By C. J. Pethick, H. Smith
In 1925 Einstein envisioned that at low temperatures debris in a fuel might all stay within the comparable quantum nation. This gaseous kingdom, 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 interesting new topic when it comes to simple actual rules, with out assuming particular previous wisdom. Chapters 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. challenge units also are incorporated.
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48, 1727 (1978); Phys. Rev. B 22, 5171 (1980). References 39  J. T. M. Walraven, in Fundamental Systems in Quantum Optics, ed. J. -M. Raimond, and J. Zinn-Justin (North-Holland, Amsterdam, 1992), p. 485.  V. Bagnato and D. Kleppner, Phys. Rev. A 44, 7439 (1991).  A. G¨ orlitz, J. M. Vogels, A. E. Leanhardt, C. Raman, T. L. Gustavson, J. R. Abo-Shaeer, A. P. Chikkatur, S. Gupta, S. Inouye, T. P. Rosenband, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 87, 130 402 (2001). 3 Atomic properties Atomic properties of the alkali atoms play a key role in experiments on cold atomic gases, and we shall discuss them brieﬂy in the present chapter.
28) or N0 = N 1 − T Tc α . 29) 24 The non-interacting Bose gas For particles in a box in three dimensions, α is 3/2, and the number of excited particles nex per unit volume may be obtained from Eqs. 13). It is nex = Nex = ζ(3/2) V 3/2 mkT 2π 2 . 30) The occupancy of the condensate is therefore given by the well-known result N0 = N [1 − (T /Tc )3/2 ]. For a three-dimensional harmonic-oscillator potential (α = 3), the number of particles in the condensate is N0 = N 1 − T Tc 3 . 19) for the appropriate value of α.
For negative nuclear magnetic moment the state with F = I + 1/2 has the lower energy. The hyperﬁne line for the hydrogen atom has a measured frequency of 1420 MHz, and it is the famous 21-cm line exploited by radio astronomers. 6). 793µN and |ψ(0)|2 = 1/πa30 , where a0 = 2 /me e20 is the Bohr radius, with e20 = e2 /4π 0 . 6) becomes ∆Ehf = 32 µ0 µB µp . 7) The magnitude of ∆Ehf is of order (me /mp )αfs in atomic units (a. ), where αfs = e20 / c, c being the velocity of light, is the ﬁne structure constant and the atomic unit of energy is e20 /a0 .