Physics helps people to describe the events surrounding them using the language of simple models. Everything - from the falling of a stone in a nuclear reactor to the division of an atom - can be described using equations that are based on the laws of physics. It sometimes happens that events that seem completely different can be described using similar equations. This is very fortunate for physicists, as it gives them an opportunity to apply the knowledge gained from one event to another.

Recently, a team of scientists including staff members of ITMO University, Ioffe Institute, and their colleagues at the Australian National University have predicted a quantum photonic effect that is consistent with the quantum Hall effect. In the past, such behavior could only be observed in very complex systems, requiring a time modification of low temperatures, external magnetic fields, or structure parameters. However, this time scientists predicted analogs of such effects in very simple one-dimensional quantum systems.

Unfrei Stapenko, Maxim Gorlach and Nikita Olekhno. Photographed by the Faculty of Physics and Engineering of ITMO

Unfrei Stapenko, Maksim Gorlach and Nikita Olekhno. Photographed by the Faculty of Physics and Engineering of ITMO

### Quantum hall effect

In 1879, Edwin Hall, a young American physicist, discovered a new phenomenon while working on his doctoral thesis. If you take a metal plate and conduct an electric current on one side, there will be no voltage on the transverse edge of the plate. But if you apply a magnetic field vertically in the direction of current, such a voltage will come out. What's more, the emerging voltage can easily change its value with the intensity of the magnetic field. This effect was named the Hall Effect.

A hundred years later, in 1980, the German physicist Klaus von Klitzing discovered a new effect he called the quantum hall effect. If at very low temperatures there would be an electric current along a plate of semiconductor such as silicon or gallium arsenide in the presence of a large transverse magnetic field, the phenomenon described by Edwin Hall would look slightly different.

"The quantum Hall effect is similar to the classical Hall effect, but electrical conductivity attains volume," explains Alexander Poshkinski, the first author of the article. "This means that electrical resistance can change its values in a stair-phase manner and not consistently in the classical Hall effect. This finding is very important for metrology due to the minimal character of conductivity quantization that has fundamental physical constants with high precision. Has made it possible to introduce a new standard for measuring and measuring units of resistance. "

The significance of the discovery was so great that in 1985, Klaus von Klitzing was awarded the Nobel Prize in Physics. The theory behind this phenomenon was developed in detail by physicists from various countries, and researchers also began to search for its analogs in other systems, which have nothing to do with electric current.

### Chain of fours

Recently, an international team of scientists predicted such an effect for two quanta of light in a series of superconducting quabs.

Cubits (quantum analogs of bits) are physical systems that can be realized with different platforms: atoms, ions, quantum dots or superconducting resonators. Slightly in computer memory, a qubit has two basic states. However, if a normal electrical circuit can have a bit present in either of the 0 and 1 states, then a qubit can exist simultaneously in these two states, albeit in a different ratio.

Cubits can be arranged in a series where a qubit can transfer information to neighboring qubits. "The tight-binding model where every sepulcher can only interact with its nearest neighbors is well known," explains Nikita Olekhno, a PhD student at ITMO University. "It is a village made up of small houses, where every resident can shout something to his nearest neighbor, but to none except 100 houses."

Scientists studied such chains but were placed inside a waveguide with which photons (the amount of electromagnetic radiation) could propagate. When interacting with a qubit, a photon forms a polariton, that is, a hybrid particle that behaves partly as light and partly as matter. At some point, the localized excitation in the qubit can be emitted and brought back to a photon. The polarization would then continue to move along the chain, jump to other qubits, and transfer such transfer to H.P.

### Not only the pen between neighboring qubits.

"We add a wave wave that connects all the qubits is. It is a telephone line connecting all the houses in a village, ”says Nikita Olekhno. “In physics, this is called long-distance interaction. In addition, we also take into account the repulsive interactions between the two polarizations. This means that each quint in the system can absorb one photon but cannot absorb two simultaneously. This phenomenon is called photon blockade. You see, if one says "home", the other cannot call it at the same time as the line is busy; But they can call any other. "

It turns out that an analog of the quantum Hall effect is possible in such a system. While the behavior of electrons here has nothing to do with electric current, it is described by similar equations. Therefore, in this system it is possible to apply the accumulated knowledge after von Klitting's discovery.

### Alexander Podubani

“We consider a one-dimensional series of quabs with two photons. It turns out that this system can be represented as an equivalent two-dimensional but with one photon. In this new equivalent system, there will still be long-distance interactions between the quaibets. Thanks to long-range interactions, this model corresponds to one of the two-dimensional models with magnetic fields used to study the quantum Hall effect despite the absence of external fields. In this way, two-photon analogs of electronic Landau level and edge states emerge in a series of quabs. Regarding our system, these phenomena typically correspond to specific forms of distribution, in which the probability of one photon in quat with number m is detected, while the other photon is found in quat with number n. What's more, the energy spectrum of the series of quabs becomes self-similar. In quantum hall effect theory, it is called the Hoffstatter's butterfly, ”explains Professor Alexander Podubani, head of the research project.

### Importance

Despite its focus on theoretical models, this research may have long-term practical possibilities. Two-photon systems are used in quantum computing, quantum cryptography, and ultrapasis measurement. Their application is based on the quantum entanglement theory when two photons are correlated with each other. As a result, measuring the position of one photon provides information about the position of another. "This is an unusual phenomenon that makes it possible to build quantum simulators and quantum computers, develop quantum cryptography and high-precision metrology systems," says Nikita Olekhno.

Image: Probability of detecting the first and second photons in a quab with the corresponding numbers m and n for a series of 125 qubits in a waveguide.

Image: Probability of detecting the first and second photons in a quab with the corresponding numbers m and n for a series of 125 qubits in a waveguide.

Studying the relation between such entangled pairs of photons in a waveguide filled with models of superconducting quabs and quantum Hall effects will help physicists and engineers better understand the behavior of multipoton quantum systems. In the future, it will help to get one step closer to the practical implementation of tools for quantum information processing.

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