By C. J. Pethick, H. Smith
Pethick and Smith supply a unified advent to the physics of ultracold atomic Bose and Fermi gases for college students, experimentalists and theorists alike. This publication explains the phenomena in ultracold gases from simple ideas, with no assuming an in depth wisdom of atomic, condensed topic, and nuclear physics. This booklet offers chapters to hide the statistical physics of trapped gases, atomic houses, 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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Additional resources for Bose-Einstein Condensation in Dilute Gases
37) Thus the density in momentum space is given by n(p) = N |φ0 (p)|2 = N π 3/2 c x cy cz e−px /cx e−py /cy e−pz /cz . 38) has the form of a Maxwell distribution with diﬀerent ‘temperatures’ Ti = ωi /2k for the three directions. 3 Density proﬁle and velocity distribution 27 also depends on direction. 36) where the widths ci are proportional to the square root of the oscillator frequencies. These density and momentum distributions may be contrasted with the corresponding expressions when the gas obeys classical statistics, at temperatures well above the Bose–Einstein condensation temperature.
1. As we remarked earlier, |D| is much less than both C and |A| at the ﬁelds attainable. Therefore to a good approximation we may set D equal to zero, and we also set g = 2. The dimensionless magnetic ﬁeld b is deﬁned for arbitrary nuclear spin by b= C (2I + 1)μB B = . 16) The two straight lines correspond to the energies of the states |3/2, 1/2 and |−3/2, −1/2 , which do not mix with other states. 17) 48 Atomic properties Fig. 1 Energies of hyperﬁne levels of an alkali atom with I = 3/2 and A > 0 in a magnetic ﬁeld.
1 lists Γ(α) and ζ(α) for selected values of α. 17) we now ﬁnd kTc = N 1/α . 2 Transition temperature and condensate fraction 23 For a three-dimensional harmonic-oscillator potential, α is 3 and C3 is given by Eq. 14). 21) where is the geometric mean of the three oscillator frequencies. 22) 100 Hz where f¯ = ω ¯ /2π. For a uniform Bose gas in a three-dimensional box of volume V the index α is 3/2. 23) where n = N/V is the number density. 17) diverges. Thus Bose–Einstein condensation in a two-dimensional box can occur only at zero temperature.