By C. J. Pethick, H. Smith

In 1925 Einstein anticipated that at low temperatures debris in a gasoline may well all stay within the related quantum kingdom. This gaseous nation, a Bose-Einstein condensate, used to be produced within the laboratory for the 1st time in 1995 and investigating such condensates is without doubt one of the such a lot lively parts in modern physics. The authors of this graduate-level textbook clarify this fascinating new topic when it comes to simple actual ideas, with no assuming distinctive previous wisdom. Chapters disguise the statistical physics of trapped gases, atomic homes, cooling and trapping atoms, interatomic interactions, constitution of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. challenge units also are incorporated.

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Here a0 = 2 /me e20 is the Bohr radius and e20 = e2 /4π 0 . 28) and therefore it is given in order of magnitude by α∼ ea0 = 4π 0 a30 . 29) More generally, the polarizability is a tensor, but for the ground states of alkali atoms and hydrogen, which are S states, it is a scalar, since it does not depend on the direction of the field. In order to avoid exhibiting the factor of 4π 0 we define the quantity α ˜= α . 29) then leads to the result α ˜ ∼ a30 . 31) The energy of an atom in an electric field may be evaluated quantitatively using perturbation theory.

This gives the distribution of excited particles at the transition temperature or below. 49), is also exhibited for the same value of µ. Note that in the semi-classical approximation the density has a cusp at the origin, whereas in a more precise treatment this would be smoothed over a length scale of order λT . 45) over space. 4 Thermodynamic quantities In this section we determine thermodynamic properties of ideal Bose gases and calculate the energy, entropy, and other properties of the condensed phase.

3 Response to an electric field When an atom is subjected to an electric field E it acquires an electric dipole moment, and its energy levels are shifted. This effect is exploited extensively in experiments on cold dilute gases for trapping and cooling atoms using the strong electric fields generated by lasers. Such electric fields are time dependent, but to set the scale of effects we begin by considering static fields. For the hydrogen atom we may estimate the order of magnitude of the polarizability by arguing that the average position of the electron will be displaced by an amount comparable to the atomic size ∼ a0 if an external electric field comparable in strength to the electric field in the atom E ∼ e/(4π 0 a20 ) is applied.

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