superposition principle

Two dancers on one stage: the triangle and the stripe. In a quantum gas of dysprosium atoms cooled to 62 nanokelvin, these two spatial structures have met for the first time in a single experiment. The gas is held in a trap shaped like a surfboard, and its atoms are among the most magnetic in the periodic table.

Quantum systems made of many particles are the basis of future computers and secure networks. But the more particles there are, the harder it is to understand how they are arranged: the number of possible states grows like an avalanche. The usual approach, measuring everything, takes an incredibly long time.

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.

Hot water sometimes freezes faster than warm water: this odd fact is known as the Mpemba effect. Now something similar has been found in the quantum world: a state with weak entanglement (a special quantum connection between particles) can beat a more entangled one to the finish line.

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.

At low temperatures, many materials become superconductors — current flows without resistance. But how exactly does this happen if electrons were initially trapped in an insulator? Half a century ago, Philip Anderson suggested that the answer lies in a special quantum dance of particles.

Seven dancers step onto the stage. They join hands so that any trio or quartet moves in perfect harmony with the rest — no group falls out of the overall rhythm. In the quantum world, this is called an absolutely maximally entangled state (AME for short). It's a perfect knot where every part knows everything about the whole.

An empty resonator isn't truly empty. Even in an absolute vacuum, where not a single photon exists, quantum fluctuations persist. They resemble ripples on water in a dead calm: the surface appears smooth, but molecules keep jittering. Physicists have learned to turn this jitter into real waves.

Every night, hundreds of observatories scan the sky, yet planets around other stars remain ghosts. Their light is billions of times fainter than the glare of their parent star — the task seems hopeless. But optics found a way: rather than block the star’s light, cancel it with a counter-wave of the same amplitude, shifted by half a period.

The quantum world is full of strange connections. Two particles can become “entangled”: the state of one instantly affects the other, even if they are kilometers apart. But how do you know if they are truly entangled? It's like a ball of yarn: at first glance, you can't tell whether it's a single tangled ball or just a mess of loose threads.

A pebble on a streambed lies still as sunlight sparkles dance on the water's surface. In astronomy, the contrast is similar: a real exoplanet is the stone, while myriad speckles (patches of scattered starlight) are the ripples trembling in instruments.

In a world where Reynolds numbers are minuscule, water turns into thick syrup, and the swimming tricks we know stop working. Here reigns the insidious scallop theorem: reciprocal motions produce no net displacement. Microorganisms found a way out: they grow polymer tails.

An atomic nucleus is not just a ball of protons and neutrons. It has a shape, and that shape can change. The tin-116 nucleus was long considered almost perfectly spherical: it has 50 protons — a 'magic' number that usually gives a nucleus spherical symmetry. But a new ultra-precise measurement showed otherwise.

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.

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.

A quantum computer is like an orchestra where every musician must hit their note exactly. If one plays off-key, the melody falls apart. The musicians here are qubits, storing information.

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.

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.

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.

Quantum entanglement often behaves like a synchronized dance visible from only one angle. Change the way you observe it, and the particles appear disconnected. This limits secure communications. Now physicists have created a pair of photons whose 'dance' is flawless from all perspectives.

In the depths of a diamond crystal, studded with NV centers, a symphony slumbers. Each defect is like a tuning fork, ready to respond to a passing acoustic wave. But alone, their voices are barely audible: the spin-phonon coupling is weaker than a whisper. A maestro is needed, one who can turn timid vibrations into a resounding choir.

In nuclear physics, the belief long reigned that two neutrons cannot form a bound state — they attract too weakly and immediately fly apart. However, on the surface of neutron-rich nuclei, where the matter density drops to a thousandth of normal nuclear density, the situation changes dramatically.

In pursuit of gravitational waves, ripples in spacetime left by black holes and neutron stars, detectors like LIGO pump their arms with light of dazzling intensity.

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.

Quantum electrodynamics, or QED, describes how light interacts with charged particles — for example, electrons. It is one of the most precise theories in history: its predictions match experiment to the eleventh decimal place.

In a long corridor, a crowd of people tries to keep as far apart as possible. In a spacious hall, they would simply spread out, but here the walls squeeze them so tightly that they have to move single file, coordinating every step. Electrons in graphene layers twisted by a tiny angle behave in a similar way.

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

Light cones are not about light; they are boundaries in spacetime that separate causes from effects. These cones are not rigid: a massive object curves them, like a heavy ball pressing into a stretched sheet.

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.

For almost a century, cosmologists have been grappling with the mystery: what makes the Universe expand ever faster? The standard answer — dark energy — creates a monstrous discrepancy between the theoretical vacuum density and observations. But there's another path, one that turns causality on its head.

Conventional neural networks learn from thousands of examples, burning hours and gigawatts. Physicists have found a quantum workaround. As early as Max Planck showed the discreteness of energy, today this allows generation without training.

The quantum world plays a strange game with causality. If in everyday life salt is always added to soup before serving, here the ingredients end up in the bowl at the same time, and the chef doesn't remember the order. Physicists asked: can we measure this 'recipe'? The answer is no.

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.

Light is a stream of photons. In a special waveguide, resembling a narrow corridor, a 'gatekeeper' atom usually lets them through one at a time. This phenomenon is the domain of single-particle spectroscopy.

A translator gets distracted by every rustle in the hall, and a one-hour meeting stretches into two. That's roughly how ordinary quantum mechanics works: a particle evolves in time, while space serves as the stage. But what if we swapped their roles? Then the particle 'moves' through space, and time becomes a static backdrop.

An orchestra where every musician plays their own part, yet together they weave a complex melody: that's what a cloud of atoms looks like when their spins (intrinsic rotations, like tiny tops) oscillate in sync. Usually, these tops behave independently.

In a football stadium, the crowd's emotions arise from the chatter of individual fans. If mood could be both joyful and sorrowful at once, you'd have a quantum superposition. But the murmur of thousands of voices instantly forces that blend into a single definite state.