Bose Einstein condensate properties. Scientists have created a “superphoton” - a Bose-Einstein condensate from photons. Bose-Einstein condensate
The first experiment on cooling atoms took place on the International Space Station. Experts have managed to create a Bose-Einstein condensate (BEC), which appears only at extremely low temperatures not found on Earth, Space Daily reports.
In May 2018, the Cold Atom Laboratory (CAL) was sent to the ISS to study the processes occurring with these particles at temperatures close to absolute zero (−273.15 °C). Using CAL, scientists wanted to slow down the motion of particles and end up with an exotic form of matter, somewhere between a gas and a liquid, known as a Bose-Einstein condensate.
In 2014, engineers at NASA's Jet Propulsion Laboratory were able to build a chamber to cool atoms to temperatures close to absolute zero. That same year, scientists obtained condensate in the Earth-based CAL prototype. To do this, two types of cooling devices were introduced into the chamber - lasers, which suppress the vibrations of atoms and force the particles to cool, and a magnetic trap, which rejects the “hottest” atoms and leaves only the coldest and most motionless particles inside.
However, on Earth, after turning off the magnetic trap, cold atoms were attracted “down” and “died,” that is, they existed for only a few seconds (that amount of time is not enough to study these atoms), but in space they can “live” much longer, up to two to four minutes, due to the fact that there is no gravity there. That is why CAL was sent to the ISS.
Late last week, on July 27, CAL project officials reported to the media that their installation on the International Space Station had produced CBEs of rubidium atoms at temperatures up to 100 nanokelvins, or slightly above absolute zero (−273°C). This is lower than the average temperature in intergalactic space (approximately −270°C). The experiment took place remotely and was controlled by specialists from Earth.
“At these ultracold temperatures, the behavior of the atoms that make up the Bose-Einstein condensate is quite different from anything on Earth. In fact, this condensate is characterized as the fifth state of matter, distinguishable from gases, liquids, solids and plasma. It is noteworthy that BBE atoms are more like waves than particles.”, said Robert Shotwell, an engineer at NASA's Jet Propulsion Laboratory.
“Cold atoms are long-lived quantum wave-particles that can be controlled”, explains physicist Robert Thompson, a member of the CAL project. — “With these wave-particles we will be able to hone our quantum technologies, study some quantum phenomena, learn to make more accurate measurements of gravity, and explore the wave nature of the atom itself.”.
The wave nature of atoms is usually observed only on microscopic scales, but KBE allows this phenomenon to be observed with the naked eye, hence it becomes much easier to study. All ultracold atoms assume the lowest energy state and the same wave identity, becoming indistinguishable from each other. Instead of a cloud of atoms, a single “super atom” appears, which can be easily examined without magnifying instruments.
Bose-Einstein condensate
The existence of the QBE was theoretically predicted as a consequence of the law of quantum mechanics by Albert Einstein based on the work of Indian physicist Shatyendranath Bose in 1925, and the first experiment was carried out 70 years later. In 1995, Eric Cornell, Carl Wieman and Wolfgang Ketterle at the Joint Institute for Laboratory Astrophysics (JILA) obtained the first Bose condensate from a gas of rubidium atoms, cooled to 170 nanokelvins, and 6 years later they were awarded the Nobel Prize in Physics for this work.
Since then, scientists have conducted dozens of experiments with CBE on Earth and even in space on board some rockets. But all the experiments were short-term and did not bring significant benefit. The Cold Atom Laboratory is the first and only facility today where scientists can conduct daily experiments to produce and study Bose-Einstein condensates and achieve real scientific results that can reveal the fundamental secrets of the Universe.
In the future, at CAL, scientists will work at temperatures lower than those they worked with at facilities on Earth.
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In a gas of boson atoms, some of the atoms completely lose their kinetic energy and momentum at a fairly low but finite temperature. Such atoms are called Bose condensate from lat. condenso - “thicken”. The wave functions of the condensate atoms are mutually consistent in phase. On this basis, developed atomic lasers emitting atoms with coherent wave functions.
The phenomenon of complete loss of kinetic energy from a part of an ideal bosonic gas at low temperature was theoretically discovered by A. Einstein in 1925. The process is called Bose condensation of particles in momentum space . It was studied in detail by Fritz and Heinz London in 1938. Bose condensation is a consequence of the fact that the chemical potential of a bosonic gas cannot be positive. At normal temperature, the chemical potential of a gas is negative. As the temperature decreases, the chemical potential increases, and at a sufficiently low temperature it reaches its highest possible value. A further decrease in temperature causes a decrease in the number of particles in the gas phase and some of the atoms precipitate into the condensate.
