Post-industrial global warming is not the Earth's first major climate change event. If we are to appreciate the significance and relevance to biology of current climate change, it is important to be aware of past climate events, at least the significant ones. This chapter summarises some of the major episodes between the Earth's formation and the beginning of the current, Quaternary, ice age. When reading this chapter you may also want to refer to Appendix 2.

Early biology and climate of the Hadean and Archaean eons (4.6–2.5 bya)

The Pre-Biotic Earth (4.6–3.8 bya)

The Earth and the Solar System formed some 4.6 billion years ago (bya), give or take a few hundred million years. The Earth formed with the Solar System (containing ‘Sol’, our sun) accreting out of a dust and gas cloud. The dust, ice (composed of not just water but various volatile compounds) and rocks were not all small and particulate but themselves had accreted into small and large asteroid-sized bodies that ranged in size up to, and including, small planets. One of these, a Mars-sized planetoid (Thea) is thought to have had a glancing blow with the proto-Earth, exchanged material, and formed the Moon (Luna) 4.5 bya. This is not irrelevant to the nature of the Earth's climate. The lunar/Earth ratio of mass of 1:81.3 is much greater than any satellite/planet mass ratio for any other planet in the Solar System. Taking the Copernican principle, that there is nothing cosmologically special about the Earth as a life-bearing planet, this begs the question as to whether our large moon is a necessary factor facilitating a biosphere, or at least a biosphere with longevity. There is a suggestion that the Earth–lunar system is one that confers some axial stability to the Earth (affecting the variation in its angle of tilt), and hence climate stability, so enabling complex ecosystems to form. Indeed, in Chapter 1 we discussed axial tilt as a dimension of Milankovitch forcing of climate, but planets without large moons are prone to larger axial tilting and this means that good portions of such worlds spend half the year in sunlight and half the year in darkness. On Earth this only takes place within the polar circles, which form a minor proportion of the planet.

Recent climate change

The Latter Half of the Little Ice Age

The 17th century was not just the time of the Little Ice Age, it is also noted (and for some better noted) for the Renaissance, which saw the gathering of scientific understanding that in turn was to drive the Industrial Revolution of the 18th and 19th centuries. In Britain in the 1640s and 1650s scientists sought what they termed ‘a great insaturation’, which drew on the philosophies exposed by the likes of Francis Bacon. Among these, Bacon's principles of exact observation, measurement and inductive reasoning provided the intellectual tools for scientific advance. These advances had yet to percolate through to day-to-day application in technology, so life, society and its economy were still largely powered by humans and animals together with the burning of wood. Major global impacts from human activity were not yet manifest (although, of course, trace global signatures such as metals in Greenland ice cores can be found dating to thousands of years earlier).

In terms of climate and weather, 1659 – within the Little Ice Age – is an important date. Before that date we rely solely on the proxy indicators (see Chapter 2) for climatic information. After 1659 there began a source of new information: direct meteorological measurement. The first significant series of measurements began in 1659 and (much later) were compiled into a monthly series of temperature readings for rural sites in central England by Gordon Manley (1974). This is the longest homogeneous record and is still kept up to date by the UK Meteorological Office. The earlier measurements were varied but increasingly included, and were soon dominated by, instrumental measurements. The Central England Temperature (CET) records were soon accompanied by others to ultimately be built into a series such as those for De Bilt in The Netherlands from 1705. Such records are fundamentally important. As we have seen, although we can use a variety of proxies to build up, piece by piece, quite a good picture of past climate, deep-time climatic proxy indicators simply are either not sensitive or representative enough to tell us what was going on. This is especially true with regard to finer changes. For example, ice-core isotopic records are very fine for charting regional glacial and interglacial transitions of a few degrees but are less useful for discerning trends in changes of fractions of a degree within our current interglacial.

We are currently in the middle of an ice age! This ice age is known as the Quaternary ice age, and it began roughly 2 million years ago (mya) (I say ‘roughly’ because how much ice do you need on the planet to say that it is an ice age?). We might not think we are in an ice age and this is because we are in a warm part, called an interglacial. As we shall see, there have been a number of glacials and interglacials in our Quaternary ice age. However, this ice age did not just start by itself but arose out of a number of factors that became relevant earlier, in the Oligocene (34–23 mya) and Miocene (23–5.3 mya) epochs, well before the beginning of our ice age and the Pliocene and Pleistocene glaciations (Zachos et al., 2001). These glaciations actually had their beginnings some 5.3 mya. To understand how our Quaternary ice age came about we will need to briefly re-cap part of the previous chapter and note some other material to provide a more biological perspective while leaving out the extinction events.

The Oligocene (33.9–23.03 mya)

Between 35 and 15 mya the Earth's temperature was roughly 3–4°C warmer than today and atmospheric carbon dioxide concentrations were twice as high. However, climate forcing factors were coming into play that were to cool the planet. Carbon dioxide levels were falling and, as noted in the previous chapter, this fall could only have been furthered by the new C4 plants (even though their period of major expansion was not to take place until 8 mya: see below).

In most places on this planet's terrestrial surface there are the signs of life. Even in places where there is not much life today, there are frequently signs of past life, be it fossils, coal or chalk. Further, it is almost a rule of thumb that if you do discover signs of past life, either tens of thousands or millions of years ago, then such signs will most likely point to different species than those found there today. Why? There are a number of answers, not least of which is evolution. Yet a key feature of why broad types of species (be they broad-leaved tree species as opposed to ones with narrow, needle-type leaves) live in one place and not another has to do with climate. Climate has a fundamental influence on biology. Consequently, a key factor (among others) as to why different species existed in a particular place 5000, 50000, 500000 or even 5000000 years ago (to take some arbitrary snapshots in time) is because different climatic regimens existed at that place at those times.

