Bose–Einstein condensate

The Bose -Einstein condensate (after Satyendranath Bose and Albert Einstein; abbreviation BEK, English BEC. ) Is an extreme aggregate state of a system of indistinguishable particles, where the majority of the particles is in the same quantum mechanical state. This is only possible if the particles are bosons and therefore subject to Bose -Einstein statistics.

Bose -Einstein condensates are macroscopic quantum objects, in which the individual bosons are completely delocalized. The probability of any boson to meet it at a certain point, that is the same everywhere within the condensate. The condition may, therefore, be described by a single wave function.

This results in properties such as superfluidity, superconductivity or coherence over macroscopic distances. The latter allows interference experiments with Bose - Einstein condensates and to generate an atom laser, which can be obtained from which the condensate holding the case by controlled extraction of part of the matter wave.

Discovery

Theoretically, in 1924 - predicted by Albert Einstein, that a homogeneous ideal Bose gas at absolute zero ( -273.15 ° C or 0 K) condensed - based on a work of Satyendranath Bose on the quantum statistics of photons.

Thereafter, the liquid properties of superconductivity at liquid helium temperatures have been reduced below 2.17 K. Bose -Einstein condensation. However, the direct observation of the effect is extremely difficult in this system, because the interaction between the atoms can not be neglected here. Therefore, are in contrast to the Bose -Einstein theory does not exceed 100%, but only 8 % of the atoms in the ground state.

Attempts to achieve Bose -Einstein condensation in a gas of polarized hydrogen atoms, initially did not lead to success.

The first Bose -Einstein condensates were made ​​in June and September 1995 experimentally by Eric A. Cornell and Carl E. Wieman at JILA and Wolfgang Ketterle, Kendall Davis and Marc -Oliver Mewes at MIT. In 2001, Cornell, Wiemann and Ketterle received the Nobel Prize for Physics.

Conditions of existence

The phase transition of a conventional atomic gas to a Bose -Einstein condensate occurs when a critical phase bulk density is achieved, ie, when the density of particles having almost the same pulse is large enough.

Clearly you can understand this: the atoms are quantum particles, whose motion is represented by a wave packet. The extension of this wave packet is the thermal de Broglie wavelength. This is all the greater, the farther the temperature drops. Achieved the de Broglie wavelength of the average distance between two atoms, so come the quantum properties to bear. In a three-dimensional ensemble is where the Bose -Einstein condensation. Therefore, it is necessary to increase the density of the gas and to reduce the temperature to reach the phase transition.

In the framework of statistical physics can calculate the critical temperature of an ideal Bose gas, below which uses the Bose -Einstein condensation using the Bose -Einstein statistics:

Where:

" Ideal Bose gas " means that for the calculation of an infinitely extended, homogeneous, non-interacting gas is considered. The inclusion of atoms in the trapping potential and the interactions between them lead to a slight deviation of the actually observed critical temperature of the calculated value, the formula is, however, the correct order again. For typical experimental parameters can be found feasible temperatures of significantly less than 0.1 micro- Kelvin ( K = 10-7 ), so-called ultra-low temperatures.

Generation

The usual method for generating Bose -Einstein condensates of atoms consists of two phases:

• First, the atoms are trapped in a magneto-optical trap and precooled by the laser cooling. However, the laser cooling system has a lower limit temperature (typically about 100 μK ), which is due to the recoil of the spontaneous emission of photons.

• The average speed of the thus-cooled atoms of only a few centimeters per second, however, is small enough to catch them in a magnetic or optical trap. By evaporative cooling, i.e., continuous removal of the most energetic atoms, the temperature of the cloud of atoms is further reduced. In this process, usually more than 99.9 % of the atoms are selectively removed. Thus, the remaining atoms reach the necessary phase space density to make the phase transition in a Bose -Einstein condensate.

In this way it was possible until 2004 to reach at ultralow temperatures of 10-7 K and including Bose -Einstein condensation for many different isotopes ( 7Li, 23Na, 41K, 52Cr, 85Rb, 87Rb, 133Cs and 174Yb ). Also hydrogen when it was finally successful, though with some other methods.

That the above-mentioned gases bosonic and not - would like expected solid-state physicist or chemist of alkali atoms - show fermionic behavior ( for which the Pauli principle would apply ), based on a subtle interplay of electron and nuclear spin at ultralow temperatures: at correspondingly low excitation energies the half-integer total spin of the electron shell of atoms and also half-integer nuclear spin by the weak hyperfine interaction are coupled to an integer total spin of the system. In contrast, the behavior at room temperature ( the "chemistry" of the systems) determined solely by the spin of the electron shell, because here the thermal energies are much larger than the hyperfine field energies.

In 2006 Demokritov employees and Bose -Einstein condensation of magnons ( quantized spin waves ) have achieved at room temperature, but by the application of pumping processes.

2009, it is the first time the PTB succeeded in producing a Bose - Einstein condensate of calcium atoms. Such alkaline earth metals have - in contrast to the alkali metals used so far - one a million times smaller optical transition and are thus for novel precision measurements such as gravitational fields, can be used.

In November 2010, reported a team of researchers at the University of Bonn from the generation of a Bose -Einstein condensate of photons. The photons were trapped in an optical cavity between two curved mirrors. Since cooling of photons is not possible to dye molecules were placed in the resonator to set a thermal equilibrium. The made ​​after the optical pumping condensation could be detected in the form of a coherent beam of light yellow. According to the research group led by Martin Weitz photonic Bose -Einstein condensate for the production of short-wave lasers in the UV or X-rays could be used.

Experimental Evidence

Evidence that actually a Bose -Einstein condensate was produced, performed at atomic gases usually with the help of absorption images after a flight.

For this, the case in which the gas was trapped, cut off abruptly. Then, expanding the gas cloud and is irradiated by a time of flight with resonant laser light. The photons of the beam scattered by the atoms of the gas cloud, so the beam weakened effectively. The resulting ( semi-) shadows can be captured with a sensitive CCD camera, from his image allows the density distribution of the gas cloud reconstruct.

This is for Bose- Einstein condensates anisotropic, while a classical gas always expands isotropically in thermal equilibrium. In many cases, the density distribution is parabolic, which can be interpreted as a consequence of the interaction between the atoms and the Bose -Einstein condensate is different from an ideal Bose gas.