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Photon statistics

A. M. Fox

Published Apr 27, 2006• 1 citation
Publisher

Abstract

Abstract The task of quantum optics is to study the consequences of considering a beam of light as a stream of photons rather than as a classical wave. It turns out that the differences are rather subtle, and we have to look quite hard to see significant departures from the predictions of the classical theories. In this chapter we shall approach the subject from the perspective of the statistical properties of the photon stream. We shall study the three different types of photon statistics that can occur, namely: Poissonian, super-Poissonian, and sub-Poissonian.

DOI
10.1093/oso/9780198566724.003.0005

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Abstract The task of quantum optics is to study the consequences of considering a beam of light as a stream of photons rather than as a classical wave. It turns out that the differences are rather subtle, and we have to look quite hard to see significant departures from the predictions of the classical theories. In this chapter we shall approach the subject from the perspective of the statistical properties of the photon stream. We shall study the three different types of photon statistics that can occur, namely: Poissonian, super-Poissonian, and sub-Poissonian.
The previous chapter surveyed part of the rich variety of physical phenomena that can be understood using the ideas of quantum physics. Now that we are beginning the task of looking more deeply into the subject we shall find it useful to concentrate on examples that are comparatively simple to understand but which still illustrate the fundamental principles and highlight the basic conceptual problems. Some years ago most writers discussing such topics would probably have turned to the example of a ‘particle’ passing through a two-slit apparatus (as in Figure 1.2), whose wave properties are revealed in the interference pattern. Much of the discussion would have been in terms of wave–particle duality and the problems involved in position and momentum measurements, as in the discussion of the uncertainty principle in the last chapter. However, there are essentially an infinite number of places where the particle can be and an infinite number of possible values of its momentum, and this complicates the discussion considerably. We can illustrate all the points of principle we want to discuss by considering situations where a measurement has only a small number of possible outcomes. One such quantity relating to the physics of light beams and photons is known as polarisation . In the next section we discuss it in the context of the classical wave theory of light, and the rest of the chapter extends the concept to situations where the photon nature of light is important.
It is pointed out that, although squeezing and sub-Poissonian photon statistics need not go together, in the sense that an electromagnetic field may exhibit one but not the other, the method that is normally used to detect a squeezed state automatically generates sub-Poissonian photon statistics. However, when these considerations are applied to the fluorescence from a coherently driven atom, which exhibits both squeezing and sub-Poisson fluctuations, one finds that the statistics of the emitted photons show even larger departures from classical field theory than the squeezing.
The previous chapter surveyed part of the rich variety of physical phenomena that can be understood using the ideas of quantum physics. Now that we are beginning the task of looking more deeply into the subject we shall find it useful to concentrate on examples that are comparatively simple to understand but which still illustrate the fundamental principles and highlight the basic conceptual problems. Some years ago most writers discussing such topics would probably have turned to the example of a ‘particle’ passing through a two-slit apparatus (as in Figure 1.2), whose wave properties are revealed in the interference pattern. Much of the discussion would have been in terms of wave–particle duality and the problems involved in position and momentum measurements, as in the discussion of the uncertainty principle in the last chapter. However, there are essentially an infinite number of places where the particle can be and an infinite number of possible values of its momentum, and this complicates the discussion considerably. We can illustrate all the points of principle we want to discuss by considering situations where a measurement has only a small number of possible outcomes. One such quantity relating to the physics of light beams and photons is known as polarisation . In the next section we discuss it in the context of the classical wave theory of light, and the rest of the chapter extends the concept to situations where the photon nature of light is important.
Statistical and quantum optics provides a clear, up-to-date and comprehensive introduction to the recent field of modern optics dealing with coherence and fluctuations of light. The first two chapters discuss the statistical frame work needed for later part of the book followed by systematic account of coherence theory with a detailed discussed on photon statistics. Description of quantum theory of coherence is preceded by a introductory chapter on field quantization. A detailed description of non-classical light highlighted by phenomena of anti-bunching, Sub-Poissonian statistics, production and detection of squeezed light and coherent state follows. Next is the discussion on E-P-R paradox on reality, locality and completeness of quantum mechanics bringing out clearly the importance of Bell's inequalities. The concluding two chapters put forward forcefully the new fundamental concepts based on quantum superposition and entanglement leading to two photon interference, quantum cryptography and teleportation.