Fock space

Two observers, Alice and Bob, sit at opposite ends of the same lab. Between them is a source that fires off two pulses in turn. Each pulse gives birth to a wave packet flying toward its own detector. So far, this looks like an ordinary experiment with quantum particles.

The quantum world is like a kitchen where particles suddenly appear out of "nothing." But you need a chef — a classical field acting as an external source. Glauber's theorem, long known in optics, has now been generalized: it shows exactly how the field "cooks up" particles, be they photons or gravitons.

In a pot of boiling water, steam bubbles appear and disappear — a similar struggle takes place in two-dimensional materials. Here, electrons both create magnetism and try to extinguish it.

In the big world, there's a simple rule: energy density can't be negative, and its flow can't outrun light. In a café, that would look like this: a waiter can't deliver orders faster than he can run. Physicists call this restriction the energy dominance condition. But in the microworld, where quanta rule and spacetime can bend, energy starts acting up.

Building a house on sand is a bad idea. In physics, it was long believed that a quantum theory of gravity could not be built on a fixed "sand"—a pre-existing spacetime.

In the microcosm, long-range forces, gravity or electricity, do not switch off even at enormous distances. Therefore, any particle drags behind it a trail of soft (i.e., very low-energy) photons or gravitons. This trail is called the "dress"; without it, calculations fall apart and infinities appear.

The early universe expanded at an unimaginable rate — faster than light could cross it. In this boiling cauldron, any region of space resembled an open can of paint: its boundaries continuously captured new 'vapor' from outside, while some of its own contents irrevocably escaped.

You're pouring water into a glass, but you want exactly one million drops — not approximately, but exactly. An ordinary faucet pours a stream where the number of drops always varies. In the quantum world, photons have the same problem: a laser emits light where the number of particles fluctuates like a crowd in a square.

The familiar metronomes placed on a movable platform eventually start to swing in sync. In the quantum world, this trick long eluded scientists. But now physicists have synchronized even the most exotic state — a Fock state, where the number of light particles is precisely defined, like in a counter.

The end of the Universe is not just the fading of light. If dark energy, the mysterious substance accelerating cosmic expansion, tears it apart in a Big Rip scenario, or if expansion reverses into a contraction that pulls everything back to a point like a big bang in reverse, a…

The mystery of dark energy is a chasm. Quantum field theory predicts a density 10¹²⁰ times larger than observed. In the string landscape, this abyss takes shape — myriads of vacua with different energies, and we are nestled in one of them.

A light pulse can be compared to a musical chord: several notes sound simultaneously, each with its own loudness and phase. In quantum optics, such 'chords' are called multimode squeezed states.

An ultracold cloud of atoms trapped in laser light can 'breathe': it rhythmically contracts and expands, much like lungs. Physicists have long been able to observe this breathing, but only now have they realized that its amplitude is not just a pretty picture: it is a precise measure of hidden energy jitters inside the cloud.

Quantum computers promise to solve problems that are beyond the reach of ordinary computers. But their components, quantum bits, are very sensitive. One type of quantum bit is an oscillating circuit that can exist in two states, like a pendulum swinging left or right. These states store information.

A snowdrift grows by strict rules: falling snowflakes form bumps, those attract more snow, and the bumps amplify. The same mathematics describes city growth, patterns on bark, ripples on water, and clusters of cosmic dust. Physicists call this uniformity universality.

A spring compressed to the limit breaks. Likewise, classical gravity theory leads to a singularity — a point where all laws break down. Quantum mechanics turns this end into an elastic bounce.

A photon is like a car in a multi-story parking lot, where each floor is its frequency (color). Usually it gets stuck on one level, but scientists added an elevator — a programmable modulator that moves the photon between floors on command.

Schrödinger's cat usually hides in thought experiments — alive and dead at the same time. This time, it was caught in the lab: a light pulse was made to be in two opposite states at once, like a coin hovering in the air, heads and tails at the same time.

Creating light with an exact number of photons is like stamping exactly 100,000 flawless coins. Until now, physicists could only control dozens of particles. The 'optical lathe' technology breaks this barrier: virtual lenses, like milling cutters, eliminate 'blurriness' and ensure each bunch contains exactly the specified number of photons. Counting becomes perfect.

Ice cubes in a glass melt, and the water mixes on its own. Many quantum systems behave this way: particles exchange energy, and after a while, order disappears. But if you add a spoonful of honey to the glass, mixing slows down, and in intense cold, the water freezes into glass — without a crystal lattice, but also without flow.

In the familiar world, we have three spatial dimensions. However, theoretical physics allows for additional, hidden directions — compactified, that is, curled up to microscopic sizes.

Hundreds of cooks in a kitchen — total chaos. Usually disorder grows. In quantum physics, the measure of such disorder is called entropy John von Neumann. For a many-particle system, entropy typically increases with their number. But scientists have found an exception. The secret lies in a strict rule: two cooks cannot enter the same aisle at the same time.

At night, an astronomer points a telescope at the edge of the visible universe and sees not stars but ripples — the imprint of the first moments. He knows these ripples should obey statistics, like the heights of people in a crowd. But he has only one crowd, and nothing to compare it with. This is cosmic variance.