Among the most surprising and counter-intuitive phenomena discovered since the advent of quantum mechanics is that of “quantum tunneling”.
Quantum tunneling demonstrates the ability of a particle to overcome a barrier which, in classical physics, it could not because it doesn’t have the energy needed to do so. The phenomenon arises because of Heisenberg’s Uncertainty Principle, which in simple terms, states that a quantum system’s velocity and position cannot be precisely known at the same time.
Describing a particle as a probability wave means there is always a small probability that a particle can appear on the other side of an insurmountable barrier. When it does, it hasn’t leapt the barrier, but has quantum tunneled through it, which, unlike traditional tunneling, doesn’t have an effect on the barrier itself.
As an analogy, imagine a child throwing a ball against a tall wall. The child doesn’t have the energy to clear the wall, yet somehow the ball still finds itself in the next door’s prize petunias. The ball wasn’t given an extra boost by the wind, and are no holes in the wall that the ball could have slipped through, it just appeared on the other side of the wall.
This may seem esoteric, but quantum tunneling is essential for life itself to exist. The thermonuclear fusion processes that power the Sun, as well as every other star in the Universe, would not be possible if hydrogen nuclei couldn’t use it to overcome the electromagnetic repulsion keeping them apart. No quantum tunneling, and there is no starlight, the universe would be a cold, dark, and empty place without it.
In addition to this, understanding quantum tunneling can also help develop new materials and technologies based on the principles of quantum mechanics. It can even be used in medicine during cancer therapy, in which the phenomenon is used to send drugs to target tumor cells.
Experimenting with quantum tunneling
It’s little wonder researchers are working intently to better understand quantum tunneling. A new study published in the journal Natural Sciences by researchers from the Department of Dynamics at Surfaces at Max-Planck-Institute for Multidisciplinary Sciences, including Alec Wodtke and Dirk Schwarzer, investigates a form of this quantum phenomenon called resonance-enhanced condensed phase tunneling.
“In the condensed phase, reactant molecules are located in potential wells separated by barriers. For quantum systems of bound particles, only certain discrete energy states exist. If two states in neighboring potential wells have the same energy, this is called resonance.” said Schwarzer. “Whereas the phenomenon of resonant tunneling is well known for electron transmission through barriers in quantum-well structures, it has never been observed before for heavy particles in a condensed phase chemical reaction.”
The researchers investigated the orientational isomerization — the transformation of the conformation of a molecule — of a carbon monoxide (CO) molecule bound to a sodium chloride (NaCl) crystal surface.
Quantum tunnelling is defined by the probability of a particle being found on the opposite side of a barrier. Through their experiments, the team found, quite by accident, that this probability is enhanced with systems in resonance (in phase with one another) compared to systems that aren’t in resonance. They discovered something else too, something surprising.
“In the most stable configuration, the CO molecule is bound with the carbon atom to the Na+ ion on the surface. We found out that there also exists a metastable upside-down configuration with the oxygen bound to the Na+ ion,” Schwarzer said. “We learned to prepare the upside-down state and measured the back flipping reaction rate vs temperature, and most importantly, varied the reactant mass by isotopic exchange [the replacement of the lighter carbon atom 12C by the heavier isotope 13C, or replacement of the lighter oxygen atom 16O by the heavier isotope 18O, or both].”
He added that the reaction rate measured by the team showed an unexpectedly strong and non-intuitive mass dependence, which can only be explained by assuming resonance tunneling. But why is this surprising?
Escaping the quantum well
The waves associated with particles, called de Broglie waves, increase in size as the mass of particles decreases. That’s why everyday objects don’t exhibit quantum, wave-like behaviors; their mass is too great and their de Broglie waves are too small.
Imagine, again, a ball thrown by a child without the energy needed to clear the height of the wall. It can’t quantum tunnel to the other side as its mass creates a probability wave too small for there to be any probability of it finding itself on the other side of the barrier. Common quantum theories predict that the smaller the mass of a particle, the larger the de Broglie wave and the greater the chance of a particle quantum tunneling through a barrier.
This means when you have lots of lighter particles and lots of heavier particles and a quantum barrier, both will tunnel, but the lighter particles should quantum tunnel faster than the heavy particles. But, what Schwarzer and colleagues found was, in fact, the relationship between quantum tunneling is more chaotic than previously thought.
“In our studies, we surprisingly found examples where the tunneling rate increased when the mass was increased by isotopic substitution,” Schwarzer said. “This observation is a clear indication of tunneling resonance, whose occurrence depends on mass in an erratic manner.”
The team now intends to apply what they have learned to how tunneling occurs in the material in the cold of space, in particular, the gas and dust clouds that exist between stars and their potential to create complex molecules via quantum tunneling.
“This is particularly relevant for chemical reactions taking place in cold interstellar clouds where the temperatures [and thus energy] are so low that ‘over-the-barrier’ processes are suppressed, and many reactions are believed to be determined entirely by quantum tunneling,” Schwarzer explained.
Even before this application, the study exemplifies how far quantum research has come since its beginnings, and how it continues to deliver surprises.
“I think that while the founders of quantum mechanics had already developed the basic theories of tunnelling and had clear ideas about concepts such as resonance enhancement, they certainly could not imagine how important this field would become in technology and science,” Schwarzer said. “They would be amazed and excited by the sophisticated techniques used nowadays to explore the fundamentals of quantum mechanics.”
References: A. M. Wodtke., et al., Manipulating tunnelling gateways in condensed phase isomerization, Natural Sciences (2023). DOI: 10.1002/ntls.20230006
Feature image credit: Milad Fakurian on Unsplash