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Experimental Demonstrator of the Uncertainty Principle

Philip Ekfeldt, Anders Pettersson

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

The goal of this project was to create an intuitive and clear demonstrator of the dening properties of quantum mechanics using single slit diraction of light, which has quantum mechanical properties because of light's waveparticle duality. In this report we will describe the process and thoughts behind our project of creating a portable demonstration of the uncertainty principle. By designing and building both a physical setup with a laser, a slit, mirrors, lenses, beam-splitters, attenuators and cameras, and developing software which displays images from the cameras in a clear user interface with calculations we hope that students from high schools and gymnasiums that visit Vetenskapens Hus at Alba Nova will learn something new while using the demonstrator.

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The goal of this project was to create an intuitive and clear demonstrator of the dening properties of quantum mechanics using single slit diraction of light, which has quantum mechanical properties because of light's waveparticle duality. In this report we will describe the process and thoughts behind our project of creating a portable demonstration of the uncertainty principle. By designing and building both a physical setup with a laser, a slit, mirrors, lenses, beam-splitters, attenuators and cameras, and developing software which displays images from the cameras in a clear user interface with calculations we hope that students from high schools and gymnasiums that visit Vetenskapens Hus at Alba Nova will learn something new while using the demonstrator.
We described a simple idea for experimental verification of the uncertainty principle for light waves. We used a single-slit diffraction of a laser beam for measuring the angular width of zero-order diffraction maximum and obtained the corresponding wave number uncertainty. We will assume that the uncertainty in position is the slit width. For the acquisition of the experimental data and their further analysis, we used a computer. Because of its simplicity this experiment is very suitable for demonstration, as well as for a quantitative exercise at universities and final year of high school studies.
A thought experiment, in which a light beam is sent through slits of different sizes thereby producing a diffraction pattern, is used to illustrate the uncertainty principle. Attempts to reduce the uncertainty in the measurement of the position of the light beam ( ) succeed, but at the expense of increasing the uncertainty in the measurement of the momentum ( ), so that the product of the two magnitudes, x, is still larger than h, Planck's constant. This experiment introduces the idea that one can know the value of a physical observable with as high a precision as necessary, but the act of measuring this observable has an effect on how much we can know about another observable. This thought experiment can be physically performed using a diode laser and a series of slits. A derivation is presented to relate the uncertainties in position and momentum to variables that can be measured with a ruler in a classroom or laboratory. Data from a typical experiment are also presented.
This experiment investigates the Heisenberg Uncertainty Principle (HUP) through an optical analogue using Single-slit diffraction of a monochromatic He–Ne laser. The spatial confinement of light through slits of varying width is compared with the resulting diffraction patterns, providing a means to examine the relationship between position uncertainty ∆x and transverse momentum uncertainty ∆px. Diffraction patterns were recorded using a photodiode detector, and the angular positions of the first minima were determined and used to estimate the spread in momentum via the de-Broglie relation. The results demonstrates and are consistent with the expected inverse relationship. The measured diffraction patterns were also found to adhere to the Fraunhofer diffraction relation, supporting the validity of the experimental model and the goodness of fit of the data.The calculated uncertainty products were further found to be consistent with the expected magnitude of Planck's constant. and therefore the the findings support the interpretation of diffraction as a classifcal manifestation of the Foruier relation between position and momentum space. Thus providing a physically intuituve demonstration of Heisenberg's Uncertainty Principle.
The wave-particle duality of light plays a fundamental role in introductory courses on quantum mechanics. Traditionally the wave and particle aspects of light are demonstrated in separate experiments which makes it difficult for students to understand their complementary nature. We present an experiment using a single apparatus that demonstrates the wave aspect, the particle aspect, and most importantly, their coexistence. The apparatus is based on a Mach-Zehnder interferometer in which a light beam is attenuated so that at each instant there is only a single photon in the interferometer. In this way the observation of single photon interference becomes possible. By integrating the single photon events in a storage oscilloscope the evolution toward classical interference fringes can be shown in real time. A second strong laser beam, derived from the same pointer, but slightly displaced, traverses the interferometer at the same time, allowing the simultaneous demonstration of wave aspects. Special features of the setup are low cost, simplicity, didactical power and suitability for presentations in large lecture halls using both multimedia projections and audible signals.