Heinz London (1907–1970) and Fritz London (1900–1954) –
founder of the theory of superconductivity and quantum chemistry
It has not been possible to obtain condensation experimentally for more than 50 years, since at low temperatures interatomic interaction attracts atoms to each other, clusters are formed and then a liquid or solid state before the onset of Bose condensation. A cluster occurs when three or more particles collide, which is more likely at high concentrations. At low particle concentrations, pair collisions predominate, ensuring the establishment of thermal equilibrium. To prevent the formation of clusters, the gas concentration must be reduced. A metastable Bose condensate in rarefied gases of rubidium, sodium, and lithium atoms was first obtained by W. Ketterle, K. Wieman and E. Cornell in 1995. Hydrogen atoms were condensed in 1997. The Bose condensate exhibits unique properties: temperature, speed of light 
, sound speed .
Wolfgang Ketterle, Carl Wieman, Eric Cornell
Atoms bosons. The spin of an atom consists of the spins of the electrons of the shell and the nucleons of the nucleus; their spins are equal to 1/2. The number of electrons is equal to the number of protons, so their total spin in an electrically neutral atom is an integer. The spin of an atom is determined by the number of neutrons. Bosons are atoms with an even number of neutrons , for example: 1 H 1, 2 He 4, 3 Li 7, 11 Na 23, 37 Rb 87, where the lower number is the serial number of the element in the periodic table, or the number of protons in the nucleus, the upper number is the mass number, or the number of protons and neutrons in the nucleus. An atom with an even number difference is a boson. At ultralow temperatures, the atoms are in the ground state, so the first two have zero spin, and the last three have spin equal to one. Number of spin states
The baryon number of nucleons is conserved, so the number of atoms in an isolated system does not change.
Boson energy distribution. We use the Bose–Einstein distribution (4.10) for the average number of particles in one state
,
and density of states of three-dimensional gas (3.8)
, 
.
We obtain the number of particles in the energy range in a gas of volume V
. (4.77)
Total number of particles we find from (4.77)
. (4.78)
Chemical Potential is determined from (4.78). When the temperature changes, the number of particles remains the same, then from T does not depend
,
where taken into account . Consequently, as the temperature decreases, |m| decreases, and the chemical potential increases from negative values to zero. If is the temperature at which the chemical potential becomes zero:
then when is fulfilled
. (4.79)
When the temperature drops below, an increase in μ is impossible, and (4.78) is satisfied due to a decrease in the number of gas particles.
Condensation threshold is the upper limit of the temperature range where the chemical potential is zero. From (4.78) we obtain
,
Where N– number of gas particles at normal temperature. Using
for , we find the integral
,
we get
. (4.80)
The condensation threshold temperature increases with increasing atomic concentration and with decreasing atomic mass .
The mass of an atom is expressed through the molar mass
we express the concentration of atoms in terms of molar volume
.
From (4.80) in the CGS system of units we obtain
[TO]. (4.81)
For 2 He 4 with parameters:
, , 
,
We obtain the de Broglie wavelength at . For an atom with average energy
and impulse
we use (4.80) and get
,
.
Considering where d is the average distance between atoms, we find
.
As the temperature decreases, the de Broglie wavelength of the atom increases and, when the condensation threshold is reached, it is compared with the distance between the atoms. The wave functions of the particles overlap and interfere, and the Bose condensate exhibits quantum properties.
Number of condensed particles. In the temperature range, the chemical potential is zero. At temperatures below T 0 equation (4.78)
, ,
performed by reducing the number of particles in the gas phase from the original N to current N 1 (T). Similarly to (4.80) we obtain
, .
Divide the result by (4.80)
,
and find the number and concentration of particles remaining in the gas phase:
, (4.82)
. (4.82a)
Number of condensed particles
. (4.83)
The relative number of condensed particles is shown in the figure.
Internal energy and heat capacity. Using (4.77)
,
we get internal energy
, (4.84)
In the condensation region we find
, (4.85)
.
