What Has Schrödinger’s Cat Got To Do With Our Particle Analytics?

In the year 1935, Austrian physicist Erwin Schrödinger invented his famous cat to demonstrate conceptual difficulties in quantum mechanics. Even though he himself called his cat example “burlesque”, it still successfully illustrates major peculiarities of quantum objects. In the following, we take a look at how Schrödinger’s cat is relevant to modern particle analytics.

The quantum world has characteristics that are contrary to common sense. One such characteristic is the superposition, which plays a vital role in Schrödinger’s cat example. A cat is locked into a tightly sealed container together with a “hell machine” (picture 1). Triggered by the radioactive decay of an atom, the hell machine releases poison at a random moment and thereby kills the cat. Before the container is opened and the state of the cat is determined, the rules of quantum mechanics state that the cat is in a superposition, meaning it is both alive and dead at the same time. Once the container is opened and the state of the cat observed, then it is either alive or dead. Apart from its cruelty towards the cat, this thought experiment is unreal for several reasons – mostly because real cats as macroscopic beings do not care about the rules of quantum mechanics. However, the quantum world does work in this strange way, as the following example of an interferometer shows.

By Dhatfield (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0) or GFDL (http://www.gnu.org/copyleft/fdl.html)], via Wikimedia Commons
Picture 1: Schrödinger’s Cat
Source: By Dhatfield (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0) or GFDL (http://www.gnu.org/copyleft/fdl.html)], via Wikimedia Commons
A Mach-Zehnder interferometer (picture 2) is a setup of two normal and two semi-transparent mirrors. On the latter, the glass is coated with metal on one surface in such a way that half of the light is reflected and the other half is transmitted. Because of this, semi-transparent mirrors resemble storefront displays in bright daylight, where we are given a poor view of the goods on display as well as a mirror image of ourselves. If the lower and upper light path through the interferometer are exactly equal, all light goes to detector 1, while no light falls on detector 2.

Picture 2: Mach-Zehnder interferometer
Source: https://commons.wikimedia.org/wiki/File:Mach-Zehnder-Interferometer001.png

How does the light travel to detector 1? On both paths towards detector 1, the light is reflected twice; on the upper path off the reflecting side of the semi-transparent mirror 1 and off mirror 2; on the lower path off mirror 3 and off the reflecting side of semi-transparent mirror 4. These reflections each lead to a phase shift of half the light’s wavelength. This means that the light of both paths is in phase, it interferes constructively – and detector 1 is hit by all of the incident light.

Why does no light arrive at detector 2? At the lower path towards detector 2, the light is only reflected off mirror 3, where a phase shift of half the light’s wavelength occurs. At the upper path towards detector 2, the light is reflected three times. However, it only goes through two phase shifts, as it hits the non-reflecting side of semi-transparent mirror 4 and is only reflected off its backside, where no phase shift occurs. The phase difference between the two light paths is half the light’s wavelength; the wave crests of one path meet the wave troughs of the other path and vice versa, which leads to destructive interference. This is why no light arrives at detector 2.

Where is Schrödinger’s cat hidden in all of this?

The link to Schrödinger’s cat becomes apparent once we send single photons into the interferometer. To this end, a normal light source can be toned down to such an extent that, due to light’s particle properties, the source starts to flash irregularly, thereby emitting one photon with every flash. As we know, this photon is the smallest possible portion of light and thus indivisible. We can therefore assume that single photons will either take the lower or the upper path through the interferometer, which would lead to both detectors responding in equal rates. However, if we actually perform the experiment, only detector 1 responds. How come?

The answer is superposition: When several different paths to reach the target are available for a quantum particle such as the photon, it behaves as if it could take all possible paths at once. The different possibilities interfere with each other. This interference with itself means that the photon can only reach detector 1, as shown above in the classic wave model of light. This is where we see the similarity with Schrödinger’s cat: While the cat before observation is in a simultaneous superposition of the states “alive” and “dead”, the photon inside the interferometer simultaneously exists in a superposition of the states “above” and “below” before it interferes with itself and is registered by the detector. By now, such superpositions have not only been proven with small particles like photons or electrons, but even with large molecules: http://www.quantumnano.at/outreach.3916.html

Superposition and particle characterization

Interferometers are of important practical use: They allow high-precision measurements of lengths and speeds in micro-mechanical systems, the navigation of airplanes and rockets with laser gyroscopes, chemical analysis via infrared spectroscopy and much more. A total of two interferometers are integrated in the new particle analysis system from Anton Paar: Litesizer™ 500 (picture 3).

Litesizer(TM) 500
Picture 3: Litesizer™ 500 particle analysis system from Anton Paar

Litesizer™ 500 determines particle size and size distributions in the nanometer range via the dynamic light scattering method. The zeta potential, a measure of the particles’ surface charge, is also determined using the electrophoretic light scattering (ELS) technique. The precise determination of this zeta potential is important for evaluating the stability of emulsions and suspensions as used for medical infusions, for example. In Litesizer™ 500, considerably faster measurements and improved measurement results compared to competitors’ products have been achieved by the use of two interferometers. One interferometer determines the velocity of the particles in an electric field based on the Doppler shift; the other determines the speed of a mirror used to modulate the reference path of the first interferometer. The new evaluation procedure is called cmPALS and is patented (EP 2735870).

How is Schrödinger’s cat relevant to ELS electrophoretic light scattering? In his groundbreaking work “The Principles of Quantum Mechanics” the grandmaster of quantum mechanics Paul Dirac writes (as late as 1967): “Each photon then interferes only with itself. Interference between two different photons never occurs.” If photons could really only interfere with themselves, as he thought, the superposition of single photons as illustrated by Schrödinger’s cat would strongly contribute to the function of interferometers and thus the ELS method. However, the current theory states that it is not the photons themselves that interfere, but rather their abstract wave functions. That the wave functions of different photons interfere has been proven in many experiments by now. Seeing that ELS measurements are not performed with single photons but with “normal” laser intensity, a superposition in the vein of Schrödinger’s cat may be meaningful on a basic level but is barely relevant in the practical application of the method.

Cat lovers everywhere can therefore rejoice: Schrödinger’s cat is neither sacrificed for any real experiments in quantum physics, nor is it forced to make any major contributions with regard to particle analysis.

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