Candidate for unobtanium when obtaining Rydberg polaritons, gems turned out to be better than artificial crystals

(ORDO NEWS) — Using cuprous oxide crystals, scientists have obtained Rydberg polaritons of record parameters. These quasiparticles can become the basis of quantum computers, however, crystals of the required quality turned out to be possible to find only in nature.

At first glance, copper oxide (I) Cu 2 O, or cuprous oxide, is a fairly common substance, especially familiar to those who deal with electricity.

It is formed during the oxidation of copper in conditions of lack of oxygen. This matte reddish film on the wire, along with the smell of burnt wiring, is a sure sign that the wire has overheated and lost insulation, and something is wrong in the electrical circuit.

However, if a single crystal is grown from this compound, the frog turns into a princess. Cuprous oxide is a semiconductor that can be used to create solar cells and electronic components.

But the most interesting thing is the optical properties of cuprous oxide, thanks to which its single crystals are able to please both jewelers and physicists.

Light of certain wavelengths actively interacts with copper atoms and the crystal lattice of Cu 2 O, propagating through it, which leads to unusual and useful effects.

Candidate for unobtanium when obtaining Rydberg polaritons gems turned out to be better than artificial crystals 2
Faceted crystal of cuprite, or cuprous oxide

Physicists from the University of St. Andrews, led by Hamid Ohadi, in collaboration with scientists from Harvard University, Macquarie University and Aarhus University, managed to obtain record-breaking Rydberg polaritons in a copper oxide single crystal.

In order to explain the essence of their achievement and the difficulties they encountered, we first describe what quasiparticles are and what place Rydberg polaritons occupy among them.

Particles and quasiparticles

“Classical” elementary particles are the fundamental building blocks of which matter is built. They can be really elementary, like electrons and photons, or composite, like protons and neutrons, but they can exist in vacuum separately from everything.

In contrast, quasiparticles are formed in a medium other than vacuum, for example, in a plasma or a crystal lattice, and exist “against the background” of this medium.

It is impossible to draw an unambiguous boundary between particles and quasiparticles. An electron in a semiconductor can be considered both as one and as another, they are simply different “facets” of the same entity.

A quasi-particle is that charge carrier that moves in the crystal lattice, since in this case its properties differ from the vacuum ones and change during the transition from one crystal to another.

The effective mass of an electron in crystals can differ tenfold from the true mass. But if an electron is removed from a crystal using the photoelectric effect and placed in a vacuum, it will cease to be a quasiparticle and remain an ordinary electron.

Where do other quasiparticles come from, and what are they? Here we need a little digression into quantum mechanics.

One of its main properties – the discreteness of physical quantities, which becomes noticeable in the microcosm and dominates on the scales of atoms, molecules and chemical bonds – is manifested due to the wave properties of particles and any restriction imposed on the function.

Only an integer number of periods of the electron wave function can fit around the atomic nucleus. This is expressed using the principal quantum number , n.

Candidate for unobtanium when obtaining Rydberg polaritons gems turned out to be better than artificial crystals 1
Wave functions of an electron in various bound states near a proton (ie, in excited states of a hydrogen atom). The quantum numbers of the electron wave function are shown in parentheses. The first is the main one, the second is the orbital, and the third is the magnetic quantum number. The scale is not the same; in the bottom row with the main quantum number 4, the size of the depicted area is 4 times larger than with the main quantum number 2

Differing principal quantum numbers correspond to different average distances of the electron from the nucleus and, accordingly, to different energy levels: the binding energy of the electron with the nucleus, which is inversely proportional to this distance, can only take on strictly defined values.

The transition between them is accompanied by the emission or absorption of a quantum of light, a photon, which, in turn, can be represented as an abrupt change in the amplitude of an electromagnetic wave oscillation.

This approach is universal, and it greatly simplifies the description and study of various systems and phenomena. If a certain quantity (for example, the energy of oscillations of a standing wave in an optical resonator) can change only abruptly, then very often its change can be represented by the birth or disappearance of the corresponding (quasi)particle.

In solids, many phenomena can be described in this way. The physics of a solid state is very diverse: it also contains interactions of ions with charge carriers (electrons or their absence ), various vibrations of the medium formed by charge carriers, vibrations of the crystal lattice itself, interaction with electromagnetic radiation quanta, and much more.

Quasiparticle-oscillations: phonons :

In solids, even sound, which in the familiar world is unambiguously associated with continuous waves, exhibits quantum nature.

This is due to the relationship between the period of the crystal lattice and the wavelength of sound vibrations, which impose restrictions on the propagation of mechanical vibrations. A quantum of vibrations of a crystal lattice is called a phonon .

With the help of phonons, one can describe not only sound, but also thermal vibrations of the crystal lattice. Heating a solid body leads to an increase in the number of phonons propagating in it, and this description makes it possible to accurately reproduce some of the thermal properties of solids.

Plasmons :

Conduction electrons in a metal are a separate strongly interacting medium. Since their concentration is very high, each electron “feels” many neighbors.

