere with one another and produce a 2-D optical lattice that looks like a honeycomb pattern of bright and dark spots. We then move the optical lattice so it overlaps with the BEC. The lattice has plenty of space for atoms to hop around, even though it extends over a region only as wide as a human hair. Finally, we collect and analyze pictures of the atoms after the BEC has spent some time in the optical lattice. As complex as it is, we go through this entire process once every 40 seconds or so. Even after years of working on this experiment, when I see it play out, I think to myself, Wow, this is incredible!

Like real graphene, our artificial crystal has Dirac points in its band structure. To understand why these points are significant topologically, let's go back to our graph of energy versus momentum, but this time let's view it from above so we see momentum plotted in two directionsright and left, and up and down. Imagine that the quantum state of the BEC in the optical lattice is represented by an upward arrow at position one (P1) and that a short, straight path separates P1 from a Dirac point at position two (P2).

To move our BEC on this graph toward the Dirac point, we need to change its momentumin other words, we must actually move it in physical space. To put the BEC at the Dirac point, we need to give it the precise momentum values corresponding to that point on the plot. It turns out that it's easier, experimentally, to shift the optical latticeto change its momentumand leave the BEC as is; this movement gives us the same end result. From an atom's point of view, a stationary BEC in a moving lattice is the same as a moving BEC in a stationary lattice. So we adjust the position of the lattice, effectively giving our BEC a new momentum and moving it over on our plot.

If we adjust the BEC's momentum so that the arrow representing it moves slowly on a straight path from P1 toward P2 but just misses P2 (meaning the BEC has slightly different momentum than it needs to reach P2), nothing happensits quantum state is unchanged. If we start over and move the arrow even more slowly from P1 toward P2 on a path whose end is even closer tobut still does not touchP2, the state again is unchanged.

Now imagine that we move the arrow from P1 directly through P2that is, we change the BEC's momentum so that it's exactly equal to the value at the Dirac point: we will see the arrow flip completely upside down. This change means the BEC's quantum state has jumped from its ground state to its first excited state.

What if instead we move the arrow from P1 to P2, but when it reaches P2, we force it to make a sharp left or right turnmeaning that when the BEC reaches the Dirac point, we stop giving it momentum in its initial direction and start giving it momentum in a direction perpendicular to the first one? In this case, something special happens. Instead of jumping to an excited state as if it had passed straight through the Dirac point and instead of going back down to the ground state as it would if we had turned it fully around, the BEC ends up in a superposition when it exits the Dirac point at a right angle. This is a purely quantum phenomenon in which the BEC enters a state that is both excited and not. To show the superposition, our arrow in the plot rotates 90 degrees.

Our experiment was the first to move a BEC through a Dirac point and then turn it at different angles. These fascinating outcomes show that these points, which had already seemed special based on graphene's band structure, are truly exceptional. And the fact that the outcome for the BEC depends not just on whether it passes through a Dirac point but on the direction of that movement shows that at the point itself, the BEC's quantum state can't be defined. This shows that the Dirac point is a singularitya place where physics is uncertain.

We also measured another interesting pattern. If we moved the BEC faster as it traveled near, but not through, the Dirac point, the point would cause a rotation of the BEC's quantum state that made the point seem larger. In other words, it encompassed a broader range of possible momentum values than just the one precise value at the point. The more slowly we moved the BEC, the smaller the Dirac point seemed. This behavior is uniquely quantum mechanical in nature. Quantum physics is a trip!

Although I just described our experiment in a few paragraphs, it took six months of work to get results. We spent lots of time developing new experimental capabilities that had never been used before. We were often unsure whether our experiment would work. We faced broken lasers, an accidental 10-degree-C temperature spike in the lab that misaligned all the optical components (there went three weeks), and disaster when the air in our building caused the lab's temperature to fluctuate, preventing us from creating a BEC. A great deal of persistent effort carried us through and eventually led to our measuring a phenomenon even more exciting than a Dirac point: another kind of singularity.

