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9746 results in Engineering: general interest

Page 29 of 488

  • 1 - Preliminary Concepts

  • from Part I - Fundamental Principles
  • Mark Fox, University of Sheffield
  • Book:
    A Student's Guide to Atomic Physics
    Published online:
    21 June 2018
    Print publication:
    14 June 2018, pp 3-19

  • Summary

    Atomic physics is the subject that studies the inner workings of the atom. It remains one of the most important testing grounds for quantum theory and is therefore a very active area of research, both for its contribution to fundamental physics and to technology. Furthermore, many other branches of science rely heavily on atomic physics, especially astrophysics, laser physics, solid-state physics, quantum information science, and chemistry. So much so, that Richard Feynman once wrote (1964):

    If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or atomic fact, or whatever you wish to call it) that all things are made of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence you will see an enormous amount of information about the world, if just a little imagination and thinking are applied.

    The task of atomic physics is to understand the structure of atoms, and hence to explain experimental observations such as the wavelengths of spectral lines. For all elements apart from hydrogen, we have to deal with a complicated many-body problem consisting of a nucleus and more than one electron. Atomic physics proceeds by a series of approximations that make this problem tractable. Before we set about this task, it is first necessary to cover a number of important basic concepts and definitions.

    Quantized Energy States in Atoms

    The first basic concept we need is that of bound states. Atoms are held together by the attractive force between the positively charged nucleus and the negatively charged electrons: the electrons are bound to the atom, rather than being free to move though space. In the limit where the electron is very far away from the nucleus, the attractive force is negligible; the electron is free to move with velocity (v) without any influence from the nucleus, as illustrated schematically in Figure 1.1(a). It is natural to define the energy (E) of this free (or unbound) state as being zero when v = 0.

  • 10 - Cold Atoms

  • from Part II - Applications of Atomic Physics
  • Mark Fox, University of Sheffield
  • Book:
    A Student's Guide to Atomic Physics
    Published online:
    21 June 2018
    Print publication:
    14 June 2018, pp 184-201

  • Summary

    The resonant force between atoms and light was first observed in 1933, when Otto Frisch measured the deflection of a sodium beam by a sodium lamp. The invention of lasers opened up new possibilities, leading to the development of the laser-cooling techniques that are the subject of this chapter.

    There are two aspects of laser cooling that make it particularly remarkable:

  • (i) It is highly surprising that the technique works at all. We would normally expect a powerful laser to cause heating rather than cooling. This makes us realize that the technique will only work when special conditions are satisfied.

  • (ii) The very low temperatures achieved by laser cooling are extremely impressive, but this in itself is not the main point, as techniques for achieving very low temperatures have been used for decades by condensed-matter physicists. For example, commercial dilution refrigerators routinely achieve temperatures in the milli-Kelvin range, and as early as the 1950s, Nicholas Kurti and coworkers at Oxford University used adiabatic demagnetisation to achieve nuclear spin temperatures in the micro-Kelvin range. The novelty of laser cooling is that it produces an ultracold gas of atoms, in contrast to the condensed-matter techniques that work on all liquids or solids. These ultracold atoms only interact weakly with each other, which makes it possible to study them with unsurpassed precision.

    • The ability to cool a gas of atoms to very low temperatures has given rise to a whole host of related benefits. Atomic clocks have been made with greater accuracy, and a whole range of new quantum phenomena have been discovered. The most spectacular of these is Bose–Einstein condensation, which was first observed in 1995 and is discussed in Section 10.7.

    The description of laser cooling and Bose–Einstein condensation in this chapter focuses on the basic principles. The reader is referred to specialized texts or articles for a more detailed discussion. See, for example, Foot (2004), Metcalf and van der Straten (1999), or Phillips (1998).

    Gas Temperatures

    In order to understand how laser cooling works, we first need to clarify how the temperature of a gas of atoms is measured. The key point is the link between the thermal motion of the atoms and the temperature. Starting from the Maxwell–Boltzmann distribution (see Eq. [3.39]), it is possible to define a number of different characteristic velocities for the gas.

  • 5 - Angular Momentum

  • from Part I - Fundamental Principles
  • Mark Fox, University of Sheffield
  • Book:
    A Student's Guide to Atomic Physics
    Published online:
    21 June 2018
    Print publication:
    14 June 2018, pp 84-105

  • Summary

    The treatment of angular momentum is very important to understand the properties of atoms. It is now time to explore these effects in detail, and to see how this leads to the classification of the quantized states of atoms by their angular momentum.

    Conservation of Angular Momentum

    In the sections that follow, we will consider several different types of angular momentum and the ways in which they are coupled together. Before going into the details, it is useful to stress one very important point related to conservation of angular momentum. In an isolated atom, there are many forces (and hence torques) acting inside the atom. These internal forces cannot change the total angular momentum of the atom, since conservation of angular momentum demands that the angular momentum of the atom as a whole must be constant in the absence of any external torques. The total angular momentum of the atom is normally determined by its electrons. The total electronic angular momentum is written J and is specified by the quantum number J. The principle of conservation of angular momentum therefore requires that isolated atoms always have well-defined J-states. It is this J-value that determines, for example, the magnetic dipole moment of the atom.

    It should be noted in passing that the nucleus can possess angular momentum and that electrons can exchange angular momentum with the nucleus through hyperfine interactions. (See Section 7.8.2.) These interactions are very weak, and can usually be neglected except when explicitly considering nuclear effects. With this caveat, we can safely regard the total electronic angular momentum J as a conserved quantity.

    The principle of conservation of angular momentum does not apply, of course, when external perturbations are applied. The most obvious example is the perturbation caused by the emission or absorption of a photon. In this case the angular momentum of the atom must change because the photon itself carries angular momentum, and the angular momentum of the whole system (atom + photon) has to be conserved. The change in J is then governed by selection rules, as discussed, for example, in Section 5.8. Another obvious example is the effect of a strong external DC magnetic field.

Page 29 of 488