Due to this, waves can propagate in their environment, which are also subject to quantum phenomena. A quantum of vibrations of an electron “liquid”, as well as other media with a pronounced electrostatic interaction between particles, is called a plasmon .

Plasma oscillations have a limiting frequency that increases with particle concentration. Photons with a frequency exceeding the plasmon frequency can freely propagate in the medium, since the electrons “do not keep up” with the oscillation frequency of the photon’s electromagnetic field.

That is why low-frequency radio waves are reflected from the ionosphere, and metals have a shiny surface. The concentration of electrons in them is sufficient to reflect photons of visible light.

Excitons: atom-like quasiparticles :

As a rule, a photon absorbed by a semiconductor “unhooks” an electron from an atom and sends it free floating around the semiconductor crystal.

If the photon energy is slightly less than the binding energy of an ion with an electron, a process similar to the formation of excited atoms can take place. In this case, the electron moves away from the site of the crystal lattice, but retains a weak connection with it.

This combination of a lattice site and an electron loosely bound to it is called an exciton . As in the case of excited atoms, the larger the principal quantum number of the electron, the greater the distance of the electron from the original atom.

Candidate for unobtanium when obtaining Rydberg polaritons gems turned out to be better than artificial crystals 2
Schematic representation of an exciton.

Rydberg atoms and excitons :

In the ground state, the size of the atom is small, and the binding energy of the outer electrons is high. Typically these values ​​are tenths of a nanometer and units of electronvolts . But if you give an electron an energy slightly less than its binding energy, you can “throw” it into a very high “orbit” and still remain bound to the atom.

Such a state is called a Rydberg atom . Their dimensions, that is, the average distance of an electron from the nucleus, grow in proportion to the square of the main quantum number, and the binding energy, on the contrary, is inversely proportional to its square.

Candidate for unobtanium when obtaining Rydberg polaritons gems turned out to be better than artificial crystals 3 1
The wave function of an electron in a Rydberg atom with a principal quantum number of 12. The scale of the image is about 20 nanometers; an ordinary hydrogen atom would take up several pixels on it

In the absence of external perturbations, Rydberg atoms are very stable. In space, they can reach tenths of a millimeter in size and exist for seconds – hundreds of millions of times longer than the lifetime of ordinary excited states of atoms.

However, due to their low binding energy, they are very susceptible to external disturbances, and their laboratory study requires carefully shielded and cooled facilities. A Rydberg atom, consisting of a proton and an electron with a principal quantum number of 100, has a binding energy of 1.36 millielectronvolts.

This corresponds to the average energy of thermal motion at a temperature of 15 K (-258 ° C ), and to achieve stability, the installation must be cooled much more!

Rydberg atoms and similar formations may be one of the keys to the creation of a quantum computer. Due to their large size and low binding energy of the electron with the center, they have a huge polarizability and are able to strongly interact with each other.

The bound states of Rydberg atoms can retain the coherence of the wave function for a long time and thus form the physical basis of qubits in quantum computing.

A particularly promising possible application of Rydberg atoms is the quantum simulator, a special kind of quantum computer that allows you to simulate the behavior of physical and chemical systems by directly displaying their properties in an array of qubits.

The possible applications of quantum simulators are very wide . They include optimizing the compositions of high-temperature superconductors and studying their properties, improving the efficiency of fertilizer synthesis processes, studying the process of protein folding and improving the effectiveness of drugs, and much more.

Excitons with a high principal quantum number are called Rydberg, like Rydberg atoms, and can also reach almost macroscopic sizes. In cuprous oxide , giant excitons with a principal quantum number of up to 25 and a size of up to several micrometers have been obtained .

Polaritons :

These quasi-particles are formed during the intense interaction of photons with the medium in which they propagate. The photon is, as it were, constantly absorbed with the formation of an exciton or other quasi-particle, and is re-emitted when it is destroyed.

In fact, of course, no transformations occur – the polariton is simply to some extent both a photon and a quasiparticle generated by it. Thus, these quasi-particles can be called “a hybrid of light and matter.”

The type of polariton is determined by what quasiparticles the photon interacts with, and this interaction is the stronger, the more accurate the coincidence of the frequencies and wave vectors of the photon and the quasiparticle. There are exciton, plasmon, phonon and many other polaritons.

How can a phonon polariton exist if the speeds of light and sound differ by hundreds of thousands of times? This becomes possible due to the drop in the group speed of light in the material, that is, the speed of propagation of the photon together with the associated “cloud of perturbations”.

Quasiparticles, as it were, “hang” on the photon, slowing down its propagation – this is how physicists “stopped the light” with the help of Bose-Einstein condensates. And if the parameters of several types of quasiparticles coincide, the appearance of hybrids is possible, in which “everything interacts with everything.”

These phenomena, which can usually be observed only in exotic states of matter, have also been observed in cuprous oxide single crystals.

The group velocity of photons of certain energies drops in them almost to the speed of sound. Moreover, in copper oxide, light interacts intensely with both phonons and excitons, causing the formation of quasiparticles, which physicists have called phonoritons.

