Quantum Tunneling: From Schrödinger to Real-World Applications
Few concepts in quantum physics are as counterintuitive—or as crucial—as quantum tunneling. It defies the rules of classical mechanics and forces us to rethink how particles behave at the smallest scales. This phenomenon has shifted from a theoretical puzzle to a real-world mechanism driving innovations in electronics, biology, and quantum computing.
Quantum tunneling is where probability overrides certainty, and once-impossible outcomes become physically meaningful. In this article, you’ll find out how quantum tunneling has evolved into a foundational principle of quantum mechanics and a tool for advancing science and technology.
Classical Physics Vs. Quantum Physics
To understand quantum tunneling, it’s worth getting familiar with the quantum computing basics—quantum physics, in particular, and how it differs from its classical counterpart.
Classical physics, the rules we experience in our day-to-day lives, is deterministic. Think of pushing a ball over a hill—we can accurately predict the ball's position and speed at any given moment. Classical physics essentially allows us to trace the trajectory of objects with precision.
Quantum physics, which governs the world of subatomic particles, operates differently. It introduces us to the probabilistic nature of reality—the Heisenberg Uncertainty Principle, which states that we can never simultaneously know a subatomic particle's exact position and momentum. This principle is not a limitation of our measuring tools but a fundamental property of quantum particles.
Despite this uncertainty, we aren't entirely left in the dark. Quantum physicists use a wave function tool to determine the probability of finding a particle in a specific location at a given time. Intriguingly, waves have the characteristic of not completely halting when they encounter a barrier. Much like how sound waves permeate through a closed door or sunlight radiates through windows, the wave functions of quantum particles can extend into, and sometimes beyond, barriers.
This suggests that the particles, bound by the laws of quantum physics, occasionally end up on the other side of barriers—a fundamental concept in understanding the quantum tunneling definition.
What Is Quantum Tunneling?
Quantum tunneling refers to a phenomenon in which particles appear on the other side of an energy barrier without having enough classical energy to cross it. In classical mechanics, a particle lacking the required energy would be stopped entirely. But in the quantum mechanical model, particles behave like waves with probability distributions that can extend beyond the barrier. This means there’s a non-zero chance of the particle being detected on the other side. The effect comes from the probabilistic nature of quantum systems and could have measurable, real-world implications.
Quantum Tunneling Explained
Quantum mechanical tunneling happens when a particle’s wave function—which represents the probability of its location—extends into and beyond a potential energy barrier. Even if the particle doesn’t have enough classical energy to overcome the barrier, the wave function doesn’t drop to zero at the boundary. Instead, it decays exponentially inside the barrier and may still have a small but non-zero value on the other side. The process doesn’t involve the particle physically breaking the barrier, but rather bypassing it through quantum tunneling probability.
Historical Milestones
The history of quantum tunneling dates back to the early 20th century, during the advent of quantum mechanics.
The English physicist George Gamow introduced quantum tunneling into scientific discussion in 1928. He applied the concept to explain the alpha decay process in atomic nuclei, where an alpha particle manages to escape, or tunnel out, from the potential barrier encircling the nucleus. This idea challenged classical physics, paving the way for potential barrier tunneling in quantum mechanics.
Fast forward to 1957, when Leo Esaki, a Japanese physicist, provided the first evidence of quantum tunneling in semiconductors. He demonstrated that electrons could tunnel through a thin insulating barrier in a semiconductor, leading to a real-life application of quantum tunneling. This discovery significantly influenced modern technology development and earned Esaki the Nobel Prize in Physics in 1973.
The 1980s saw another quantum leap in the applications of tunneling. Gerd Binnig and Heinrich Rohrer invented the Scanning Tunneling Microscope (STM) in 1981. This instrument, which used the quantum tunneling of electrons to image atomic surfaces, changed how we can see and manipulate the atomic and molecular world. As a result, Binnig and Rohrer were awarded the Nobel Prize in Physics in 1986.
Quantum tunneling took an even more astounding leap when a 2020 study suggested that it might occur at a speed faster than light. However, this is still an active research area, with much debate and theoretical work to follow.
