Bose-Einstein condensate (BEC), a state of matter in which separate atoms or subatomic particles, cooled to near absolute zero (0 K, − °C, or − ° F. Bose-Einstein condensate (plural Bose-Einstein condensates). (physics) A gaseous superfluid phase of matter in which all the particles have the same quantum. In the left plot, no Bose Einstein Condensation took place. One can see that the energy distribution of the atoms is given by the Bose Einstein statistics. In the.
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A Bose—Einstein condensate BEC is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero Under such conditions, a large fraction of bosons occupy the lowest quantum stateat which point microscopic quantum phenomena, particularly wavefunction interference, become apparent macroscopically. A BEC is formed by cooling a gas of extremely low density, about one-hundred-thousandth the density of normal airto ultra-low temperatures.
Satyendra Nath Bose first sent a paper to Einstein on the quantum statistics of light quanta now called photonsin which he derived Planck’s quantum radiation law without any reference to classical physics. Einstein then extended Bose’s ideas to matter in two other papers. Bosons, which include the photon as well as atoms such as helium-4 4 Heare allowed to share a quantum state. Einstein proposed that cooling bosonic atoms to a very low temperature would cause them to fall or “condense” into the lowest accessible quantum stateresulting in a new form of matter.
Many isotopes were soon condensed, then molecules, quasi-particles, and photons in This transition to BEC occurs below a critical temperature, which for a uniform three-dimensional gas consisting of non-interacting particles with no apparent internal degrees of freedom is given by:.
This formula is derived from finding the gas degeneracy in the Bose gas using Bose—Einstein statistics. If the two states are equal in energy, each different configuration is equally likely. The balance is a statistical effect: In the indistinguishable case, each value of K is a single state, which has its own separate Boltzmann probability.
So the probability distribution is exponential:. It does not grow when N is large; it just approaches a constant. This will be a negligible fraction of the total number of particles. So a collection of enough Bose particles in thermal equilibrium will mostly be in the ground state, with only a few in any excited state, no matter how small the energy difference. If the number of particles is less than the number of thermally accessible states, for high temperatures and low densities, the particles will all be in different states.
In this limit, the gas is classical. As the density increases or the temperature decreases, the number of accessible states per particle becomes smaller, and at some point, more particles will be forced into a single state than the maximum allowed for that state by statistical weighting. From this point on, any extra particle added will go into the ground state. Nikolay Bogoliubov considered perturbations on the limit of dilute gas,  finding a finite pressure at zero temperature and positive chemical potential.
This leads to corrections for the ground state.
The original interacting system can be converted to a system of non-interacting particles with a dispersion law. The validity of this approach is actually limited to the case of ultracold temperatures, which fits well for the most alkali atoms experiments.
It is not applicable, for example, for the condensates of excitons, magnons and photons, where the critical temperature is comparable to room temperature. The Gross-Pitaevskii equation is a partial differential equation in space and time variables. Usually it does not have analytic solution and different numerical methods, such as split-step Crank-Nicolson  and Fourier spectral  methods, are used for its solution. There are different Fortran and C programs for its solution for contact interaction   and long-range dipolar interaction  which can be freely used.
By construction, the GPE uses the following simplifications: If one relaxes any of these assumptions, the equation for the condensate wavefunction acquires the terms bse higher-order powers of the wavefunction. Moreover, for some physical systems the amount of such terms turns out to be infinite, therefore, the equation becomes essentially non-polynomial. The examples where this could happen are the Bose—Fermi composite condensates,     effectively lower-dimensional condensates,  and dense condensates and superfluid clusters and droplets.
However, it is clear that in a general case the kohdensat of Bose—Einstein condensate can be described by coupled evolution equations for condensate density, superfluid velocity and distribution function of elementary excitations. This problem was in by Peletminskii et al.
The Peletminskii equations are valid for kondejsat finite temperatures below the critical point. Years after, inKirkpatrick and Dorfman obtained similar equations using another microscopical approach. The Peletminskii equations also reproduce Khalatnikov hydrodynamical equations for superfluid as a limiting case.
The phenomena of superfluidity of a Bose gas and superconductivity of a strongly-correlated Fermi gas a gas of Cooper pairs are tightly connected to Bose—Einstein condensation. Under corresponding conditions, below the einsetin of phase transition, these phenomena were observed in helium-4 and different classes of superconductors. In this sense, the superconductivity is often called the superfluidity of Fermi gas. In the simplest form, the origin of superfluidity can be seen from the weakly interacting bosons model.
InPyotr KapitsaJohn Allen and Don Misener discovered that helium-4 became a new kind of fluid, now known as a superfluidat temperatures less than 2. Superfluid helium has many unusual properties, including zero viscosity the ability to flow without dissipating energy kkndensat the existence of quantized vortices. It was quickly believed that the superfluidity was due to partial Bose—Einstein condensation of the liquid.
In fact, many properties of superfluid helium also appear in gaseous condensates created by Cornell, Wieman and Ketterle see below.
Superfluid helium-4 is a liquid rather than a gas, which means that the interactions between the atoms are relatively strong; the original theory of Bose—Einstein condensation must be heavily modified in eindtein to describe it. Bose—Einstein condensation remains, however, fundamental to the superfluid properties of helium Note that helium-3a fermionalso enters a superfluid phase at a much lower temperature which can be explained by the formation of bosonic Cooper pairs of two atoms see also fermionic condensate.
