By C. J. Pethick, H. Smith

Pethick and Smith supply a unified creation to the physics of ultracold atomic Bose and Fermi gases for college students, experimentalists and theorists alike. This e-book explains the phenomena in ultracold gases from easy rules, with out assuming an in depth wisdom of atomic, condensed subject, and nuclear physics. This publication presents chapters to hide 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. difficulties are incorporated on the finish of every bankruptcy.

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**Sample text**

43) to calculate the number of particles in the condensate for an isotropic harmonicoscillator potential. Indicate how the calculation may be generalized to an anisotropic harmonic oscillator. 2 Consider a gas of N identical bosons, each of mass m, in 40 The non-interacting Bose gas the quadrupole trap potential V (x, y, z) = A(x2 + y 2 + 4z 2 )1/2 , where A is a positive constant (the physics of this trap will be explained in Sec. 1). Use the semi-classical approach to determine the density of single-particle states as a function of energy and calculate the transition temperature, the depletion of the condensate as a function of temperature, and the jump in the speciﬁc heat at the transition temperature.

5) For a free particle in d dimensions the corresponding result is g( ) ∝ (d/2−1) , and therefore the density of states is independent of energy for a free particle in two dimensions. 6) 2 which we will refer to as a harmonic trap. Here the quantities Ki (i = x, y, z) denote the three force constants, which are generally unequal. The corresponding classical oscillation frequencies ωi are given by ωi2 = Ki /m, and we shall therefore write the potential as 1 V (r) = m(ωx2 x2 + ωy2 y 2 + ωz2 z 2 ).

If a thermal cloud is allowed to expand to a size much greater than its original one, the resulting cloud will be spherically symmetric due to the isotropy of the velocity distribution, as we shall demonstrate explicitly in Sec. 1 below. This is quite diﬀerent from the anisotropic shape of an expanding cloud of condensate. In early experiments the anisotropy of clouds after expansion provided strong evidence for the existence of a Bose–Einstein condensate. 28 The non-interacting Bose gas Interactions between the atoms alter the sizes of clouds somewhat, as we shall see in Sec.