Quantum mechanics and the Planck-spectrum

[The following is a guest post from Bjoern Malte Schaefer. Bjoern is one of the curators of the Cosmology Question of the Week blog, which is worth checking out. This post is a historical look at some of the early parts in the history of quantum mechanics, in particular, the black-body spectrum. Questions are welcome and I'll make sure he sees any of them. Image captions (and hyper-links, in this case) are, as usual, by me, because guest posters don't ever seem to provide their own.]

Two unusual systems

Quantum mechanics surprises with the statement that the microscopic world works very differently from the macroscopic world. Therefore, it took a while until quantum mechanics was formally established as the theory of the microworld. In particular, despite the fact that two of the natural systems on which theories of quantum mechanics could initially be tested were very simple, even from the point of view of the physicists of the time, one needed to introduce a number of novel concepts for their description. These two physical systems were the hydrogen atom and the spectrum of a thermal radiation source. The hydrogen atom was the lightest of all atoms with the most simply structured spectrum. It exhibited many regularities involving rational numbers relating its discrete energy levels. It could only be ionised once implying that it had only a single electron and from these reasons it was the obvious test case for any theory of mechanics in the quantum regime. Werner Heisenberg was the first to be successful in solving this quantum mechanical analogue of the Kepler-problem, i.e. the equation of motion of a charge moving in a Coulomb-potential, paving the way for a systematic understanding of atomic spectra, their fine structure, the theory of chemical bonds, interactions of atoms with fields and ultimately quantum electrodynamics.

The Planck-spectrum was equally puzzling: It is the distribution of photon energies emitted from a body at thermal equilibrium and does not, in particular, require any further specification of the body apart that it should be black, meaning ideally emitting and absorbing radiation irrespective of wave length: From this point of view it is really the simplest macroscopic body one could imagine because its internal structure does not matter. In contrast to the hydrogen atom it is described with a continuous spectrum. In fact, there are at least two beautiful examples of Planck-spectra in Nature: the thermal spectrum of the Sun and the cosmic microwave background. The solution to the Planck-spectrum involves quantum mechanics, quantum statistics and relativity, and unites three of the four the great constants of Nature: the Planck-quantum h, the Boltzmann-constant \(k_B\) and the speed of light c.

The spectrum (basically intensity against wavelength or frequency) of the light from the sun (in yellow) and a blackbody with the same temperature (grey). I'm actually surprised by how similar they are.

Limits of the Planck-spectrum

Although criticised at the time by many physicists as phenomenological, the high energy part of the Planck-spectrum is relatively straightforward to understand, as had been realised by Wilhelm Wien: Starting with the result that photons as relativistic particles carry energies proportional to their frequency as well as momenta inversely proportional to their wave length (the constant of proportionality in both cases being the Planck-constant h), imposing isotropy of the photon momenta and assuming a thermal distribution of energies according to Boltzmann leads directly to Wien's result which is an excellent fit at high photon energies but shows discrepancies at low photon energies, implying that at low temperatures the system exhibits quantum behaviour of some type.

David J. Wineland: trapping ions for clocks and computers

Simon Thwaite recently completed a D.Phil. in Atomic & Laser Physics at the University of Oxford, and is currently a postdoctoral researcher at the Ludwig Maximilian University in Munich. The first part of his post series commenting on the 2012 Nobel Prize in Physics can be found here.

In this post he gives an overview of the field of trapped ions, describes two of its most important applications, and describes what goes on behind the scenes when a trapped ion interacts with a laser beam.

David J. Wineland – probing trapped atoms with light

David Wineland, an experimental physicist at the National Institute for Standards and Technology (NIST) in Boulder, Colorado, is one of the leading researchers in the field of trapped ions: that is, the study of how positively-charged ions (i.e. atoms stripped of one or more electrons) may be trapped, cooled, and manipulated.  This field shares many similarities with experiments on neutral atoms (laser cooling, for example, is just as useful for ions as it is for neutral atoms), but also has a number of significant differences. The most important difference that distinguishes ions from atoms is, obviously enough, the fact that ions have a non-zero net electrical charge. This has two very important consequences.

