As was demonstrated in the previous chapter, the process of observation and acquisition of information or at least the possibility of ‘knowing’ (whether or not we bother to ‘look’) can profoundly change the outcome of an experiment. For example, in the case of the micromaser which-path detector, we do not need to ‘look at’ or ‘interrogate’ the masers in order to lose the interference cross term; it is enough that we could have known. Experiments along these lines provide a dramatic example of the importance of which-path, or ‘Welcher-Weg’, information.

The present chapter treats the Welcher-Weg quantum eraser problem from a different vantage. We first consider the interference of light as it is scattered from simple atomic systems consisting of single atoms located at two neighboring sites. From this simple model, we can gain a wealth of insight into such problems as complementarity, delayed choice, and the quantum eraser via field–field and photon–photon correlation functions, i.e., via G(1)(r, t) and G(2)(r,r′t, t′). The chapter concludes with a demonstration that such considerations can, in principle, even lead to new kinds of high-resolution spectroscopy.

Quantum mechanics is an immensely successful theory, occupying a unique position in the history of science. It has solved mysteries ranging from macroscopic superconductivity to the microscopic theory of elementary particles and has provided deep insights into the nature of vacuum on the one hand and the description of the nucleon on the other. Whole new fields such as quantum optics and quantum electronics owe their very existence to this body of knowledge.

However, despite the stunning successes of quantum mechanics, there is no general agreement on the conceptual foundations and interpretation of the subject. The theory provides unambiguous information about the outcome of a measurement of a physical object. However, many feel that it does not provide a satisfactory answer to the nature of the “reality” we should attribute to the physical objects between the acts of measurement.

The conceptual difficulty comes about because the wave function |ψ〉 is usually given by a coherent superposition of various distinguishable experimental outcomes. If we denote the collection of states that represent the possible outcomes of an experiment by |ψj〉, then |ψ〉 = ∑jcj|ψj〉 where cj = 〈ψj|ψ〉. The probability of the outcome |ψj〉 is Pj=|cj|2. In the process of measurement, the so called collapse of the wave function takes place and a single, definite state |ψi〉 of the physical object is chosen. The difficulty comes about in the interpretation of the mechanism by which this definite state is chosen from amongst all the possible outcomes.

The development of a single-atom maser or a micromaser allows a detailed study of the atom–field interaction. The situation realized is very close to the ideal case of a single two-level atom interacting with a single-mode quantized field as treated in Section 6.2. In a micromaser a stream of two-level atoms is injected into a superconducting cavity with a high quality factor. The injection rate can be such that only one atom is present inside the resonator at any time. Due to the high quality factor of the cavity, the radiation decay time is much larger than the characteristic time of the atom–field interaction, which is given by the inverse of the single-photon Rabi frequency. Therefore, a field is built up inside the cavity when the mean time between the atoms injected into the cavity is shorter than the cavity decay time. A micromaser, therefore, allows sustained oscillations with less than one atom on the average in the cavity.

The realization of a single-atom maser or a micromaser has been made possible due to the enormous progress in the construction of superconducting cavities together with the laser preparation of highly excited atoms called Rydberg atoms. The quality factor of the superconducting cavities is high enough for periodic energy exchanges between atom and cavity field to be observed. The interesting properties of the Rydberg atoms make them ideal for micromasers. In Rydberg atoms the probability of induced transitions between adjacent states becomes very large and scales as n4, where n denotes the principle quantum number.

As we have seen in the previous chapters, there are quantum fluctuations associated with the states corresponding to classically welldefined electromagnetic fields. The general description of fluctuation phenomena requires the density operator. However, it is possible to give an alternative but equivalent description in terms of distribution functions. In the present chapter, we extend our treatment of quantum statistical phenomena by developing the theory of quasi-classical distributions. This is of interest for several reasons.

First of all, the extension of the quantum theory of radiation to involve nonquantum stochastic effects such as thermal fluctuations is needed. This is an important ingredient in the theory of partial coherence. Furthermore, the interface between classical and quantum physics is elucidated by the use of such distributions. The arch type example being the Wigner distribution.

In this chapter, we introduce various distribution functions. These include the coherent state representation or the Glauber–Sudarshan Prepresentation. The P-representation is used to evaluate the normally ordered correlation functions of the field operators. As we shall see in the next chapter, the P-representation forms a correspondence between the quantum and the classical coherence theory. This distribution function does not have all of the properties of the classical distribution functions for certain states of the field, e.g., it can be negative. We also discuss the so-called Q-representation associated with the antinormally ordered correlation functions. Other distribution functions and their properties are also presented.