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Physical Review A

Optical coherence: A convenient fiction

Klaus Mølmer

Published Apr 1, 1997• 223 citations
Publisher

Abstract

We conjecture that optical coherences, i.e., quantum-mechanical coherences between states separated by Bohr frequencies in the optical regime, do not exist in optics experiments. We claim the exact vanishing of optical field amplitudes and atomic dipole expectation values, and we discuss the seemingly contradictory success of assigning finite values to such quantities in theoretical calculations. We show that our conjecture is not at variance with the observed interference between different light sources. The connection to the concept of spontaneous symmetry breaking and the identification of entangled states as pointer basis states is discussed.

DOI
10.1103/physreva.55.3195

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We conjecture that optical coherences, i.e., quantum-mechanical coherences between states separated by Bohr frequencies in the optical regime, do not exist in optics experiments. We claim the exact vanishing of optical field amplitudes and atomic dipole expectation values, and we discuss the seemingly contradictory success of assigning finite values to such quantities in theoretical calculations. We show that our conjecture is not at variance with the observed interference between different light sources. The connection to the concept of spontaneous symmetry breaking and the identification of entangled states as pointer basis states is discussed.
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].
When any two optical fields are superposed, a fringe pattern will be formed if the observation interval is short enough (within the coherent time) and a phase value may be extracted from the fringe and assigned as the phase difference between the fields. When measured against a common reference field, phase can be defined for an optical field. However, when the intensities of the optical fields are low or the observation time is so short that only a few photons are detected, the fringe pattern is unrecognizable due to the particle nature of light. By analyzing the fringe patterns simulated by a quantum Monte Carlo method, we find that there exist uncertainties in determining the phase value. This uncertainty is universal for any optical field with a finite photon number and decreases to zero as the photon number of the field increases to infinity or the classical limit is approached. The existence of this uncertainty in determining the phase value makes it problematic to define a quantum mechanical phase. An interference experiment with coherent state is performed to confirm the theoretical predictions. The implication of the above is that phase is a classical quantity that is associated with a large number of particles and may not have a quantum mechanical analogy.
The pure quantum correlations totally independent of the classical coherence of light have been experimentally demonstrated. By measuring the visibility of the interference fringes and the correlation variances of amplitude and phase quadratures between a pair of bright twin optical beams with different frequencies produced from a non-degenerate optical parametric oscillator, we found that when classical interference became worse even vanished, the quadrature quantum correlations were not influenced, completely. The presented experiment obviously shows the quantum correlations of light do not necessarily imply the classical coherence.
The concept of coherence which has conventionally been used in optics is found to be inadequate to the needs of recently opened areas of experiment. To provide a fuller discussion of coherence, a succession of correlation functions for the complex field strengths is defined. The nthn\mathrm{th}nth order function expresses the correlation of values of the fields at 2n2n2n different points of space and time. Certain values of these functions are measurable by means of nnn-fold delayed coincidence detection of photons. A fully coherent field is defined as one whose correlation functions satisfy an infinite succession of stated conditions. Various orders of incomplete coherence are distinguished, according to the number of coherence conditions actually satisfied. It is noted that the fields historically described as coherent in optics have only first-order coherence. On the other hand, the existence, in principle, of fields coherent to all orders is shown both in quantum theory and classical theory. The methods used in these discussions apply to fields of arbitrary time dependence. It is shown, as a result, that coherence does not require monochromaticity. Coherent fields can be generated with arbitrary spectra.
The concept of coherence which has conventionally been used in optics is found to be inadequate to the needs of recently opened areas of experiment. To provide a fuller discussion of coherence, a succession of correlation functions for the complex field strengths is defined. The nthn\mathrm{th}nth order function expresses the correlation of values of the fields at 2n2n2n different points of space and time. Certain values of these functions are measurable by means of nnn-fold delayed coincidence detection of photons. A fully coherent field is defined as one whose correlation functions satisfy an infinite succession of stated conditions. Various orders of incomplete coherence are distinguished, according to the number of coherence conditions actually satisfied. It is noted that the fields historically described as coherent in optics have only first-order coherence. On the other hand, the existence, in principle, of fields coherent to all orders is shown both in quantum theory and classical theory. The methods used in these discussions apply to fields of arbitrary time dependence. It is shown, as a result, that coherence does not require monochromaticity. Coherent fields can be generated with arbitrary spectra.