Ultracold quantum gases are like man-made universes that allow us, as we will see, to study interesting quantum many-body phenomena in detail. Although it turns out that these quantum gases are extremely well suited for manipulation by experimentalists, there are some limitations. A typical trapped alkali gas consists of about 105 – 109 atoms and has, for realistic trap parameters, a central density of n ≃ 1012 – 1015 cm−3. This is many orders of magnitude less dense than air, which has a typical density of about 1019 cm−3. Nevertheless, the gas can be cooled down to such low temperatures that it reaches the quantum degenerate regime where the thermal de Broglie wavelength Λ = (27πħ2/mkBT)1/2 is on the same order as the average interatomic distance n −1/3. For the densities quoted this means that the temperature has to be as low as 1–100 nK. This makes ultracold gases the coldest objects in the universe. The physics of how to cool dilute alkali gases to quantum degeneracy is extensively described elsewhere [40,41] and we do not cover this subject here. A crucial ingredient, however, is that the gas is trapped in an external potential to keep the gas away from physical walls that can never be cooled to such low temperatures. The traps used in practice can almost always be well approximated by an anisotropic harmonic oscillator potential with frequencies of about 1–100 Hz. The associated energy level splittings ħωiare then typically much smaller than the thermal energy kBT or the chemical potential μ. However, this is not always the case, and it turns out to be also possible to create such steep potentials in certain directions, that in these directions only the quantum state with the lowest energy can be occupied by the atoms. As a result, the atomic motion is essentially frozen out in these directions, which allows for the creation of effectively one-dimensional and two-dimensional quantum gases.
In this chapter, we look at the relevant atomic physics that is necessary to understand the microscopic origin of the relevant physical parameters for interacting atomic quantum gases. In the following chapters, we then combine this knowledge with the quantum field theory formalism developed in the previous chapters to describe realistic ultracold atomic many-body systems. We start with discussing the fine and hyperfine structure of the atomic energy levels, as well as the Zeeman effect, because these are crucial for the ability to trap atoms by applying external magnetic or electric fields. The electric fields that are generated by a laser can also be used to create periodic trapping potentials, called optical lattices, which are discussed in Chap. 16. Next, we treat two-body scattering of atoms, which is the dominant interaction mechanism in ultracold atomic gases. We first discuss two-body scattering in vacuum, and then generalize the treatment to include also the presence of a medium. Finally, we end this chapter with a detailed discussion of the different physical regimes that we can explore with ultracold atomic gases, depending on the atomic density, the temperature and the interaction strength.
KeywordsNuclear Spin Atomic Physic Feshbach Resonance Zeeman Effect Alkali Atom
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