# 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 in which the majority of the particles are in the same quantum mechanical state . This is only possible if the particles are bosons and are therefore subject to Bose-Einstein statistics .

Bose-Einstein condensates are macroscopic quantum objects in which the individual bosons are completely de- localized . This is also known as the macroscopic quantum state . The bosons are completely indistinguishable. The state can therefore be described by a single wave function .

The resulting properties are superfluidity , superconductivity , suprasolidity or coherence over macroscopic distances. The latter allows interference experiments with Bose-Einstein condensates and the production of an atomic laser , which can be obtained by controlled decoupling of part of the matter wave from the trap holding the condensate.

## discovery

Theoretically,  Albert Einstein predicted in 1924 - based on a work by Satyendranath Bose on the quantum statistics of photons - that a homogeneous, ideal Bose gas would condense at low temperatures .

The superfluid properties of liquid helium at temperatures below 2.17 K were then attributed to the Bose-Einstein condensation. However, direct observation of the effect in this system is extremely difficult because here the interaction between the atoms cannot be neglected. Therefore, contrary to the Bose-Einstein theory, which has since been proven experimentally in ultracold gases, in superfluid helium not a maximum of 100%, but only 8% of the atoms are in the ground state .

Attempts to achieve a Bose-Einstein condensation in a gas composed of polarized hydrogen atoms were initially unsuccessful.

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

## Conditions of existence

The phase transition from a classical atomic gas to a Bose-Einstein condensate takes place when a critical phase space density is reached, that is, when the density of the particles with almost the same momentum is large enough.

You can understand it this way: the atoms are quantum particles , the movement of which is represented by a wave packet . The expansion of this wave packet is the thermal De Broglie wavelength . This becomes greater the further the temperature drops. When the De Broglie wavelength reaches the mean distance between two atoms, the quantum properties come into play. Bose-Einstein condensation now sets in in a three-dimensional ensemble . It is therefore necessary to increase the density of the gas and lower the temperature in order to achieve the phase transition.

In the context of statistical physics , the Bose-Einstein statistics can be used to calculate the critical temperature of an ideal Bose gas , below which the Bose-Einstein condensation begins: ${\ displaystyle T _ {\ mathrm {C}}}$

${\ displaystyle T _ {\ mathrm {C}} = {\ frac {h ^ {2}} {2 \ pi \ cdot m \ cdot k _ {\ mathrm {B}}}} \ left ({\ frac {n} {(2S + 1) \ cdot \ zeta (3/2)}} \ right) ^ {2/3}}$

Where:

${\ displaystyle h}$: Planck's quantum of action
${\ displaystyle m}$: Mass of the particles
${\ displaystyle k _ {\ mathrm {B}}}$: Boltzmann constant
${\ displaystyle n}$: Density of particles
${\ displaystyle S}$: Spin of the particles
${\ displaystyle \ zeta (x)}$: Riemann zeta function ,${\ displaystyle \ zeta (3/2) \ approx 2 {,} 6124}$

“Ideal Bosegas” means that an infinitely extensive, homogeneous, non-interacting gas is considered for the calculation. The inclusion of the atoms in the falling potential and the interactions between them lead to a slight deviation of the actually observed critical temperature from the calculated value, but the formula gives the correct order of magnitude. For typical, experimentally realizable parameters, one finds temperatures of significantly less than 100 nK, so-called ultra - low temperatures .

## generation

The usual method of creating Bose-Einstein condensates from atoms consists of two phases:

• First, the atoms are caught in a magneto-optical trap and pre-cooled by laser cooling . The laser cooling, however, has a lower limit for temperatures (typically about 100 µK), which is caused by the recoil during the spontaneous emission of photons.
• However, the mean speed of the atoms cooled in this way, only a few centimeters per second, is small enough to catch them in a magnetic or optical trap. The temperature of the atomic cloud is further reduced through evaporative cooling , i.e. continuous removal of the most energetic atoms. In this process, mostly over 99.9% of the atoms are deliberately removed. In this way, the remaining atoms achieve the necessary phase space density to complete the phase transition into a Bose-Einstein condensate.

In this way, it was possible until 2004 to achieve Bose-Einstein condensation for many different isotopes at ultra-low temperatures of 100 nK and below ( 7 Li , 23 Na , 41 K , 52 Cr , 85 Rb , 87 Rb, 133 Cs and 174 Yb ). In the end, they were also successful with hydrogen, albeit with slightly different methods.

The fact that the above-mentioned gases show bosonic behavior and not - as solid-state physicists or chemists would expect from alkali atoms - fermionic behavior (for which the Pauli principle would apply) is based on a subtle interplay of electron and nuclear spin at ultra-low temperatures: with correspondingly low excitation energies the half- integer total spin of the electron shell of the atoms and the half- integer nuclear spin are coupled by the weak hyperfine interaction to form an integer total spin of the system. In contrast, the behavior at room temperature (the “chemistry” of the systems) is determined solely by the spin of the electron shell, because here the thermal energies are much greater than the hyperfine field energies.

In 2006 Demokritov and co-workers achieved the Bose-Einstein condensation of magnons (quantized spin waves) at room temperature, but by using optical pumping processes .

