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European Journal of Physics

A new interpretation of the quantum theory of light

Alan V. Durrant

Published Apr 1, 1980• 6 citations
Publisher

Abstract

An approach to the quantum theory of light is described using absorber theory and source field theory. It is assumed that all optical fields have atomic sources, and that the so-called free field is a source field of the surrounding absorbing material of the universe. The field operators are defined to be functions of the atomic operators and act on the states of the atomic sources. The source field of a completely enclosing perfect absorber is found to be mathematically equivalent to the quantised free field of conventional theory, but the physical basis of the theory is different.

DOI
10.1088/0143-0807/1/2/008

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An approach to the quantum theory of light is described using absorber theory and source field theory. It is assumed that all optical fields have atomic sources, and that the so-called free field is a source field of the surrounding absorbing material of the universe. The field operators are defined to be functions of the atomic operators and act on the states of the atomic sources. The source field of a completely enclosing perfect absorber is found to be mathematically equivalent to the quantised free field of conventional theory, but the physical basis of the theory is different.
Abstract A quantum absorber theory of optical field quantization is developed, in which only matter is quantized by postulate. The amplitudes of the optical field in an absorbing universe are expressed, by using Maxwell’s source equations, in terms of the atomic source operators of the surrounding absorber atoms treated as a single quantum system. Stationary twolevel absorbing atoms are assumed and only electric dipole fields are considered. The resulting optical field is found to be quantized with a mathematical description identical to that of the conventionally quantized optical field, but the physical interpretation is different.
This paper discusses the nature of the boundary condition applying to the direct-action theory of fields, also known as the 'absorber' theory, first developed in a classical version by Wheeler and Feynman. The traditional understanding of these authors and others who followed is that the direct-action theory requires that 'all emitted radiation be absorbed,' or that 'the universe is a perfect (or complete) of absorber of radiation,' implying the need for a specific sort of cosmological boundary condition that may or may not obtain in our universe. It is pointed out that this interpretation requires critical scrutiny even at the classical level, and in any case does not apply to the fully quantum form of the direct-action theory (QDAT), which involves discrete energy transfers by way of photons. In the latter case, the absorption boundary condition describes a specific interactive relationship between emitters and absorbers that is independent of cosmological boundary conditions. Thus, the quantum direct-action theory does not require any special cosmological boundary condition in order for it describe the physical world.
Abstract The new quantum theory, based on the assumption that the dynamical variables do not obey the commutative law of multiplication, has by now been developed sufficiently to form a fairly complete theory of dynamics. One can treat mathematically the problem of any dynamical system composed of a number of particles with instantaneous forces acting between them, provided it is describable by a Hamiltonian function, and one can interpret the mathematics physically by a quite definite general method. On the other hand, hardly anything has been done up to the present on quantum electrodynamics. The questions of the correct treatment of a system in which the forces are propagated with the velocity of light instead of instantaneously, of the production of an electromagnetic field by a moving electron, and of the reaction of this field on the electron have not yet been touched. In addition, there is a serious difficulty in making the theory satisfy all the requirements of the restricted principle of relativity, since a Hamiltonian function can no longer be used. This relativity question is, of course, connected with the previous ones, and it will be impossible to answer any one question completely without at the same time answering them all. However, it appears to be possible to build up a fairly satisfactory theory of the emission of radiation and of the reaction of the radiation field on the emitting system on the basis of a kinematics and dynamics which are not strictly relativistic. This is the main object of the present paper. The theory is noil-relativistic only on account of the time being counted throughout as a c-number, instead of being treated symmetrically with the space co-ordinates. The relativity variation of mass with velocity is taken into account without difficulty. The underlying ideas of the theory are very simple. Consider an atom interacting with a field of radiation, which we may suppose for definiteness to be confined in an enclosure so as to have only a discrete set of degrees of freedom. Resolving the radiation into its Fourier components, we can consider the energy and phase of each of the components to be dynamical variables describing the radiation field. Thus if Er is the energy of a component labelled r and θr is the corresponding phase (defined as the time since the wave was in a standard phase), we can suppose each Er and θr to form a pair of canonically conjugate variables. In the absence of any interaction between the field and the atom, the whole system of field plus atom will be describable by the Hamiltonian H ═ ΣrEr + Ho equal to the total energy, Ho being the Hamiltonian for the atom alone, since the variables Er, θr obviously satisfy their canonical equations of motion Er ═ — ∂H/∂θr ═ 0, θr ═ ∂H/∂Er ═ 1.
In the classical theory, an electromagnetic field obeying Maxwell's equations cannot be absorbed quickly by matter, so that it remains a zero point field. Splitting the total, genuine electromagnetic field into the sum of a conventional field and a zero point field is physically meaningless until a receiver attenuates the genuine field down to the zero point field, or studying the amplification of the zero point field by a source. In classical optics all optical effects must be written using the genuine field, so that at low light levels the nonlinear effects become linear in relation to the conventional field. The result of the interpretation of all observations, even at low light levels, is exactly the same in quantum electrodynamics and in the semi- classical theory. The zero point field is stochastic only far from the sources and the receivers; elsewhere, it is shaped by matter, it may be studied through fields visible before an absorption or after an amplification. A classical study of the reduction of the wave packet extends the domain of equivalence of the classical and quantum zero point field; using both interpretations of this field makes the results more reliable, because the traps are different.
We propose and analyze a scheme for controlling coherent photon transmission and reflection in a cavity-quantum-electrodynamics (CQED) system consisting of an optical resonator coupled with three-level atoms coherently prepared by a control laser from free space. When the control laser is off and the cavity is excited by two identical light fields from two ends of the cavity, the two input light fields can be completely absorbed by the CQED system and the light energy is converted into the excitation of the polariton states, but no light can escape from the cavity. Two distinct cases of controlling the perfect photon absorption are analyzed: (a) when the control laser is tuned to the atomic resonance and creates electromagnetically induced transparency, the perfect photon absorption is suppressed and the input light fields are nearly completely transmitted through the cavity; (b) when the control laser is tuned to the polariton state resonance and inhibits the polariton state excitation, the perfect photon absorption is again suppressed and the input light fields are nearly completely reflected from the cavity. Thus, the CQED system can act as a perfect absorber or near-perfect transmitter and/or reflector by simply turning the control laser off or on. Such interference control of the coherent photon-atom interaction in the CQED system should be useful for a variety of applications in optical logical devices.