Trapped ions: trapping and interactions

A string of trapped ions (red dots) lined up in a Paul trap
can be imaged with a tightly-focused laser beam and CCD camera.

Image credit: Rainer Blatt experimental group, University of Innsbruck.

Applying an electric field to an ion produces a force on the ion: positive ions are drawn in the direction of the field. [In contrast, applying an electric field to a neutral atom changes the ‘shape’ of the atom slightly, since the positively-charged nucleus and negatively-charged electron cloud are drawn in opposite directions, but produces no net force.] Consequently, whereas traps for neutral atoms must rely on combinations of laser light and magnetic fields, ions can be trapped just by electric fields. Most of the recent trapped-ion experiments use some variation on the Paul trap (a.k.a. the quadrupole ion trap) which uses a combination of static (DC) and oscillating (AC) electric fields to trap ions along a 1-dimensional line.

The 2012 Nobel Prize in Physics: The background

[The following is a guest post from Simon Thwaite. Simon recently completed his doctorate in the subdepartment of Atomic & Laser Physics at the University of Oxford. He is currently in the limbo that lies between the submission of a doctoral thesis and its examination, and is looking forward to taking up a postdoctoral research fellowship in the Theoretical Nanophysics group at the Ludwig Maximilian University, Munich, from January 2013.

In Part 1 of this post he discusses the foundations of the field of atomic, molecular, and optical physics, and describes the process of laser cooling, an experimental technique for cooling atoms to extremely low temperatures. This technique forms the foundation for many of the current experiments in the field.

In Part 2 of this post he describes the experiments carried out by Haroche and Wineland, and discusses the possible applications and future directions of their work.]

2012 Nobel Laureates in Physics Serge Haroche (left) and David J. Wineland (photo credit: CNRS, NIST).

The 2012 Nobel Prize in Physics: score one more for AMO physics

Those with their finger on the physics pulse will have seen that the 2012 Nobel Prize in Physics was recently awarded jointly to Serge Haroche and David J. Wineland for their development of "ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems". This announcement raises a number of questions for physicists and physics followers alike: what is meant by an ‘individual quantum system’, and why would anyone want to measure and manipulate such a thing? What kind of experiments do Haroche and Wineland do, and what new scientific and technological possibilities does their research unlock? And -- last but not least -- will Prof. Wineland be involved in the imminent month of Movember? Because if he is, everyone else might as well just go home right now.


Atomic, molecular, and optical physics: a brief history

The research of Haroche and Wineland falls within the field of atomic, molecular, and optical (AMO) physics, which studies how particles of matter (atoms, ions, and molecules) interact both with one another and with particles of light (photons: see figure), and how these interactions can be controlled and exploited to engineer systems of particular scientific or technological interest. AMO physics is currently a highly active and dynamic area of research, with applications which range from questions of fundamental scientific interest (e.g. is it possible that the fine structure constant is actually changing slowly with time?) through to real-world technologies (e.g. the development of ultra-precise atomic clocks for the definition of universal time and frequency standards). It has also enjoyed somewhat of a Golden Age in recent years, with the 2012 Nobel Prize in Physics being the third in the last 15 years (after 1997 and 2001) to be awarded for work in the field.

The physical theory that governs the world in the ultra-small regime of atoms, molecules, and photons is the theory of quantum mechanics, which describes both the behavior of these individual quantum systems and the way in which they interact. The roots of AMO physics can thus be traced back to the early part of the 20th century, when quantum mechanics was developed in the course of the search for a better understanding of such phenomena as the radiation emitted by hot objects and the internal structure of atoms.

A rough sketch of an atom (not actual size).    

The electrons orbiting the nucleus are only 

permitted to occupy a certain discrete set of 

energy levels.

Building on the theory of quantum mechanics, the state of atomic physics improved at a breathtaking pace throughout the first half of the 20th century. In contrast, research into the ‘optical’ part of AMO physics progressed at a more sedate pace. While much of the required theoretical knowledge already existed – the wave theory of light and the electronic structure of atoms both being well-understood by this point – rapid progress in any field requires interaction between theory and experiment, and the absence of any technology that could produce a focused, powerful, and wavelength-specific (i.e. single-colour) source of light severely restricted the sophistication of possible atom-light experiments.