In 2009 the Physikalisch-Technische Bundesanstalt succeeded for the first time in producing a Bose-Einstein condensate from calcium atoms. Such alkaline earth metals have - in contrast to the previously used alkali metals  - an optical transition that is one million times narrower and are therefore suitable for new types of precision measurements, e.g. B. of gravitational fields , usable.

In November 2010, a research group at the University of Bonn reported on the generation of a Bose-Einstein condensate from photons. The photons were trapped in an optical resonator between two curved mirrors. Since photons cannot be cooled down, dye molecules were placed in the resonator to establish a thermal equilibrium . The condensation that occurred after optical pumping could be detected in the form of a coherent yellow light beam. According to the research group around Martin Weitz, the photonic Bose-Einstein condensate can be used to produce short-wave lasers in the UV or X-ray range .

The first Bose-Einstein condensate in space was created in 2017. For this purpose, the MAIUS rocket was launched with a VSB-30 engine on the European Space and Sounding Rocket Range and brought to a weightless parabolic flight at an altitude of more than 240 km. There have been a previously created in ultra-high vacuum -Kammer rubidium -atoms by diode laser in a magneto-optical trap by evaporative cooling almost up to the absolute zero accommodated. The Bose-Einstein condensate was then generated using an atom chip . It was released from the center of the trap in weightlessness before a harmonic potential was briefly applied by means of a magnetic field and the states were measured using a Mach-Zehnder interferometer . The mission was a cooperation project in which the following institutions were involved under the leadership of the Gottfried Wilhelm Leibniz University of Hanover : Humboldt University of Berlin , Ferdinand Braun Institute, Leibniz Institute for High Frequency Technology , ZARM , Johannes Gutenberg University Mainz , University of Hamburg , University of Ulm , Darmstadt University of technology , simulation and software technology Braunschweig and the Mobile rocket base .

On May 21, 2018, the Cold Atom Laboratory (CAL) experiment was flown to the ISS space station on a Cygnus ferry .

## Experimental evidence

Density distribution of a Bose-Einstein condensate

The proof that a Bose-Einstein condensate was actually generated is usually provided with the help of absorption images after a flight time for atomic gases .

To do this, the trap in which the gas was trapped is switched off suddenly. The gas cloud then expands and is irradiated with resonant laser light after a flight time . The photons of the beam are scattered by the atoms of the gas cloud , so the beam is effectively weakened. The resulting (half) shadow can be recorded with a sensitive CCD camera, and the density distribution of the gas cloud can be reconstructed from its image.

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

## Similar effects

• In the case of the fermion condensate , the effect is also based on bosons. Due to the Pauli principle , it is not possible for fermions to be in the same state. However, this does not apply to fermions which combine in pairs to form bosons, which can then form a condensate as bosons.

## literature

• Satyendranath Bose : Planck's law and light quantum hypothesis . In: Zeitschrift für Physik No. 26, p. 178, Springer, Berlin / Heidelberg 1924 (English translation published in American Journal of Physics , Vol. 44, No. 11, November 1976).
• Albert Einstein: Quantum Theory of the Monatomic Ideal Gas - Second Treatise . In: Meeting reports of the Prussian Academy of Sciences . Berlin, 1925, pp. 3-10.
• Kai Bongs, Jakob Reichel, Klaus Sengstock: Bose Einstein Condensation: The Ideal Quantum Laboratory . In: Physics in Our Time . Volume 34, number 4, Wiley-VCH, Weinheim / Berlin 2003, , pp. 168–176.
• Jan Klaers, Julian Schmitt, Frank Vewinger, Martin Weitz: Bose-Einstein condensate from light . In: Phys. Our time . tape 42 , no. 2 , 2011, p. 58–59 ( uni-bonn.de [PDF; 196 kB ]).

## Web links

Commons : Bose-Einstein Condensate  - collection of images, videos and audio files

## Individual evidence

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2. Albert Einstein: Quantum Theory of the Monatomic Ideal Gas - Second Treatise . In: Meeting reports of the Prussian Academy of Sciences . 1925, pp. 3-10.
3. First Bose-Einstein condensate with strontium atoms. In: iqoqi.at. Austrian Academy of Sciences , November 10, 2009, accessed on September 10, 2016.
4. Michael Breu: Frozen. 100 atoms at the lowest temperatures: quantum opticians produce one-dimensional Bose-Einstein condensate. In: ethz.ch. ETH Zurich , February 26, 2004, accessed on June 6, 2010.
5. Demokritov SO, Demidov VE, Dzyapko O, et al. : Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping . In: Nature . 443, No. 7110, September 2006, pp. 430-3. doi : 10.1038 / nature05117 . PMID 17006509 .
6. Patryk Nowik-Boltyk: Magnon Bose Einstein condensation simply depicted. In: uni-muenster.de. Westfälische Wilhelms-Universität , June 6, 2012, accessed on September 10, 2016.
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10. MAIUS - Atom-optical experiments on sounding rockets ( Memento of the original from August 1, 2017 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
11. V. Schkolnik et al .: A compact and robust diode laser system for atom interferometry on a sounding rocket , 2016, arXiv 1606.0027 ( online )
12. A laboratory for "coldest point in space" orf.at, May 18, 2018, accessed May 18, 2018.
13. Launch of the space freighter “Cygnus” postponed to the ISS orf.at, May 19, 2018, accessed May 19, 2018.