It is also possible to turn this truism on its head and use biology to understand the climate. Biological remains are an aspect of past climates (which we will come to in Chapter 2). Furthermore, biology can influence climate: for example, an expanse of rainforest transpires such a quantity of water, and influences the flow of water through a catchment area, that it can modify the climate from what it otherwise would have been in the absence of living species. Climate and biology are interrelated.

The foundations of the quantum theory of radiation were laid by the work of Planck, Einstein, Dirac, Bose, Wigner, and many others. Historically Planck's [1] work on black body radiation is the foundation of any work on the quantum theory of radiation. Einstein's [2] work on the photoelectric effect established the particle nature of the radiation field. These particles were named as photons by Lewis [3]. Einstein [4] also introduced the A and B coefficients to describe the interaction of radiation and matter. He characterized stimulated emission using the B coefficient. Using thermodynamic arguments, he could also extract the A coefficient describing spontaneous emission which is at the heart of the origin of all spectral lines. This was quite a remarkable achievement. Dirac [5] implemented the quantization of the electromagnetic field and showed how Einstein's A coefficient emerges naturally from the quantization of the radiation field. It should be remembered that stimulated emission is the key to the working of any laser system. Following Dirac's quantization of the radiation field, Weisskopf and Wigner [6] were able explain in a very fundamental way the decay of the excited states of a system and hence derive the remarkable law of exponential decay. Bose [7] discovered a quantitative explanation for Planck's law. He introduced a new way of counting statistics relevant to quantum particles with zero mass. This was the beginning of quantum statistics. Bose's work was followed by Einstein [8] who produced a counting statistics for particles with finite mass (now known as Bosons).

In Chapter 13 we saw how the optical properties of a two-level system can be modified by the application of an additional strong coherent field. For example, the absorption of light by a two-level system depends on the strength and frequency of the driving field. Figure 13.5 showed that in certain frequency regions we can amplify a probe beam. We assumed in Chapter 13 that the coherent light beam was acting on the same optical transition as the weak probe beam. However, the atomic/molecular systems have many energy levels and we can take advantage of this to produce a variety of ways of controlling the optical properties. This would offer much more flexibility as different optical transitions would have different frequencies and hence one could use a variety of sources. In this chapter we present results for the optical properties of a multilevel system. We show that coherent control can make an opaque medium transparent. We also show that the dispersive properties, which are important for the linear and nonlinear propagation of light, can be manipulated by light fields [1–3].

Having discussed in the previous chapters many different aspects of single photons and nonclassical light, we are now ready to discuss interferometry with single photons. We first discuss traditional interferometers and their performance if classical light beams are replaced by quantum fields.

The earliest interferometer is the Young's double slit interferometer. Young's work on interference confirmed the wave nature of light and was a turning point in optics. A complete description of Young's double slit is more complicated as it involves the propagation of wavefronts through the slits and hence we will take it up in Chapter 8. Michelson designed an interferometer which he very successfully used in measurements of spectral lines and the diameter of stars. However, in this chapter we focus on the Mach–Zehnder and Sagnac interferometers which are currently used extensively. We note that all interferometers use the interference between light beams arising from at least two paths. In what follows we assume that the beams arising from the two paths are coherent with respect to each other. This would be the case if the path difference was short compared to the coherence length of the light sources at the input ports of the interferometer. In Chapter 8, we will consider more general cases, which will allow us to relax this assumption somewhat.

All optical interferometers use optical devices such as beam splitters, mirrors, and phase shifters. The action of all such optical devices is very well understood for classical beams of light.

In this chapter we discuss a variety of physical effects which primarily depend on the dispersive properties of the medium, i.e. how the real part of the refractive index depends on the frequency of light. For example, it is well known that the efficiency of nonlinear optical processes such as harmonic generation depends on the phase matching, which in turn depends on the refractive index at the fundamental and harmonic frequencies [1]. Thus a control of dispersion will enable us to obtain more efficient harmonic generation [2–5]. This in fact was the starting point of the work on control of dispersion [2]. Another subject where the dispersion is very important is in the propagation of the pulses which generally are distorted [6] by the dispersion of the medium and hence one needs to tailor the dispersion to obtain nearly distortionless propagation [7]. In Section 17.1, we have already shown how an appropriately chosen control field leads to a significant modification of the dispersion (Figure 17.4). We will now discuss some applications of this. We will also discuss how hole burning physics (Section 13.2) can be used to obtain very significant control of the dispersion.

Group velocity and propagation in a dispersive medium

Let us consider the one-dimensional propagation of an electromagnetic pulse in a dispersive medium characterized by susceptibility χ(ω) and refractive index n(ω).

The development of new sources of radiation that produce nonclassical and entangled light has changed the landscape of quantum optics. The production, characterization, and detection of single photons is important not only in understanding fundamental issues but also in the transfer of quantum information. Entangled light and matter sources as well as ones possessing squeezing are used for precision interferometry and for implementing quantum communication protocols. Furthermore, quantum optics is making inroads in a number of interdisciplinary areas, such as quantum information science and nano systems.

These new developments require a book which covers both the basic principles and the many emerging applications. We therefore emphasize fundamental concepts and illustrate many of the ideas with typical applications. We make every possible attempt to indicate the experimental work if an idea has already been tested. Other applications are left as exercises which contain enough guidance so that the reader can easily work them out. Important references are given, although the bibliography is hardly complete. Thus students and postdocs can use the material in the book to do independent research. We have presented the material in a self-contained manner. The book can be used for a two-semester course in quantum optics after the students have covered quantum mechanics and classical electrodynamics at a level taught in the first year of graduate courses. Some advanced topics in the book, such as exact non-Markovian dynamics of open systems, quantum walks, and nano-mechanical mirrors, can be used for seminars in quantum optics.