The internal energy is determined by the contribution of the gas phase only, the internal energy of the condensed phase is zero . From (4.85) and (4.82)
we find the energy per particle of the gas phase in the condensation region:
. (4.86)
From (4.85) we find the heat capacity below the condensation threshold:
. (4.87)
Considering (4.80)
,
from (4.87) we obtain the heat capacity at the condensation temperature
. (4.87a)
Free energy. From (4.85)
and from the Gibbs–Helmholtz equation (2.29) we find
. (4.88)
Entropy and pressure expressed in terms of free energy
Taking (4.88) into account, in the condensation region we obtain
, (4.89)
, (4.90a)
Expression (4.90b) is equation of state of a nonrelativistic ideal quantum gas , and coincides with the equation of state of a classical ideal gas. Comparing (4.89) and (4.82)
,
we find that entropy is proportional to the number of particles in the gas phase . Hence, the entropy of the condensed phase is zero . Pressure (4.90a) is determined by temperature and does not depend on volume. Condensed particles have zero momentum and create no pressure. It is determined by the concentration of gas phase particles (4.82a)
,
. (4.91)
Carrying out condensation. Two-particle collisions ensure thermodynamic equilibrium of the gas. Three-particle collisions lead to the formation of liquid and solid states. At relatively high gas densities, three-particle collisions are significant. Interatomic interaction forms a liquid or crystalline state at low temperatures. At low gas density, the probability of three-particle collisions is significantly less than two-particle collisions. As a result, at low temperatures a gaseous metastable state with a sufficiently long lifetime is possible. The first condensates were obtained from rubidium, sodium, and hydrogen atoms at a gas phase temperature of ~10–2 K, under pressure P < 10 –11 мм рт. ст. с числом частиц ~10 8 и концентрацией ~10 14 см –3 .
Throttle hold in an evacuated glass cell in an area less than 1 mm in size is carried out magnetic trap . The coil system creates a non-uniform magnetic field with an absolute minimum in the center. Magnetic moment of an atom pm in a magnetic field B receives energy (– pm×B). For point 2 in the center of the trap the field is negligible, for point 1 away from the center the field B strong. At thermodynamic equilibrium, the electrochemical potentials at all points are the same
.
Magnetic trap
In the ground state of the 2 He 4 atom, the spins of the electrons are directed in opposite directions, their magnetic moments are compensated and the atom does not have its own magnetic moment. When an external magnetic field is turned on, a circular current of electrons appears in the atom due to the phenomenon of electromagnetic induction. According to Lenz's rule, the induced magnetic moment is directed against the external field, this gives
,
The chemical potential increases with increasing particle concentration, then we get
Atoms with magnetic moments directed against the field are pushed from a strong to a weak magnetic field - “ diamagnetic atoms seek a weak field " As a result, the atoms are collected and held in the center of the trap. The retention area has the shape of a cigar with a diameter of ~(10...50) microns, a length of ~300 microns. Atoms are removed from the trap by a short pulse of high-frequency radiation, tilting the magnetic moments of the atoms. A superposition of states arises with moments directed against and along the field, the latter state being pushed out by the trap.
To retain the Bose condensate, microcircuits have also been developed that create the necessary magnetic field configuration at a distance of ~0.1 mm from their surface and consume power of ~1 W. At these distances, the chip creates a more non-uniform magnetic field than the coil, providing better gas retention. The chip is miniature, has room temperature, and its thermal radiation is weakly absorbed by the gas. By changing the chip currents, you can move the center of the trap and move the Bose condensate along the surface of the chip.
Gas cooling carried out laser method , based on the Doppler effect. If laser radiation with a frequency n is directed at chaotically moving atoms< n 0 , где n 0 – частота резонансного поглощения атома, то покоящиеся и движущиеся от лазера атомы не поглощают излучение. Атом, движущийся к лазеру со скоростью V, perceives frequency
and at n¢ = n 0 absorbs a photon. As a result, the atom receives an impulse against its speed and slows down. An excited atom emits energy isotropically on average. Radiation in the near infrared region of the spectrum, created by semiconductor lasers and directed at the gas from six mutually perpendicular sides, leads to its cooling.
Also used evaporative cooling by ejecting atoms with the highest speed from the periphery of the trap using a high-frequency magnetic field. It tilts the magnetic moments, creating a component in the direction of the field, which is ejected by the trap. Particles with higher speed reach the gas boundary faster and their concentration at the boundary is higher than the concentration of particles with low speed. Therefore, high-energy particles are more likely to evaporate. For a trap based on coils, cooling occurs to a gas phase temperature of about 10–7 K in a time from 10 s to 10 min. For the chip, the temperature required for condensation is achieved in less than 1 s. The concentration of condensate atoms is ~10 14 cm –3, the thermal energy corresponds to a temperature less than 10 –11 K.
