Quantum superposition

In a quiet room with no magnets anywhere, two electrons in a silicon trap still feel a faint trembling. It comes from the nuclei of silicon and germanium atoms, which spin randomly like the needles of broken compasses. This trembling was once considered noise, but now it has become a measuring instrument itself.

A handful of coins drops onto a table — heads and tails land wherever they please. The same goes for an instantaneous snapshot of a quantum chain: in some places a particle is present, in others it is not. But behind the disorder lurks a precise angle. In this work, a chain of particles closed into a ring was considered. It was divided into four arcs: two were measured, two were left untouched.

When a heavy atomic nucleus splits into two fragments, an invisible quantum thread remains between them. This thread is entanglement: the state of one fragment is instantly linked to the state of the other, as if they were still a single whole. For the first time, physicists have precisely calculated how long and strong such a thread can be, tracing the fission process step by step.

In a hall with a thousand spectators, applause blends into a general noise, but if someone falls out of rhythm — a ripple runs through the crowd. The quantum world works similarly: atoms in a trap can behave as a single whole, or they can fall apart into independent individuals.

Two tiny diamonds float in a vacuum, separated by a distance that light cannot cross during the experiment. Inside each, like a frozen spark, resides an entangled spin — a quantum state linking them into a single whole. Now the diamonds begin to move, but not just any motion: each one seems to split, existing in two places at once.

Imagine a huge puzzle where each piece is a quantum particle. To complete the picture, you don't just fit the pieces together: you need to entangle them in a special way. Usually, this is done by carefully applying operations one after another, like assembling the puzzle strictly by the instructions, row by row.

Coffee beans alone don't make a drink, but take two, and the cup fills. In the quantum world, there are similar states: from one copy, you can't extract pure entanglement, but from several, sometimes you can. For a long time, it wasn't known if such a thing existed at all. Scientists took a family of states specifically designed as a testing ground for this question.

A superfluid gas is like a crowd of people marching in step: each atom knows where to go and doesn't fall out of the common rhythm. But this crowd has three 'valleys'—three different directions it can take. In a new experiment, physicists made one valley slightly more 'favorable' than the others and watched how the crowd darted between them.

Quantum mechanics allows a particle to be in two places at once: this is called superposition. But massive objects, like a dust grain or a ball, don't behave that way: their position is always definite. Why? One idea is that it's an illusion: the particle is constantly "jittering" from random environmental kicks, and the blurred picture averages out.

Two massive bodies frozen in a quantum superposition resemble a pair of dancers trying to keep a single rhythm while an orchestra blares around them. Each gravitational wave is a musician throwing them off beat.

The quantum world is tricky: sometimes particles confined to a flat layer and pierced by a strong magnetic field start behaving like a liquid made not of whole electrons but of their fractions — fractional charges. This is the fractional quantum Hall effect.

A chain of a hundred tiny magnets lies on a table. Each one can point up or down, like a coin landing heads or tails. But these are not ordinary magnets: they sense each other not just individually but in threes. Three neighboring particles seem to negotiate which way to turn. Once a second, the experimenter shakes the table, and the whole system gets a short kick.

The quantum world loves balance. When a massive particle is forced to split, to go down two paths at once, something must give way in response. That "something" turns out to be the very apparatus that split the particle.

Quantum entanglement — a phenomenon where the states of two or more particles become interconnected regardless of the distance between them — usually links intrinsic properties such as spin or polarization. However, a new experiment has for the first time realized entanglement of the positions of two atoms in space.

Crystals fascinate us with their perfect spatial order: atoms frozen at lattice points, like beads on an invisible string. But what if the same symmetry unfolds in time? Time crystals are systems that, without any external cue, start repeating their states cyclically — clocks wound by nature itself. Inside this tireless rhythm, disorder seems to have no place.

Two light rays meet at a point and then diverge. Their paths form two intersecting surfaces in spacetime — null hypersurfaces (boundaries along which light propagates). It is on such a pair of surfaces that physicists can set initial data for Einstein's equations. This is called the characteristic Cauchy problem.

The classical neuron is a chamber musician, drawing only one note from each string: it takes a weighted sum of inputs, adds a bias, and passes it through a nonlinearity.

Superconducting qubits are the beating heart of quantum computers, but their rhythm is disrupted by decoherence: quantumness dissolves into noise.

For nearly forty years, high-temperature superconductivity in cuprates has remained one of the deepest riddles of condensed matter physics.

In the conventional Heisenberg picture, spins at low temperatures are supposed to line up in a strict pattern. But there are crystals — like pyrochlore — where geometry has its own way. Each ion sits at a vertex of a tetrahedron, and the main interaction enforces a rule: two spins point inward, two outward.