They cooled a dilute vapor of approximately two thousand rubidium atoms to below nK using a combination of laser cooling a technique that won its inventors Steven ChuClaude Cohen-Tannoudjiand William D.
Phillips the Nobel Prize in Physics and magnetic evaporative cooling.
Ketterle’s condensate had a hundred times more atoms, allowing important results such as the observation of quantum mechanical interference between two different condensates. Hulet’s team subsequently showed the condensate could be stabilized by confinement quantum pressure for up to about atoms.
Various isotopes have since been condensed. In the image accompanying this article, the velocity-distribution data indicates the formation of a Bose—Einstein condensate out of a gas of rubidium atoms. The false colors indicate the number of atoms at each velocity, with red being the fewest and white being the most.
The areas appearing white and light blue are at the lowest velocities. The peak is not infinitely narrow because of the Heisenberg uncertainty principle: This width is given by the curvature of the magnetic potential in the given direction.
More tightly confined directions have bigger widths in the ballistic velocity distribution. This anisotropy of the peak on the right is a purely quantum-mechanical effect and does not exist in the thermal distribution on the left. This graph served as the cover design for the textbook Thermal Physics by Ralph Baierlein. Bose—Einstein condensation also applies to quasiparticles in solids. MagnonsExcitonsand Polaritons have integer spin which means they are bosons that can form condensates.
Magnons, electron spin waves, can be controlled by a magnetic field. Densities from the limit of a dilute gas to a strongly interacting Bose liquid are possible. Magnetic ordering is the analog of superfluidity.
In condensation was demonstrated in antiferromagnetic Tl Cu Cl 3 at temperatures as knodensat as 14 K. The high transition temperature relative to atomic gases is due to the magnons small mass near an electron and greater achievable density.
Incondensation in a ferromagnetic yttrium-iron-garnet thin film was seen even einztein room temperature,   with optical pumping. Excitonselectron-hole pairs, were predicted to condense at low temperature and high density by Boer et al. Bilayer system experiments first demonstrated condensation inby Hall voltage disappearance. Fast optical exciton creation was used to form condensates in sub-kelvin Cu 2 O in on.
Polariton condensation was firstly detected for exciton-polaritons in a quantum well microcavity kept at 5 K. As in many other systems, vortices can exist in BECs.
These can be created, for example, by ‘stirring’ the condensate with lasers, or rotating the confining trap. The vortex created will be a quantum vortex. This is particularly likely for einetein axially symmetric for instance, harmonic confining potential, which is commonly used.
The notion is easily generalized. This is usually done computationally, however in a uniform medium the analytic form:. Research has, however, indicated they are metastable states, einstwin may have relatively long lifetimes.
Closely related to the creation of vortices in Sinstein is the generation of so-called dark solitons in one-dimensional BECs. These topological objects feature a phase gradient across their nodal plane, which stabilizes their shape even in propagation and interaction.
Although solitons carry no charge and are thus prone to decay, relatively long-lived dark solitons have been produced and studied extensively. Experiments led by Randall Hulet at Rice University from through showed that lithium condensates with attractive interactions could stably exist up to a critical atom number.
Quench cooling the gas, they observed the condensate to grow, then subsequently collapse as the attraction overwhelmed the zero-point energy of the confining potential, in a burst reminiscent of a supernova, with an explosion preceded by an implosion.
Their instrumentation now had better control so they used naturally attracting atoms of rubidium having negative atom—atom scattering bosee. Through Feshbach resonance involving a sweep of the magnetic field causing spin flip collisions, they lowered the characteristic, discrete energies at which rubidium bonds, making their Rb atoms sinstein and creating a stable condensate.
The reversible flip from attraction to repulsion stems from quantum interference among wave-like condensate atoms. When the JILA team raised einsyein magnetic field strength further, the condensate suddenly reverted to attraction, imploded and shrank beyond detection, then exploded, expelling about two-thirds of its 10, atoms.
About half of the atoms einsteon the condensate seemed to have disappeared from the experiment altogether, not seen in the cold remnant or expanding gas cloud. Most likely they formed molecules of two rubidium atoms;  energy gained by this bond imparts velocity sufficient to leave the trap without being detected.
Bose–Einstein condensate – Simple English Wikipedia, the free encyclopedia
The process of creation of molecular Bose condensate during the sweep of the magnetic field throughout the Feshbach resonance, as well as the reverse process, are described by the exactly solvable model that can explain many experimental observations.
Compared to more commonly encountered states of matter, Bose—Einstein condensates are extremely fragile. Nevertheless, they have proven useful in exploring a wide range of questions in fundamental physics, and the years since the initial discoveries by the JILA and MIT groups have seen an increase in experimental and theoretical activity.
Examples include experiments that have demonstrated interference between condensates due to wave—particle duality the study of superfluidity and quantized vorticesthe creation of bright matter wave solitons from Bose condensates confined to one dimension, and the slowing of light pulses to very low speeds using electromagnetically induced transparency.
Experimenters have also realized ” optical lattices “, where the interference pattern from overlapping lasers provides a periodic potential. These have been used to explore the transition between a superfluid and a Mott insulator and may be useful in studying Bose—Einstein condensation in fewer than three dimensions, for example the Tonks—Girardeau gas.
Bose—Einstein condensates composed of a wide range of isotopes have been produced.