Thus, CBE, like any other substance, consists of individual atoms, but, unlike ordinary matter, the atoms lose their individuality in it. It becomes impossible to distinguish a part from the whole, and in fact a conglomerate of atoms is obtained, possessing the quantum properties of one individual atom. This giant quasi-atom is 100 thousand times larger than usual and even larger than a human cell. Due to its size, the QBE gives experimenters a unique opportunity to directly test the theoretical principles of quantum mechanics in practice: in modern science it plays the same role as apples did in Newtonian times.
The first substance with the properties of CBE was obtained in 1938. Soviet physicist Peter Kapitsa and Canadian John Allen cooled helium-4 to a temperature below 2.2 kelvin, as a result of which this gas acquired the properties of a superfluid liquid with absolutely no viscosity. Superfluid helium exhibits unusual properties: it can pour upward from an open container (see photo below) or spread along vertical walls. Superfluidity in helium occurs due to the fact that part of the helium atoms, up to 10 percent, turns into CBE.
In laser technology the properties of the BBE are also exploited by synchronizing the waves of photons, which by definition are bosons. The process of producing a laser beam takes advantage of the predisposition of bosons to concentrate into a single quantum state.
Another area of application of CBE is superconductors. Superconductivity is achieved by low-temperature condensation of electrons into pairs. Paired electron bonds are formed only in certain substances under certain conditions, for example, in aluminum cooled to 1.2 kelvin. Single electrons cannot be used to make BBEs because they are wavefunction-incompatible fermions, but when they pair up, the resulting bosons are immediately condensed into BBEs. (A similar process of pairing and condensation occurs in superfluid helium-3, the atoms of which are fermions).
Finally, the properties of CBE are observed in exciton(from lat. excito - excite). This is a quasiparticle, which represents a bound state of an electron and a so-called “hole” - a missing electron in a node of the crystal lattice of a semiconductor. An electron and a hole generated by a laser pulse can briefly combine into such a pair, which behaves like a positively charged particle. In 1993, physicists observed the formation of a short-lived gaseous condensate from excitons in a semiconductor based on copper oxide.
However, the phenomenon of CBE in its pure form was experimentally demonstrated relatively recently. In 1995, a team of physicists - now Nobel laureates - produced this condensate using atomic traps using laser beams and magnetic fields in which rubidium atoms were cooled to an ultra-low temperature of several hundred nanokelvins. Following this, groups of scientists around the world carried out many experiments with BEC, in which it was exposed to laser beams, sound waves, magnetic fields, etc. In particular, when a laser beam passed through a gas condensate, it was achieved slowing down the speed of light up to pedestrian speed (meters per second). The results obtained were generally consistent with those expected according to the postulates of quantum mechanics. Thus, the transition from quantum theory to quantum practice was begun.
In the near future, we can expect widespread introduction of CBE into precision measurement technology, which will make it possible to create ultra-precise guidance and orientation instruments, gravitometers, and systems for determining the position of aircraft and spacecraft with an accuracy of several centimeters. Another promising area for the implementation of CBE is nanotechnology, which promises the emergence of nano-robots capable of assembling molecules of any substance from individual atoms, and super-powerful quantum computers.
The main tool for introducing the CBE phenomenon into technological progress will, apparently, be ATOMIC LASER. This device is a material analogue of an optical laser. That is, instead of a beam of light, a directed “beam” of material matter is generated. Such a beam is a coherent, freely moving stream of gas concentrate. The term “coherent” in this case means that all atoms in the beam move quantum synchronously, that is, their wave functions are mutually ordered.
First atomic laser was created in 1997 by Wolfgang Ketterl's group and was powered by gravity. The soda concentrate was irradiated with radio pulses, under the influence of which some of the atoms changed their spin. Atoms with a changed spin were not affected by the trap, and they literally fell out of it. In fact, such an atomic laser looked less like a beam of light and more like a stream of water flowing from a tap.