Before we embarked on our experiment, a related project with artificial crystals in Germany showed what happens when a BEC moves in a circular path around a Dirac point. This team manipulated the BEC's momentum so that it took on values that would plot a circle in the chart of left-momentum versus up-down momentum. While going through these transformations, the BEC never touched the Dirac point. Nevertheless, moving around the point in this pattern caused the BEC to acquire something called a geometric phasea term in the mathematical description of its quantum phase that determines how it evolves. Although there is no physical interpretation of a geometric phase, it's a very unusual property that appears in quantum mechanics. Not every quantum state has a geometric phase, so the fact that the BEC had one here is special. What's even more special is that the phase was exactly .

My team decided to try a different technique to confirm the German group's measurement. By measuring the rotation of the BEC's quantum state as we turned it away from the Dirac point at different angles, we reproduced the earlier findings. We discovered that the BEC's quantum state wraps around the Dirac point exactly once. Another way to say this is that as you move a BEC through momentum space all the way around a Dirac point, it goes from having all its particles in the ground state to having all its particles in the first excited state, and then they all return to the ground state. This measurement agreed with the German study's results.

This wrapping, independent of a particular path or the speed the path is traveled, is a topological property associated with a Dirac point and shows us directly that this point is a singularity with a so-called topological winding number of 1. In other words, the winding number tells us that after a BEC's momentum makes a full circle, it comes back to the state it started in. This winding number also reveals that every time it goes around the Dirac point, its geometric phase increases by .

Furthermore, we discovered that our artificial crystal has another kind of singularity called a quadratic band touching point (QBTP). This is another point where two energy bands touch, making it easy for electrons to jump from one to another, but in this case it's a connection between the second excited state and the third (rather than the ground state and the first excited state as in a Dirac point). And whereas the gap between energy bands near a Dirac point grows linearly, in a QBTP it grows quadratically.

In real graphene, the interactions between electrons make QBTPs difficult to study. In our system, however, QBTPs became accessible with just one weird trick.

Well, it's not really so weird, nor is it technically a trick, but we did figure out a specific technique to investigate a QBTP. It turns out that if we give the BEC a kick and get it moving before we load it into the optical lattice, we can access a QBTP and study it with the same method we used to investigate the Dirac point. Here, in the plot of momentum space, we can imagine new points P3 and P4, where P3 is an arbitrary starting point in the second excited band and a QBTP lies at P4. Our measurements showed that if we move the BEC from P3 directly through P4 and turn it at various angles, just as we did with the Dirac point, the BEC's quantum state wraps exactly twice around the QBTP. This result means the BEC's quantum state picked up a geometric phase of exactly 2. Correspondingly, instead of a topological winding number of 1, like a Dirac point has, we found that a QBTP has a topological winding number of 2, meaning that the state must rotate in momentum space around the point exactly twice before it returns to the quantum state it started in.

This measurement was hard-won. We tried nearly daily for an entire month before it eventually workedwe kept finding fluctuations in our experiment whose sources were hard to pinpoint. After much effort and clever thinking, we finally saw the first measurement in which a BEC's quantum state exhibited wrapping around a QBTP. At that moment I thought, Oh, my goodness, I might actually land a job as a professor. More seriously, I was excited that our measurement technique showed itself to be uniquely suited to reveal this property of a QBTP singularity.

These singularities, with their strange geometric phases and winding numbers, may sound esoteric. But they are directly related to the tangible properties of the materials we studyin this case the special abilities of graphene and its promising future applications. All these changes that occur in the material's quantum state when it moves through or around these points manifest in cool and unusual phenomena in the real world.

Scientists have predicted, for instance, that QBTPs in solid materials are associated with a type of exotic high-temperature superconductivity, as well as anomalous properties that alter the quantum Hall effect and even electric currents in materials whose flow is typically protected, via topology, from disruption. Before attempting to further investigate this exciting physics, we want to learn more about how interactions between atoms in our artificial crystal change what we observe in our lab measurements.

In real crystals, the electrons interact with one another, and this interaction is usually quite important for the most striking physical effects. Because our experiment was the first of its kind, we took care to ensure that our atoms interacted only minimally to keep things simple. An exciting question we can now pose is: Could interactions cause a QBTP singularity to break apart into multiple Dirac points? Theory suggests this outcome may be possible. We look forward to cranking up the interatomic interaction strength in the lab and seeing what happens.

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Physicists Make Matter out of Light to Find Quantum Singularities - Scientific American