L. Mandel

Absorption and Emission of Evanescent Photons

Experiments have been carried out to investigate the excitation of molecules by evanescent light, and the emission of evanescent light in the fluorescence of excited molecules. It is confirmed that the absorption proceeds at a rate proportional to the second-order (normally ordered) product of the complex field amplitude, whether the light field is homogeneous or evanescent, and that the emission process follows a reciprocity principle.

Squeezing and photon antibunching in harmonic generation

Abstract With the help of the perturbative expansion used by Kozierowski and Tanas (1977) it is shown that in the process of harmonic generation in a non-linear crystal the fundamental mode becomes squeezed. When the squeezing is detected in the usual way by interference with a coherent field, the resulting field shows photon statistics that are narrower than poissonian by the same amount as the photons of the fundamental mode.

Measurement of the Pancharatnam phase for a light beam

By using a Michelson interferometer arrangement, we have measured the phase shift (the Pancharatnam phase) experienced by a light beam whose state of polarization is made to follow, by successive unitary transformations, a closed circuit on the Poincare sphere. We confirm that the phase shift equals half of the solid angle subtended by the closed circuit at the center of the sphere. This phase is closely related to the topological Berry phase.

Relation between input and output states for a beam splitter

Abstract The state of the optical field at the output of a beam splitter is expressed directly in terms of the state at the input via the diagonal coherent state representation. The conclusion is illustrated for a two-photon Fock state, and it is shown that an output having some features of the two-photon singlet state can be produced.

Phase-Shift Measurement of Evanescent Electromagnetic Waves*

Phase shifts suffered by evanescent electromagnetic waves traversing an air gap between two glass prisms have been measured. Because the evanescent waves propagate parallel to the glass-to-air interface, they should be able to penetrate in a direction normal to the interface, without change of phase, although the amplitude is expected to decrease with depth of penetration. This has been confirmed by the experiment, which showed that the phase shifts are substantially independent of the width of the air gap.

Coherence properties of the linear photon amplifier

Abstract The behavior of an amplifier consisting of N two-level atoms interacting with an incident optical field through first-order processes is considered. The statistics of the photons emerging at the output are related to the corresponding photon statistics at the input, and certain cross-correlation functions are evaluated. It is shown that if the input to the amplifier is in a squeezed state, then the output may be squeezed also, but only if the gain is not too high.

Further Experiments on Interference of Independent Photon Beams at Low Light Levels

Interference fringes produced by the superposition of light beams from two independent lasers have been investigated under conditions where the light flux was so low that one photon was usually received at the detector before the next one was emitted by one or the other source. Because the average number of photons detected in each observation was only about 10, a photon correlation technique was used to demonstrate the presence of interference fringes. The measurement procedure was automated, and this led to much greater statistical accuracy than was previously reported. The effect of varying the observation time and the number of interference fringes sampled was investigated, and found to be in good agreement with theory.

Some Properties of Coherent Light

The present paper is concerned with the study of some general properties of coherent light. A clear definition of coherence is given, which appears to be preferable to definitions previously proposed by other authors. Several new theorems relating to correlation functions and the spectral density functions of coherent light are derived. The results are used to establish the Huygens-Fresnel principle for a coherent optical field. This principle has previously been freely applied to such a field, although the validity of the principle has only been justified for the much more idealized (and physically unrealizable) case of a field which is strictly monochromatic. The present formulation of the Huygens-Fresenel principle involves only observable quantities and not the instantaneous amplitudes and the instantaneous phases of the light vibrations.

Image Reconstruction from the Modulus of the Correlation Function: A Practical Approach to the Phase Problem of Coherence Theory

The problem of reconstructing an unknown light source from measurements of the modulus of the correlation function of the optical field has been investigated experimentally. The practical feasibility of two different techniques is compared. The first method involves the introduction of a reference point source to the side of the unknown source. The second method depends upon the use of filters with exponential response functions in front of the source. Both methods permit the source to be reconstructed from measurements of the modulus alone. The latter technique involves more-sophisticated numerical procedures. Both methods have the advantage that the recovered phase is largely independent of the instrumental transfer function.

Coherence properties of squeezed light and the degree of squeezing

Certain two-time correlation functions of squeezed optical fields and their Fourier conjugates are investigated. These functions are related to the autocorrelation function and the spectral density of the photoelectric current that appears in measurements made of the squeezed light by a homodyne technique. Because the field is often assumed to contain a monochromatic carrier, it is only quasi-stationary, and modified quantum correlation functions, specially constructed to be time independent, are used to describe its properties. The symmetries of the corresponding conjugate spectral functions, which are not always spectral densities, are investigated. The concepts of homogeneous squeezing, inhomogeneous squeezing, and spectral component squeezing are introduced, and it is shown that the condition for cross-spectral purity, when satisfied, leads to homogeneous squeezing. A frequency-dependent parameter called the degree of squeezing, which lies between 0 and −1 for a squeezed state and is simply related to photoelectric measurements, is introduced. These ideas are then applied to the squeezing produced in resonance fluorescence, in parametric downconversion, and in four-wave mixing, and the degrees of squeezing under different conditions are compared.