Quantum Tunneling – Making the Impossible Possible

Where classical physics reaches its limits, quantum mechanics opens up new possibilities. Quantum tunneling allows processes and reactions which would not be possible in classical mechanics – for example: that the sun shines and produces heat. In this post we look at the use of quantum tunneling in material characterization and analysis.

What is quantum tunneling?

Imagine you have two hemispherical bowls and let a ball roll down the side of each of them from just under the bowl’s edge. One ball behaves classically, the other quantum-mechanically (Figure 1). What would you see? If you ignore friction, the classical ball will roll back and forth forever, and reach the starting height every time. However, you would never exactly know which height the quantum-mechanical ball reaches because, according to Heisenberg, this ball’s path must remain uncertain. And at some point the quantum-mechanical ball will have disappeared from the bowl. This is due to quantum tunneling.

Figure 1: Classical and quantum-mechanical balls

Quantum tunneling is a quantum-mechanical effect which allows quantum objects to surmount barriers although they do not have enough energy to do this – they are “too slow”. This phenomenon is not possible in classical physics – but possible in quantum mechanics. The dashed line with the arrow in Figure 1 indicates that sooner or later the quantum-mechanical ball will jump over the edge of the bowl. That is not incorrect but true quantum objects tunnel through – penetrate through – the barrier and appear on the other side. Therefore the name “quantum tunneling”. Within the scientific community there is currently lively discussion about how long a quantum object takes to tunnel through a barrier. Recent results suggest that this happens faster than with the speed of light.
Where can we find quantum tunneling? Without it there would be no USB sticks with several billion bits of memory, our sun would not be able to shine and many chemical and biochemical reactions could not take place. In the field of chemical-physical material analysis and characterization there are two methods in particular which use quantum tunneling: scanning tunneling microscopy and infrared spectroscopy in an ATR configuration. We will take a closer look at these two methods.

Scanning tunneling microscopy and quantum tunneling

Using quantum tunneling, scanning tunneling microscopes can image the surfaces of materials with atomic resolution. A sharp tip scans the surface at a constant distance of approximately one nanometer above it.  A low voltage is applied between the tip and the sample. This would not result in a flow of current if quantum tunneling did not occur. The distance between the tip and the sample is adjusted so that a constant tunneling current flows between them. The self-adjusting height position of the tip over each point of the sample and the location of the measuring points are combined to make an image. If the tip is sharp enough it is possible to obtain images with atomic resolution. In Figure 2 the left side shows the principle and the right side shows the image of a graphite surface in which every single mound represents a carbon atom.

Figure 2: Principle of the scanning tunneling microscope and image of a graphite surface.
Sources: http://www3.physnet.uni-hamburg.de/iap/group_ds/information/F_Praktikum/Rastertunnelmikroskopie/versuch_stm.html https://upload.wikimedia.org/wikipedia/commons/7/76/Graphite_ambient_STM.jpg

The ATR method and quantum tunneling

A type of infrared spectroscopy used in chemical analysis is the ATR method. ATR stands for “attenuated total reflection”. Many solids and, in particular, aqueous samples absorb infrared light so strongly that it is only possible to measure through an extremely thin sample layer. To avoid the resulting practical problems the ATR method is used instead. Attenuated total reflection (ATR) can be regarded as quantum tunneling of light.

Figure 3: ATR measuring principle with triple total reflection

Light is completely reflected on an interface when the beam hits the interface at a flat angle. Nevertheless a small proportion of the light tunnels through to the other side of the interface – and then comes back. In an ATR configuration the sample is on the other side of the interface. The penetration depth of the light into the sample is around one quarter of the light’s wavelength. If certain spectral components of the penetrating light are selectively absorbed by constituents of the sample then spectroscopic analysis is possible. This enables the concentration of constituents in the sample to be determined, for example. Figure 3 shows a configuration for such a measurement with triple total reflection. This configuration is particularly suitable for use directly in a flow of sample.

Beverage analysis using quantum tunneling

Figure 4: Carbo 520 inline CO₂ sensor

An important application of the ATR method is the determination of dissolved carbon dioxide in beverages. The right carbon dioxide content in beverages is essential for the taste and for consistent product quality. The Carbo 520 inline CO2 sensor from Anton Paar determines the carbon dioxide content of beverages using ATR infrared spectroscopy (Figure 4). The ATR crystal is a sapphire which has the shape of a cone with the tip cut off. The sensor is mounted directly in the flow of sample, measures quickly and accurately and is maintenance-free. In this way quantum tunneling helps make sure that your favorite drink tastes just the way you like it.

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