Lecture

Photon Properties: Average Values and Uncertainties

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In course

MICRO-444: La science quantique : une vision singulière

Les étudiants comprennent les caractéristiques de la science quantique. Ils en maitrisent le formalisme et l'appliquent dans les systèmes de base: puits, fils et boites quantiques, qubits. ...

Description

This lecture discusses the average values and uncertainties associated with photons, focusing on the mathematical formulations of mean and variance. The instructor presents the concepts of amplitude and intensity uncertainties, emphasizing the relationship between them through Fourier analysis. The lecture covers Heisenberg's uncertainty principle and its implications for photon behavior, including coherence and interference phenomena. The instructor explains the significance of coherent and incoherent light sources, particularly in the context of interferometers like the Michelson and Mach-Zehnder setups. The discussion extends to optical coherence tomography and the importance of coherence length in various applications. Exercises are included to illustrate practical applications of these concepts, such as calculating average positions and analyzing the behavior of single photons in beam splitters. The lecture concludes with a review of the Crookes radiometer experiment, demonstrating the interaction of light with matter and the resulting motion of the device.

Instructor

Pierre-André Besse

Teaching & PhD Past EPFL PhD Students Klaus Ehrmann Courses La science quantique : une vision singulière MICRO-444 Students understand the characteristics of quantum science. They master the formalism and use it in basic quantum systems: quantum wells, wires, dots or qubits. Physics of semiconductors devices MICRO-312 The students are able to explain the physics of semiconductor devices like diodes, transistors, and MOS devices. They use such devices in fundamental electroni

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Related concepts (32)

Optical coherence tomography

Optical coherence tomography (OCT) is an imaging technique that uses low-coherence light to capture micrometer-resolution, two- and three-dimensional images from within optical scattering media (e.g., biological tissue). It is used for medical imaging and industrial nondestructive testing (NDT). Optical coherence tomography is based on low-coherence interferometry, typically employing near-infrared light. The use of relatively long wavelength light allows it to penetrate into the scattering medium.

Coherence (physics)

In physics, coherence expresses the potential for two waves to interfere. Two monochromatic beams from a single source always interfere. Physical sources are not strictly monochromatic: they may be partly coherent. Beams from different sources are mutually incoherent. When interfering, two waves add together to create a wave of greater amplitude than either one (constructive interference) or subtract from each other to create a wave of minima which may be zero (destructive interference), depending on their relative phase.

Coherence length

In physics, coherence length is the propagation distance over which a coherent wave (e.g. an electromagnetic wave) maintains a specified degree of coherence. Wave interference is strong when the paths taken by all of the interfering waves differ by less than the coherence length. A wave with a longer coherence length is closer to a perfect sinusoidal wave. Coherence length is important in holography and telecommunications engineering. This article focuses on the coherence of classical electromagnetic fields.

Mean

There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the arithmetic mean, also known as "arithmetic average", is a measure of central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x1, x2, ..., xn is typically denoted using an overhead bar, .

Fourier analysis

In mathematics, Fourier analysis (ˈfʊrieɪ,_-iər) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics.

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