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Applied Optics

Coherence–a Sticky Subject

Marlan O. Scully, Stephen F. Jacobs

Published Nov 1, 1970• 7 citations
Publisher

Abstract

The concept of coherence has been applied in the quantum theory of radiation and matter as well as in classical optics. We review here the meaning of the term in each case and show how these apparently different uses of the word coherence can be understood in terms of a single concept involving interference (nonzero cross terms), minimum uncertainty, and cohering (uniform variance) of the wave packet that describes the system. Self-induced transparency, superradiance, and superconductivity are discussed as dramatic examples of coherence.

DOI
10.1364/ao.9.002414

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The concept of coherence has been applied in the quantum theory of radiation and matter as well as in classical optics. We review here the meaning of the term in each case and show how these apparently different uses of the word coherence can be understood in terms of a single concept involving interference (nonzero cross terms), minimum uncertainty, and cohering (uniform variance) of the wave packet that describes the system. Self-induced transparency, superradiance, and superconductivity are discussed as dramatic examples of coherence.
Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.
Optical interference is regarded as a classical phenomenon and is usually completely described in classical terms, in which optical fields are represented by classical waves. Does it mean that optical interference, which is fundamentally ascribable to the phenomenon of a superposition of wave amplitudes, cannot be applied to test quantum phenomena? The superposition principle is at the heart of quantum physics and one could expect that it should distinguish the quantum nature of light from thewave nature. Our experience based on extensive theoretical analysis and experimental observations shows that classical and quantum theories of optical interference readily explain the presence of an interference pattern resulting from the first-order coherence. However, there are interference effects involving the higher order (second-order) coherence that distinguish the quantum (photon) nature of light from the wave nature. Quantum interference has recently returned to prominence because of its utility in manipulating spontaneous emission and other radiative properties of atomic systems. In this chapter, we present elementary concepts and definitions of both the classical and quantum theory of optical interference and discuss similarities and differences between these two approaches [80].
The formalism of collective (Dicke-like) states and operators is used to describe the relaxation of the initially prepared state of a material in the presence of a laser field. The material states are shown to be expressible as minimum uncertainty wave packets formed from those special collective states that couple with the radiation field. It is shown that these coherent states of matter exhibit all the features that are usually attributed to ensemble averages of two-level molecules in a conventional statistical picture. However, there are new features in the quantum mechanical model when there are correlations among the molecules in the ensemble. The loss of minimum uncertainty characteristics of the wave packet correspnds to the transverse (T2) relaxation of the statistical model. Different types of T2 processes can be defined corresponding to the decay of different orders of coherence of the wave packet. Only for the case that the system decays in all orders of coherence do the quantum and statistical results coincide. There is expected to be a transverse relaxation that preserves one or more orders of coherence. Experiments are suggested that can test these ideas. A particular case of the formalism of collective states applies to molecular crystals and it provides a quantum mechanical picture of the dephasing of molecular excitons in terms of orders of coherence analogous to the usual manner of describing states of the radiation field.
There are many striking phenomena which are attributed to ‘quantum coherence’. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical applications. A useful starting point for such discussions is a definition of ‘quantum coherence’. In this article I give a definition of quantum coherence and use a number of illustrations to explore the implications of this definition. I point to topics of current interest in the fields of cosmology and quantum computation where questions of quantum coherence arise, and I emphasize the impact that interactions with the environment can have on quantum coherence.