The Mathematics of Quantum Tunneling
To understand how quantum tunneling works, it helps to look at the underlying mathematics. The Schrödinger equation and the concept of wave functions explain how particles can exist in places that are impossible in classical physics.
Schrödinger Equation and Tunneling
When it comes to explaining quantum tunneling, one of the main tools is the Schrödinger equation. Invented by Austrian physicist Erwin Schrödinger, this equation is the basis of quantum mechanics, providing a probabilistic framework for particle behavior. The solutions of this equation reveal the idea of a wave function, which captures the probability distribution of a particle's position. Interestingly, the wave function doesn't completely nullify when it encounters a barrier. Instead, it declines exponentially. This reflects the possibility of a particle being detected on the other side of the barrier without ever having the energy to cross it.
Wave Functions and Probability Density
Understanding quantum tunneling requires a closer look at wave functions and probability density. A wave function is a mathematical description of the quantum state of a particle. This function, symbolized by the Greek letter psi (ψ), encodes all the potential properties of our quantum system. The probability density, on the other hand, is the square of the absolute value of the wave function. It gives us the likelihood of finding a particle in a certain location. In the context of quantum tunneling, the wave function allows a particle to have a non-zero probability in regions where classical particles wouldn't be found.
The Nature of Barriers
The idea of barriers, specifically energy barriers, is a major aspect of the quantum tunneling phenomenon. Take, for example, a hill as a barrier. In classical physics, a particle without enough energy cannot surpass this hill. However, in the quantum world, things operate differently due to the phenomenon known as barrier penetration.
Energy barriers in quantum mechanics are analogous to potential barriers, often visualized as walls or impediments that particles encounter. The height of these barriers corresponds to the energy required for a particle to go beyond them in a classical sense. Yet, through quantum potential, particles exhibit unique behavior. They don't need to possess the energy to overcome the barrier. Instead, they can use quantum tunneling in order to seemingly pass through.
Quantum Tunneling in Real Life
As abstract a concept as it may seem, quantum tunneling affects our everyday lives. Be it powering modern electronic devices or facilitating vital biological processes, the influence of quantum tunneling is much more ubiquitous than one might think.
Quantum Tunneling to Solve Optimization Problems
Quantum tunneling offers a new approach to solving complex optimization problems. Traditional algorithms often get stuck in local minima, unable to reach the global best solution. Quantum systems, however, can “tunnel” through these energy barriers rather than climb over them, allowing for faster and more efficient exploration of solution spaces.
This tunneling advantage is the basis of quantum annealing, used by systems like D-Wave to solve real-world optimization challenges. With the help of superposition and tunneling, quantum computers can process multiple possibilities at the same time and escape suboptimal traps. This makes them powerful tools for logistics, finance, machine learning, and other data-intensive applications.
Applications in Nanotechnology
Quantum tunneling plays a major role in nanotechnology, particularly in tools like the Scanning Tunneling Microscope (STM). This sophisticated device uses the principles of quantum tunneling to map out the topography of surfaces at the atomic level, providing a detailed visualization of atomic and molecular arrangements.
Meanwhile, Quantum Tunneling Composite (QTC) materials showcase another practical utilization of tunneling. These are smart materials that change their electrical resistance under pressure, an effect largely attributed to the tunneling of electrons between the filler particles.
Quantum Tunneling in Biology
Research suggests that our DNA's complex processes, such as replication and mutation, might involve protons "hopping" from one location to another, overcoming an energy barrier larger than their kinetic energy.
This unexpected "hopping" motion is a manifestation of quantum tunneling, allowing for the proton to access regions classically considered impossible. These tunneling events can potentially lead to mutations, influencing species' evolution over time. This insight, which implies the influence of quantum mechanics on biological processes, is key to the progress of quantum biology.
Radioactive Decay
One of the earliest demonstrations of quantum tunneling comes from nuclear physics, specifically in the process of radioactive decay. Alpha decay, a type of radioactive decay, relies heavily on the concept of quantum tunneling.
In alpha decay, an unstable atomic nucleus releases an alpha particle, which is confined within a potential well created by nuclear forces. Classically, the alpha particle wouldn't have enough energy to overcome this well. In quantum mechanics, the alpha particle can "tunnel" through this potential barrier, thanks to quantum tunneling, even if it doesn’t have enough energy to surpass it classically. This ability of alpha particles to escape from the nucleus through quantum tunneling is a fundamental mechanism behind the phenomenon of radioactive decay.