In 1998, Theodor Hönsch of the University of Munich demonstrated a similar system that involved a continuous flow of rubidium atoms. The rubidium atomic beam was a million times brighter than all its kind. Around the same time, William Phillips and Stephen Rolston of the National Institute of Standards and Technology finally created an atomic laser, the beam of which could be sent in any direction, not just down. In their design, they used optical lasers that knock out atoms from the condensate through a rotating hole at the edge of the trap - the so-called “circle of death.” Using a specific sequence of laser pulses carefully synchronized with the circle of death, the scientists produced a coherent, intense and continuous stream of atoms - analogous to the bright beam of an optical laser.
Currently, atomic rays are already used in a number of scientific and industrial instruments, in particular, in atomic clocks, in high-precision measuring instruments for determining fundamental constants and in the production of computer chips. However, it can be assumed that the widespread introduction of atomic lasers will take quite a long time, judging by the fact that 30 years passed between the invention of the optical laser and its widespread use in household appliances. The main problem with using an atomic laser so far is that its beam only propagates in a vacuum.
Among the scientifically predicted areas of application of the atomic laser that border on science fiction are: atomic holography. It is theoretically possible to create in the future atomic laser printers and faxes, which will make it possible to print and transmit over long distances not flat images of objects, but their material three-dimensional models.
Quantum mechanics, which is one of the most important branches of modern theoretical physics, was created relatively recently - in the 20s of our century.
Its main objective is to study the behavior of microparticles, such as electrons in an atom, molecule, solid, electromagnetic fields, etc.
In the history of the development of each branch of theoretical physics, several stages should be distinguished: firstly, the accumulation of experimental facts that could not be explained using existing theories, secondly, the discovery of individual semi-empirical laws and the creation of preliminary hypotheses and theories, and thirdly, the creation general theories that allow us to understand the totality of many phenomena from a single point of view.
As the Maxwell-Lorentz theory was used, an increasing number of phenomena of the microworld were explained (the problem of radiation, the propagation of light, the dispersion of light in media, the movement of electrons in electric and magnetic fields, etc.). Gradually, experimental facts began to accumulate that did not fit into the framework of classical ideas.
At the same time, in order to construct the theory of equilibrium electromagnetic radiation, the photoelectric effect and the Compton effect, it was necessary to introduce the assumption that light, along with wave properties, should also have corpuscular properties. This was taken into account in the Planck-Einstein quantum theory. The discrete structure of light found its description by introducing Planck’s constant h=6.62*IO" 27 erg-sec. Quantum theory was also successfully used in the construction of the first quantum theory of the atom, Bohr's theory, which was based on the planetary model of the atom, which followed from Rutherford's experiments on the scattering of alpha particles by various substances. On the other hand, a number of experimental data, such as diffraction and electron beam interference, told us that electrons, along with corpuscular ones, also exhibit wave properties
The first generalizing result of a thorough analysis of all preliminary theories, as well as experimental data confirming both the quantum nature of light and the wave properties of electrons, was Schrödinger’s wave equation (1926), which made it possible to reveal the laws of motion of electrons and other atomic particles and to construct, after the discovery of secondary quantization, equations Maxwell-Lorentz, a relatively consistent theory of radiation taking into account the quantum nature of light. With the advent of the Schrödinger equation, scientists who studied the atom received into their hands the same powerful weapon that was once given to astronomers after the advent of Newton's basic laws of mechanics, including the law of universal gravitation
Therefore, it is not surprising that with the advent of the Schrödinger equation, many facts related to the movement of electrons inside an atom found their theoretical justification.
However, as it turned out later, Schrödinger’s theory did not describe all the properties of atoms; with its help it was impossible, in particular, to correctly explain the interaction of an atom with a magnetic field, or to construct a theory of complex atoms. This was mainly due to the fact that Schrödinger's theory did not take into account the relativistic and spin properties of the electron.
A further development of Schrödenger's theory was the relativistic theory of Dirac. The Dirac equation made it possible to describe both relativistic and spin effects of electrons. It turned out that if taking into account relativistic effects in atoms with one electron leads to relatively small quantitative corrections, then when studying the structure of atoms with several electrons, taking into account spin effects is of decisive importance. Only after the spin properties of electrons were taken into account was it possible to explain the rule for filling electron shells in an atom and give Mendeleev’s periodic law a rigorous justification.
With the advent of the Dirac equation, fundamental questions related to the structure of the electron shell of the atom could be considered largely resolved, although the deepening of our knowledge in the development of individual details had to continue. In this regard, it should be noted that the influence of the so-called electromagnetic and electron-positron vacuums, as well as the influence of the magnetic moments of nuclei and the sizes of nuclear particles, are currently being studied in detail. A energy levels of atoms.
