Bose-Einstein Condensation

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Bose-Einstein condensation

When a gas of bosonic particles is cooled below a critical temperature, it condenses into a Bose-Einstein condensate. The condensate consists of a macroscopic number of particles, which are all in the ground state of the system. Bose-Einstein condensation is a phase transition, which does not depend on the specific interactions between particles. It is based on the indistinguishability and wave nature of particles, both of which are at the heart of quantum mechanics.

Basic phenomenon in ideal gas

In a simplified picture, particles in a gas may be regarded as quantum-mechanical wavepackets which have a spatial extent on the order of a thermal de Broglie wavelength, given by Eq. (1),

where T is the temperature, m the mass of the particle, kB is the Boltzmann constant, and ℏ is Planck's constant divided by 2&pgr;. The wavelength λdB can be regarded as the position uncertainty associated with the thermal momentum distribution of the particles. At high temperature, λdB is small, and the probability of finding two particles within this distance of each other is extremely low. Therefore, the indistinguishability of particles is not important, and a classical description applies (namely, Boltzmann statistics). When the gas is cooled to the point where λdB is comparable to the distance between particles, the individual wavepackets start to overlap and the indistinguishability of particles becomes crucial—an identity crisis can be said to occur. For fermions, the Pauli exclusion principle prevents two particles from occupying the same quantum state; whereas for bosons, quantum statistics (in this case, Bose-Einstein statistics) dramatically increases the probability of finding several particles in the same quantum state. The system undergoes a phase transition and forms a Bose-Einstein condensate, where a macroscopic number of particles occupy the lowest-energy quantum state (Fig. 1). See Boltzmann statistics

Criterion for Bose-Einstein condensation in a gas of weakly interacting particlesenlarge picture
Criterion for Bose-Einstein condensation in a gas of weakly interacting particles

Bose-Einstein condensation can be described intuitively in the following way: When the quantum-mechanical wave functions of bosonic particles spatially overlap, the matter waves start to oscillate in concert. A coherent matter wave forms that comprises all particles in the ground state of the system. This transition from disordered to coherent matter waves can be compared to the step from incoherent light to laser light. Indeed, atom lasers based on Bose-Einstein condensation have been realized. See Coherence, Laser

Experimental techniques

The phenomenon of Bose-Einstein condensation is responsible for the superfluidity of helium and for the superconductivity of an electron gas, which involves Bose-condensed electron pairs. However, these phenomena happen at high density, and their understanding requires a detailed treatment of the interactions. See Superconductivity, Superfluidity

The quest to realize Bose-Einstein condensation in a dilute weakly interacting gas focused on atomic gases. At ultralow temperatures, all atomic gases liquefy or solidify in thermal equilibrium. Keeping the gas at sufficiently low density can prevent this from occurring. Typical number densities of atoms between 1012 and 1015 cm3 imply transition temperatures for Bose-Einstein condensation in the nanokelvin or microkelvin regime.

The realization of Bose-Einstein condensation in atomic gases required techniques to cool gases to such low temperatures, and atom traps to confine the gases at the required density and keep them away from the much warmer walls of the vacuum chamber. The experiments on alkali vapors (lithium, rubidium, and sodium) use several laser-cooling techniques as precooling, then hold the atoms in a magnetic trap and cool them further by forced evaporative cooling. For atomic hydrogen, the laser-cooling step is replaced by cryogenic cooling.

Macroscopic wave function

In superconductors and liquid helium, the existence of coherence and of a macroscopic wave function is impressively demonstrated through the Josephson effect. In the dilute atomic gases, the coherence has been demonstrated even more directly by interfering two Bose condensates (Fig. 2). The interference fringes typically have a spacing of 15 μm, a huge length for matter waves. (In contrast, the matter wavelength of atoms at room temperature is only 0.05 nm, less than the size of the atoms.)

Interference pattern of two expanding condensates, demonstrating the coherence of Bose-Einstein condensatesenlarge picture
Interference pattern of two expanding condensates, demonstrating the coherence of Bose-Einstein condensates

Bose-Einstein Condensation


a quantum phenomenon in a system of bosons which consists of the fact that at a temperature below a certain critical value (called the degeneration temperature), a portion of the particles is aggregated in a state with zero momentum (if the system as a whole is at rest). The term “Bose-Einstein condensation” is created by analogy with the condensation of molecules of a vapor into a liquid upon cooling. However, condensation in the ordinary sense does not take place; the distribution of particles in space remains as before, and it is a matter of “condensation in momentum space.”

The degeneration temperature for the overwhelming majority of gases is very low, and the substance passes into the solid state long before Bose-Einstein condensation can set in. The exception is helium, which at T = 4.2° K (under normal conditions) passes into the liquid state and remains a liquid down to temperatures very close to absolute zero. At T = 2.18° K, liquid 4He passes into a special, so-called superfluid state, whose emergence is connected with Bose-Einstein condensation.


Bose-Einstein condensation

[¦bōz ¦īn‚stīn kän·den′sā·shən]
A phase transition that occurs when a gas of bosonic particles is cooled below a critical temperature very close to absolute zero, in which a large number of the particles come to occupy the ground state of the system and form a coherent matter wave.
References in periodicals archive ?
Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor.
Theory of Bose-Einstein condensation in trapped gases", Rev.
The observation of Bose-Einstein condensation in atomic traps (6) has also led to increased recent interest in atom optics, e.
But bosons can occupy the same state and this property gives rise to pre-existing principles in physics known as the Bose-Einstein condensation and superconductivity.
Drawn from the proceedings of the XXII International Conference on Laser Spectroscopy (ICOL2015), held in Singapore in June and July of 2015, the eight papers in this volume discuss quantum walks with neutral atoms in state-dependent optical lattices; the role of muonic atoms in nuclear structure; the development and optimization of Doppler broadening thermometry using acetylene as a molecular target; antiferromagnetism with ultracold atoms; the generation and transfer of stable optical frequencies in optical clocks with trapped ions; precision measurement of the Newtonian gravitational constant by atom interferometry; optical sideband cooling in a Penning trap; and Bose-Einstein condensation of photons vs.
Professor Ketterle, a German physicist, received the Nobel Prize in physics in 2001 for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates.
The Gross-Pitaevskii equation is a model for phenomena such as the Bose-Einstein condensation of ultra cold atomic gases, or the dark solitons of nonlinear optics.
Cornell, Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor, Science 269, 198-201 (1995).
This work really shows that Bose-Einstein condensation is an atom laser.
The authors devote a chapter to a general introduction before going into the one-dimensional, two-dimensional, and three-dimensional cases of Bose-Einstein condensation phase transition.
Cornell received the Nobel Prize for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, which is the cooling down of gases to one-millionth of a degree above Absolute Zero.