This state of affairs changed drastically with the invention of the laser in the early 1960s. Developing out of radar and microwave research carried out during the Second World War at Bell Laboratories, lasers provided a light that was radically different from anything seen before: in addition to containing only a single pure wavelength, laser light is well collimated (i.e. forms a well-defined beam) and can easily be millions of times more intense than any other light source. At a stroke, the door was opened to a whole range of possible new atom-light experiments, ushering in a new era in the discipline of atomic, molecular and optical physics.

Laser light can be viewed as either a travelling electromagnetic wave (left) or a stream of photons (right).

Laser cooling: the beginning of the Golden Age

One particularly striking demonstration of the possibilities that laser light provides for controlling and manipulating atoms has been the development of laser cooling: using tightly-focused beams of laser light to slow down, or cool, a collection of atoms in a gas. Developed throughout the 1980s and recognized with the 1997 Nobel Prize in Physics, laser cooling is today ubiquitous in a wide range of AMO physics experiments, and forms the foundation for the fertile subfield of ultracold atoms.

But you thought lasers could only heat things up, or burn holes in them? Then read on. 

The atoms in a gas at room temperature move about very rapidly (their speed depends on the temperature of the gas, but in any case is of the order of several hundred metres per second). Now imagine that you’re an experimental physicist, and your goal is to manipulate and interact with these atoms in some kind of precise, controlled way -- for example, you might want to carry out some spectroscopy on them in order to measure the exact frequencies of light that this atomic species absorbs and emits. In this case, working with a ‘hot’ gas of rapidly-moving atoms is far from ideal -- in fact, it’s a complete disaster. Since the atoms are moving reasonably quickly, the radiation they absorb and emit is subject to a significant Doppler shift, making precise frequency measurements impossible. Further, the atoms collide both with one another and with the walls of their container, and these collisions lead to an additional ‘smearing out’ of the frequencies emitted or absorbed by each atom.

These problems could be largely nullified if only the atoms in the gas could be slowed down, or even brought to a complete stop. The great discovery of the 1980s and early 1990s was that this can be achieved by using laser light of a carefully-selected frequency to manipulate the atoms in the gas. Like many of the best achievements in science, the basic idea is both simple and elegant: a rapidly-moving atom is gradually slowed down by bouncing a stream of photons off it, one after another. Although each photon takes only a small amount of momentum away from the atom, the absorption and re-emission of a photon takes place in less than a microsecond, so that a single atom can scatter over a million photons every second. Consequently, an atom can be slowed down from a speed of several hundred metres per second (corresponding to room temperature) to a near-complete standstill in only a few thousandths of a second. These laser-cooled atoms -- which are at a far lower temperature than anything found in nature, even in the deepest depths of outer space -- can now be measured, probed, and further manipulated with an extremely high degree of accuracy.

The process of laser cooling: by arranging a set of lasers such that they remove momentum from the rapidly-moving atoms in a room-temperature gas, clouds of up to a few tens of millions of atoms can be cooled down to temperatures of less than a millionth of a degree above absolute zero .

[If you'd like to try out laser-cooling for yourself, the University of Colorado at Boulder has made a fantastic series of interactive Java applets that describe the process very well.]

Together with the invention of related techniques for trapping clouds of laser-cooled atoms using combinations of laser light and magnetic fields, the development of laser cooling stimulated a frenzy of new activity in atomic, molecular, and optical physics. Since the early 1990s, the level of experimental control in cold-atom experiments has progressed to the point where it is now routine to isolate, trap, and cool either individual atoms, or clouds of up to a few tens of millions of atoms, to temperatures of a few hundreds of nanoKelvin (billionths of a degree above absolute zero) in a controlled and repeatable fashion.  These new experimental capabilities have found applications in a diverse range of topics, which span all facets of atomic, molecular, and optical physics. Two such topics in which laser cooling plays an integral role – namely, the interaction of laser-cooled atoms with light trapped between two very small mirrors, and the interaction of light with laser-cooled ions trapped by rapidly-oscillating electric fields – are those in which the Nobel-winning research of Serge Haroche and David Wineland lies.

[Part 2, coming soon...]