A magnetic field holds a tiny particle in mid-air, like an invisible dance partner. A special tuning of the field creates a trap with two "positions." In the ordinary world, a dancer occupies only one, but in the quantum world — both at once. Physicists have learned to achieve this for dust grains weighing trillionths of a gram.

Fall 1956. Kurt Gödel puts pen to paper, drafting a question for the dying John von Neumann: Can the satisfiability of a Boolean formula be checked faster than brute-force trial and error? The answer comes 69 years later, and it turns out to be the bite of the logical ouroboros, the mythical serpent that devours its own tail. The serpent is born from randomness.

The hunt for non-Abelian anyons is a quest for a quantum ghost that leaves only one clue: entropy. These particles live in two-dimensional systems at ultralow temperatures. Their exchange doesn't just flip the sign of the wavefunction — it entangles states, creating topological order.

Graphene, a two-dimensional carbon crystal, has long tantalized physicists with the hope of high-temperature superconductivity. Its electrons obey the relativistic equation of Paul Dirac, racing at tremendous speed, barely noticing each other.

An electron and its antiparticle — the positron, predicted by Дираком, — upon meeting, momentarily form позитроний: a tiny pair circling each other, like in an atom but without a nucleus. Almost instantly it decays, emitting two photons that turn out to be mysteriously linked.

Once Richard Feynman saw in quantum systems a challenge for classical computers. Now we face the inverse problem: understanding what exactly the quantum processor has simulated. Among the states it births are veritable 'black boxes'—topological phases of matter.

A topological superconducting nanowire is like a bridge, with two inseparable sentinels — Majorana modes — stationed at its ends. These exotic quasiparticles, predicted back in the 1930s, promise to become the foundation of an error-proof quantum computer.

The very first moments of the Universe's life resemble tuning a complex musical instrument. Quantum fluctuations, stretched by rapid inflation, became the 'notes' from which galaxies later formed. In the new work, physicists considered an unusual opening chord — a superoscillating state.

A quantum computer is like an orchestra where each musician, a qubit, must play their part accurately and on time. Usually, musicians are seated in fixed positions and connected by conductors' consoles. But what if we let them move freely across the stage and turn the movement itself into part of the music?

Twins enter a room from different doors. Each gets a box with a button, and each time they press it, either a red or a green light flashes. If the twins are perfectly identical, you'd expect their lights to follow the same internal rules. But what if the rules differ even though the twins are exact copies? That's precisely the scenario the authors explored.

A quantum calculation sometimes resembles an interpreter who gets distracted by every rustle in the hall, and a one-hour meeting turns into two. In physics, such a "rustle" is called the sign problem: it arises when probabilities in formulas become negative or complex, and ordinary computer simulations start to fail.

Three dancers move as one: each feels all the others, and the overall harmony cannot be reduced to individual interactions. This is roughly how three particles behave, born from an electron and positron collision at the speed of light. They are a top quark, its antiparticle, and a Z boson.

Two dice lie in different rooms. If they are 'entangled,' a roll of one instantly determines the outcome of the other — even at a distance. In the quantum world, such a link is called steering: one party, by performing measurements on their side, seems to dictate the state of the partner.

A quantum cat is a special state of light, the idea of which was proposed by Erwin Schrödinger in his famous thought experiment.

An ordinary magnet is like a compass: its needle points north. But a quantum compass can look in both directions at once. If a magnet floating in a vacuum is gently spun, its electron 'tops' synchronize so the whole piece of metal starts living by the rules of the microworld — freezes in a superposition, like a split pointer.

A single particle can be in two places at once — that's superposition. But any interaction, like a shout, instantly 'collapses' this uncertainty. It was long thought that even gravity could interfere.

Every quantum particle has spin — an intrinsic magnetic property, like a tiny arrow. In an experiment, a beam of such particles passing through a magnet splits in two, like a coin that lands either heads or tails. That’s exactly how particles like a hydrogen atom behave.

Imagine a library where instead of books, you have every conceivable combination of a few dozen quantum particles. The number of combinations grows like a snowball: add one particle, and the volume doubles. For fifty particles, there are more shelves than atoms in the visible universe.

If you accelerate one of four entangled particles to enormous speed, their quantum entanglement doesn't just melt away: it first weakens, then strengthens again. Physicists discovered this unexpected twist while studying the behavior of a special state called the Dicke state in a world governed by the laws of relativity.

A superconductor carries current without resistance, like water running through a pipe without friction. The secret lies in electron pairs: two electrons stick together as one, even though they normally repel. In an ordinary superconductor, the spins of the electrons in a pair point in opposite directions: this is the singlet state.