One of the characteristic features of the first stage of the theory of elementary particles, called quantum field theory, is the description of the mutual convertibility of elementary particles. In particular, according to Dirac's theory, the possible transformation of gamma rays into an electron-positron pair and back was predicted, which was then confirmed experimentally
Thus, if in the classical theory there were two differences between light and electrons: a) light waves, electrons are particles, b) light can appear and be absorbed, but the number of electrons must remain unchanged, then in quantum mechanics with its characteristic wave-particle dualism the first distinction between light and electrons was erased. However, in it, as well as in Lorentz’s theory, the number of electrons had to remain unchanged. Only after the advent of quantum field theory, which describes the mutual convertibility of elementary particles, was the second difference actually erased
Since one of the main tasks of theoretical physics is the study of the real world and, first of all, the simplest forms of its movement, which also determine more complex phenomena, it is natural that all these questions are always connected with philosophical questions and, in particular, with the question of the cognizability of the microworld, therefore not It is surprising that many major physicists who made the most important discoveries in the field of physics tried at the same time to interpret these discoveries from one philosophical point of view or another. Thanks to such views, it was discovered Bose-Einstein condensation effect.
By 1920, physicists were already quite familiar with the dual nature of light: the results of some experiments with light could be explained by assuming that light was waves, while in others it behaved like a stream of particles. Since it seemed obvious that nothing could be both a wave and a particle at the same time, the situation remained unclear, causing heated debate among specialists. In 1923, the French physicist L. de Broglie, in his published notes, suggested that such paradoxical behavior may not be specific to light, but matter can also behave like particles in some cases, and like waves in others. Based on the theory of relativity, de Broglie showed that if the momentum of a particle is equal to p, then the wave “associated” with this particle must have a wavelength l = h /p. This relation is similar to the relation first obtained by Planck and Einstein E = h n between the energy of a light quantum E and frequency n corresponding wave. De Broglie also showed that this hypothesis could be easily tested in experiments similar to those demonstrating the wave nature of light, and he persistently called for such experiments to be carried out. De Broglie's notes attracted the attention of Einstein, and by 1927 K. Davisson and L. Germer in the United States, as well as J. Thomson in England, confirmed not only de Broglie's basic idea for electrons, but also his formula for wavelength. In 1926, the Austrian physicist E. Schrödinger, who was then working in Zurich, heard about de Broglie’s work and the preliminary results of experiments that confirmed it, published four articles in which he presented a new theory, which was a solid mathematical justification for these ideas.
This situation has its analogue in the history of optics. Mere confidence that light is a wave of a certain length is not enough to describe the behavior of light in detail. It is also necessary to write and solve the differential equations derived by J. Maxwell, which describe in detail the processes of interaction of light with matter and the propagation of light in space in the form of an electromagnetic field. Schrödinger wrote a differential equation for de Broglie's matter waves, similar to Maxwell's equations for light. The Schrödinger equation for one particle has the form
=d/dxWhere m– particle mass, E– her full energy, V (x) is potential energy, and y– quantity describing an electron wave. In a number of papers, Schrödinger showed how his equation could be used to calculate the energy levels of the hydrogen atom. He also established that there were simple and effective ways of solving approximately problems that could not be solved exactly, and that his theory of matter waves was mathematically completely equivalent to Heisenberg's algebraic theory of observables and in all cases led to the same results. P. Dirac of the University of Cambridge showed that the theories of Heisenberg and Schrödinger represent only two of many possible forms of theory. Dirac soon achieved an unexpectedly major success by demonstrating how quantum mechanics generalizes to the region of very high speeds, i.e. takes on a form that satisfies the requirements of the theory of relativity. Gradually it became clear that there are several relativistic wave equations, each of which in the case of low velocities can be approximated by the Schrödinger equation, and that these equations describe particles of completely different types. For example, particles can have different "spins"; this is provided for by Dirac's theory. In addition, according to the relativistic theory, each particle must correspond to an antiparticle with the opposite sign of the electric charge. At the time Dirac's work was published, only three elementary particles were known: the photon, electron and proton. In 1932, the electron's antiparticle, the positron, was discovered. Over the next few decades, many other antiparticles were discovered, most of which turned out to satisfy the Dirac equation or its generalizations. Created in 1925–1928 by the efforts of outstanding physicists, quantum mechanics has not undergone any significant changes in its fundamentals since then.
