Bose–Einstein Condensates of Weakly Interacting Dilute Gases

Abstract

Since the middle of the 90’s, it has been known how to trap and cool vapours of bosonic atoms (typically rubidium https://www.w3.org/1998/Math/MathML" display="inline"> 87 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003272427/5ca4d37a-9786-43a3-8b38-8fa9eb3d1a19/content/math_27.tif "/> Rb or sodium https://www.w3.org/1998/Math/MathML" display="inline"> 23 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003272427/5ca4d37a-9786-43a3-8b38-8fa9eb3d1a19/content/math_28.tif "/> Na) below the Bose–Einstein condensation temperature (see Section 7.4 ). These systems are very cold ( https://www.w3.org/1998/Math/MathML" display="inline"> T ∼ 100 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003272427/5ca4d37a-9786-43a3-8b38-8fa9eb3d1a19/content/math_29.tif "/> nK) and exhibit strong quantum features. They are also inhomogeneous (because the gas is confined by an external potential) and subject to non-negligible interaction effects: the condensed atoms accumulate at the bottom of the trapping potential well until reaching relatively high densities at which the physical properties of the system cannot always be described by the non-interacting model considered in Section 7.4 . The system’s low temperature is an asset for the theoretical treatment of the interactions because it is associated with a thermal wavelength that is larger than the typical distance between atoms: in this regime, it is legitimate to ignore the details of the interaction and to use a schematic potential, designed only to correctly describe the low energy scattering between two atoms. The simplicity of the resulting model enables to account, in the framework of a mean field approach, for non-trivial interaction effects for which it is possible to obtain precise experimental information.