Rydberg polaritons and quantum computers

As their name suggests, Rydberg polaritons are a hybrid of a photon and a Rydberg exciton.

Rydberg polaritons as a substrate for a quantum computer have an advantage over Rydberg atoms. Since they are formed in a semiconductor crystal, they do not require ultrahigh vacuum, and it is easier to extract information from them than from a system of qubits on Rydberg atoms. The strong coupling of polaritons with photons also acts in the same direction.

But there is a downside to putting qubits in a solid. In a solid body, to the methods of destruction of the already fragile Rydberg state, encounters with crystal lattice defects and other quasi-particle “population” of the crystal are added. Phonons, which have an energy of the order of a millielectronvolt, are unaffected by ordinary chemical bonds, but they easily destroy Rydberg excitons.

Phonons can be dealt with by cooling the crystal to the temperature of liquid helium, but defects are much more difficult. The energy of interaction between an electron and a defect can reach a few electronvolts.

If at least one defect occurs among the millions or billions of lattice sites along which the Rydberg exciton electron “walks”, the electron will immediately forget that it was part of the exciton, polariton and qubit, and all the information associated with this.

Nature vs. Laboratory

Mankind has learned to grow huge defect-free semiconductor crystals required for the electronics industry. But copper oxide is not yet one of them. This compound is subject to both oxidation to copper(II) oxide and reduction to elemental copper.

Small deviations of conditions, such as the temperature or composition of the growth medium, lead to the appearance of a large number of defects – anionic or cationic vacancies. That is why the cuprox rectifier, that is, a copper oxide semiconductor diode, for all its apparent low-tech, is not so easy to manufacture.

The rate of crystal growth, to which cuprous oxide is very sensitive, also acts in the same direction. And if people have learned to cope with the control of conditions, then the fight against defects by reducing the rate of crystal growth is much more difficult.

Candidate for unobtanium when obtaining Rydberg polaritons gems turned out to be better than artificial crystals 3
Growing a single crystal of silicon, the purest and most perfect crystalline material on Earth, by the Czochralski method

Here, the physicists, who received our record polaritons, were helped by nature. In terrestrial laboratories and industrial facilities, crystals are grown over several days or weeks.

There is nothing to think about artificial crystals grown even for a century – the Czochralski method now used to grow silicon processor crystalsjust recently turned a century old. But nature does not lack time – it has thousands and millions of years.

In addition, deep in the earth’s interior, in geothermal systems, suitable redox conditions under which cuprous oxide is stable can be created and held there for geological time intervals.

It turned out that natural crystals of cuprous oxide, or the mineral cuprite, are perfect enough to receive and study Rydberg polaritons in them. Nature was able to bypass man in creating materials not only for jewelry, but also for science!

Candidate for unobtanium when obtaining Rydberg polaritons gems turned out to be better than artificial crystals 4
Cuprite crystals from a mine in Namibia, in which Rydberg polaritons were obtained.

Physicists used intergrowths of precious cuprite crystals mined in a mine in Namibia. They cut out plates 30 micrometers thick from them, covered the plates with translucent mirror layers, thus making a Fabry-Perot resonator.

This is required to convert laser radiation into a standing wave and enhance the interaction of photons with excitons. They then cooled the plates to 1.2 degrees above absolute zero to protect the polaritons from the destructive effects of phonons, and pumped the cavity with laser light at a wavelength of about 590 nm.

The main quantum number of the obtained Rydberg polaritons reached six, which is inferior to the record for simple excitons, but it was achieved for the first time in polaritons.

The depth hidden in cuprite gemstones is astounding. The dark brilliance of these crystals hides amazing quantum phenomena that are rarely found in such simple compounds, and the compound itself can be used both in primitive devices of the beginning of the electronic age, and in quantum technologies at the very edge of progress.

We also note here the uniqueness of the situation of using natural raw materials for high-tech scientific experiments. In 2009, James Cameron described something similar in the movie Avatar, where earthlings had to fly to a neighboring star system for a natural superconductor, unobtanium (unobtanium – “unobtainable”).

Unobtanium – an ironic name for any extremely rare, expensive, or physically impossible material or substance necessary to perform a task (used in fiction or theoretical experiments)

Among fans of “strong” science fiction, such a technique is not considered good taste, since both the chemical elements and the compounds they form are the same everywhere, and man is more inventive than nature in achieving goals.

Neutron stars and the interior of gas giants do not count – the forms of matter that exist at ultra-high pressures and magnetic fields cannot really be obtained in the laboratory, but they exist “only there”.

Upon returning to more familiar conditions, they would immediately disintegrate into familiar compounds, crystal structures and chemical elements, and, as a rule, with a powerful explosion.

It turns out that this view is not entirely correct. Nature has one tool, in the possession of which we utterly yield to her, and which is able to create sustainable materials – time.

We hope that if Rydberg polaritons in copper oxide really prove their effectiveness as the basis of quantum computers, then a method for obtaining it in the form of defect-free single crystals will be found, and cuprite will not become an unobtanium!

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