Bose-Einstein condensate - the fifth state of matter
The Bose-Einstein condensate is a specific state of aggregation, a state of aggregation of matter, which is represented mostly by bosons under ultra-low temperature conditions.
It is a condensed state of a Bose gas - a gas consisting of bosons and subject to quantum mechanical effects.
In 1924, Indian physicist Satyendra Nath Bose proposed quantum statistics to describe bosons, particles with integer spin, which were also named after him. In 1925, Albert Einstein generalized Bose's work by applying his statistics to systems consisting of atoms with integer spin. Such atoms, for example, include Helium-4 atoms. Unlike fermions, bosons do not obey the Pauli exclusion principle, meaning multiple bosons can exist in the same quantum state.
Bose-Einstein statistics can describe the distribution of particles with integer or zero spin. In addition, these particles should not interact and should be identical, that is, indistinguishable.
Bose-Einstein condensate
A Bose-Einstein condensate is a gas consisting of particles or atoms with integer spin. As is known, particles are capable of taking on several quantum states at once - the so-called quantum effects. According to Einstein's work, as the temperature decreases, the number of quantum states available to the particle will decrease. The reason for this is that particles will increasingly prefer the lowest energy states as the temperature decreases. Considering that bosons are capable of being in the same state at the same time, as the temperature decreases they will go into the same state.
Thus, the Bose-Einstein condensate will consist of many non-interacting particles that are in the same state. It is noteworthy that also with decreasing temperature the wave nature of particles will become more and more apparent. At the output we will have one quantum mechanical wave on a macroscale.
Velocity distribution data (3 types) for a gas of rubidium atoms, confirming the discovery of a new phase of the substance, the Bose-Einstein condensate. Left: before the appearance of the Bose-Einstein condensate. Center: immediately after condensation appears. Right: After further evaporation, leaving a sample of almost pure condensate.
How to obtain a Bose-Einstein condensate?
This state of aggregation was first achieved in 1995 by American physicists from the National Institute of Standards and Technology - Eric Cornell and Karl Wieman. The experiment used laser cooling technology, thanks to which it was possible to lower the temperature of the sample to 20 nanokelvins. Rubidium-87 was used as a material for the gas, 2 thousand atoms of which passed into the state of Bose-Einstein condensate. Four months later, German physicist Wolfgang Ketterle also achieved condensate in much larger volumes. Thus, scientists experimentally confirmed the possibility of achieving the “fifth state of aggregation” under ultra-low temperatures, for which they received the Nobel Prize in 2001.
In 2010, German scientists from the University of Bonn under the leadership of Martin Weitz obtained a Bose-Einstein condensate from photons at room temperature. For this, a camera with two curved mirrors was used, the space between which was gradually filled with photons. At some point, the photons “launched” inside could no longer reach an equilibrium energy state, unlike the photons previously located there. These “extra” photons began to condense, passing into the same lowest energy state and thereby forming the fifth state of aggregation. That is, scientists managed to obtain a condensate from photons at room temperature, without cooling.
Already by 2012, it was possible to achieve condensate from many other isotopes, including isotopes of sodium, lithium, potassium, etc. And in 2014, an installation for creating condensate was successfully tested, which in 2017 will be sent to the International Space station for conducting experiments in zero gravity conditions.
Application of condensate
Although this phenomenon is difficult to imagine, like any quantum effects, such a substance can find application in a wide range of problems. One example of the application of a Bose-Einstein condensate is an atomic laser. As is known, the radiation emitted by a laser is coherent. That is, photons of such radiation have the same energy, phase and wavelength. If the photons are in the same quantum mechanical state, as is the case with the Bose-Einstein condensate, then it is possible to synchronize this cooled substance in order to obtain radiation for a more efficient laser. Such an atomic laser was created back in 1997 under the leadership of Wolfgang Ketterle, one of the first scientists to create the condensate.
The method of producing condensate from photons, which was used by German scientists in 2010, can be used in solar energy. According to some physicists, this will improve the efficiency of solar cells in cloudy weather conditions.
Bose-Einstein condensate - graphical visualization
Since the Bose-Einstein condensate was obtained relatively recently, the scope of its application has not yet been precisely determined. However, according to various scientists, condensate could be useful in many areas, ranging from medical equipment to quantum computers.
