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Quantum tunneling

Quantum tunneling enables processes and reactions which would not be possible in classical mechanics, e.g. that the sun shines and produces heat. This article focuses on the use of quantum tunneling in material characterization and analysis.

Definition of quantum tunneling

Figure 1: Classical and quantum-mechanical balls

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). If you ignored the friction, the classical ball would 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.

Quantum tunneling is a quantum-mechanical effect which allows quantum objects to surmount barriers although they do not have enough energy to do this. 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 entirely incorrect but true quantum objects tunnel through – penetrate through – the barrier and appear on the other side. This is where the name “quantum tunneling” comes from. There is no common agreement in the scientific community concerning how long a quantum object takes to tunnel through a barrier. Recent results suggest that this process is faster than the speed of light.

Presence of quantum tunneling

Thanks to quantum tunneling there are USB sticks with several billion bits of memory, the sun is able to shine and many chemical and biochemical reactions can 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 quantum tunneling

Figure 2: Image of a graphite surface. Source

 

Using quantum tunneling, scanning tunneling microscopes can create an image of 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.

Figure 2 shows the image of a graphite surface in which every single mound represents a carbon atom.

The ATR method and quantum tunneling

Figure 3: ATR measuring principle with triple total reflection

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.

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 exampleFigure 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.

Learn more about how attenuated total reflectance or ATR is one of the most common sampling techniques in Fourier transform infrared (FTIR) spectroscopy. 

Beverage analysis using quantum tunneling

Figure 4: An inline CO₂ sensor for measuring the CO₂ content of beverages

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. Inline CO2 sensors determine 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.

This way quantum tunneling helps make sure that the quality of beverages is ensured.