So, Is Quantum Tunneling Faster Than Light?
The speed of quantum tunneling has been a subject of much debate. For many years, scientists have tried to measure the duration of the tunneling process, producing different and sometimes contentious results. Some have even proposed that tunneling might surpass the speed of light. However, a ground-breaking, 20-year-long study led by physicists from the Canadian Institute for Advanced Research has made major progress in this field.
The team employed rudimentary principles of quantum physics in their innovative experiment. They used 8,000 rubidium atoms, cooled to a temperature near absolute zero, to prevent random, high-speed motion. Next, they used a laser to form a barrier calibrated to a thickness of approximately 1.3 micrometers (about 2,500 rubidium atoms thick). The rubidium atoms were then pushed toward this barrier using another laser, maintaining a steady speed of about 0.15 inches (3.8 mm) per second. While most of the atoms rebounded off the barrier, roughly 3% successfully tunneled through, courtesy of quantum tunneling.
The scientists' choice of rubidium was deliberate, as lasers can alter the spin of the atom. The duration of the tunneling process would affect the atom's spin, enabling scientists to measure the time it took for atoms to tunnel by comparing the spin axis before and after the barrier. The result? An average of 0.61 milliseconds. This outcome is quite perplexing, given that it's relatively slow in quantum terms, and previous studies hinted at the possibility of instantaneous tunneling.
This significant discovery offers valuable insights into quantum mechanics, allowing for the first-ever tangible measurement of the phenomenon. The team highlights their ongoing curiosity, stating, "We're working on a new measurement where we make the barrier thicker and then determine the amount of precession at different depths. It will be very interesting to see if the atoms' speed is constant.”
The Future Prospects
Quantum tunneling, a concept once confined to theoretical physics, is now progressively affecting multiple industries, opening new avenues for innovation and discovery. The advances of the scientific community in understanding this quantum phenomenon are transforming areas like nanotechnology, biology, and nuclear physics.
BlueQubit aims to bridge the gap between complex quantum concepts and practical applications. By offering a platform where researchers, developers, and engineers can simulate quantum systems, the company allows for hands-on experimentation with tunneling-based algorithms and phenomena.
Frequently Asked Questions
Has quantum tunneling ever happened?
Yes, quantum tunneling has happened and is a well-documented physical phenomenon. It has been observed and verified in numerous experiments and is key to processes like nuclear fusion and radioactive decay. Scanning tunneling microscopes (STMs), which allow us to image individual atoms, also rely on this effect.
How does quantum tunneling work?
Quantum tunneling happens when a particle passes through a potential energy barrier that it classically shouldn’t be able to surmount. Due to the probabilistic nature of quantum mechanics, particles like electrons have a chance of “appearing” on the other side of a barrier without having the energy to climb over it. This happens because quantum objects behave like waves, and part of the wave can extend beyond the barrier. If the wave doesn't vanish entirely, there’s a measurable chance the particle will tunnel through.
What are the chances of quantum tunneling?
Quantum tunneling probability depends on factors like the height and width of the barrier and the particle’s energy. In general, smaller particles and thinner or lower barriers increase the chance of tunneling. While they’re typically too small for macroscopic objects, these probabilities are significant at atomic and subatomic scales.
How rare is quantum tunneling?
Quantum tunneling may seem rare from a classical perspective, but it happens to be quite common on the quantum level. It’s responsible for key processes like alpha decay in radioactive materials and the fusion reactions that power our Sun. While the odds of large particles tunneling are astronomically low, tunneling events involving electrons or protons happen routinely. As a matter of fact, many modern technologies wouldn’t work without it.
Is there a quantum tunneling equation?
Yes, quantum tunneling is described mathematically using the Schrödinger equation, a fundamental equation in quantum mechanics. By solving the time-independent Schrödinger equation for a particle approaching a potential barrier, physicists can calculate the tunneling probability—the likelihood of the particle appearing on the other side. The solution typically shows an exponentially decaying wave function inside the barrier, which is what makes tunneling possible.
