Bose-Einstein Condensate

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A Bose–Einstein condensate (BEC) is a state of matter of bosons confined in an external potential and cooled to temperatures very near to absolute zero (0 K or −273.15 °C). Under such supercooled conditions, a large fraction of the atoms collapse into the lowest quantum state of the external potential, at which point quantum effects become apparent on a macroscopic scale.

This state of matter was first predicted by Satyendra Nath Bose in 1925. Bose submitted a paper to the Zeitschrift für Physik but was turned down by the peer review. Bose then took his work to Einstein who recognized its merit and had it published under the names Bose and Einstein, hence the acronymn.

Seventy years later, the first gaseous condensate was produced by Eric Cornell and Carl Wieman in 1995 at the University of Colorado at Boulder National Institute of Standards and Technology - JILA lab, using a gas of rubidium atoms cooled to 170 nanokelvin (nK) (1.7x10^-7 K or -273.14999983 °C). Eric Cornell, Carl Wieman and Wolfgang Ketterle at MIT were awarded the 2001 Nobel Prize in Physics in Stockholm, Sweden.

Introduction

"Condensates" are extremely low-temperature fluids which contain properties and exhibit behaviors that are currently not completely understood, such as spontaneously flowing out of their containers. The effect is the consequence of quantum mechanics, which states that systems can only acquire energy in discrete steps. If a system is at such a low temperature that it is in the lowest energy state, it is no longer possible for it to reduce its energy, not even by friction. Without friction, the fluid will easily overcome gravity because of adhesion between the fluid and the container wall, and it will take up the most favorable position, all around the container.

Bose-Einstein condensation is an exotic quantum phenomenon that was observed in dilute atomic gases for the first time in 1995, and is now the subject of intense theoretical and experimental study.

Theory

The slowing of atoms by use of cooling apparatuses produces a singular quantum state known as a Bose condensate or Bose–Einstein condensate. This phenomenon was predicted in 1925 by generalizing Satyendra Nath Bose's work on the statistical mechanics of (massless) photons to (massive) atoms. (The Einstein manuscript, believed to be lost, was found in a library at Leiden University in 2005.) The result of the efforts of Bose and Einstein is the concept of a Bose gas, governed by the Bose–Einstein statistics, which describes the statistical distribution of identical particles with integer spin, now known as bosons. Bosonic particles, which include the photon as well as atoms such as helium-4, are allowed to share quantum states with each other. Einstein demonstrated that cooling bosonic atoms to a very low temperature would cause them to fall (or "condense") into the lowest accessible quantum state, resulting in a new form of matter.

This transition 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:

$T_c=\left(\frac{n}{\zeta(3/2)}\right)^{2/3}\frac{h^2}{2\pi m k_B}$

where:

$\,T_c$	is	the critical temperature,
$\,n$	is	the particle density,
$\,m$	is	the mass per boson,
$\,h$	is	Planck's constant,
$\,k_B$	is	the Boltzmann constant, and
$\,\zeta$	is	the Riemann zeta function; $\,\zeta(3/2)\approx 2.6124.$