Properties of Macroscopic Atomic Systems

Carlos L. Garrido Alzar, Luciano Soares da Cruz, J. G. Aguirre Gómez +7 more

We present a series of experiments measuring intensity fluctuations and correlations of laser beams after propagation through an atomic vapour at room temperature in situations where coherent effects play a major role. In particular, we investigate these properties in the condition of electromagnetically induced transparency (EIT) in three-level lambda systems and in degenerate two-level systems. In a similar way, we also study the Hanle-EIT effect and electromagnetically induced absorption (EIA) in degenerate two-level systems. These results show the great influence of coherent interaction with the atomic system over the noise properties of the macroscopic laser fields, and indicate new sensitive ways of probing an atomic sample.

John Cardy

Take a large piece of material and measure some of its macroscopic properties, for example its density, compressibility or magnetisation. Now divide it into two roughly equal halves, keeping the external variables like pressure and temperature the same. The macroscopic properties of each piece will then be the same as those of the whole. The same holds true if the process is repeated. But eventually, after many iterations, something different must happen, because we know that matter is made up of atoms and molecules whose individual properties are quite different from those of the matter which they constitute. The length scale at which the overall properties of the pieces begin to differ markedly from those of the original gives a measure of what is termed the correlation length of the material. It is the distance over which the fluctuations of the microscopic degrees of freedom (the positions of the atoms and suchlike) are significantly correlated with each other. The fluctuations in two parts of the material much further apart than the correlation length are effectively disconnected from each other. Therefore it makes no appreciable difference to the macroscopic properties if the connection is completely severed. Usually the correlation length is of the order of a few inter-atomic spacings. This means that we may consider really quite small collections of atoms to get a very good idea of the macroscopic behaviour of the material.

N. G. van Kampen

David Peak

Bare essentials of statistical mechanics Atoms are examples of many-particle systems, but atoms are extraordinarily simpler than macroscopic systems consisting of 1020-1030 atoms. Despite their great size, many properties of macroscopic systems depend intimately on the microscopic behavior of their microscopic constituents. The proper quantum mechanical description of an N -particle system is a wavefunction that depends on 3N coordinates (3 ways of moving, in general, for every particle) and 4N quantum numbers (3 motional quantum numbers and 1 spin quantum number for every particle). (If the “particles” are molecules there might be additional quantum numbers describing rotations and internal vibrations.) The latter is referred to as a microstate. In a macroscopic solid or liquid there are about 1023 atoms per cm3; in a gas there are about 1020. Thus, the amount of information required to specify the wavefunction for such a system is scandalously large. A fundamental theory of macroscopic systems cannot be based on all of the microscopic details. Instead, a new way of thinking is required. This is known as statistical mechanics.