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Physik-Institut

How do quanta get into mechanics?

In classical physics, physical quantities such as energy are accustomed to being able to assume continuous values. This is not the case in quantum mechanical systems, where the permitted energies are quantized — meaning they can only take on specific, discrete values. However, the gradations of energy are so fine that we do not normally recognize them. To measure them, it is important to cool them well because heat causes various quantum mechanical oscillation states to become excited simultaneously.

Lowest Energy State

In quantum mechanics, the lowest energy state is slightly above zero. Therefore, the quantum mechanical pendulum never stands completely still. This is due to the Heisenberg uncertainty principle, which states that position and speed cannot be precisely determined simultaneously. If the pendulum had no energy, this principle would be contradicted because we would know exactly where the pendulum is and that its speed is zero.

Pendulum

As the pendulum swings, it continuously converts kinetic energy into potential energy, or vice versa. If we neglect friction, the sum of potential and kinetic energy is obtained (given by the potential energy at maximum deflection). According to our everyday classical experience, this total energy can take on any value because we can set the initial deflection of the pendulum to any value. Quantum mechanical effects can only be observed with very small pendulums or oscillations in micromechanical systems, such as cantilevers. Measurements are typically made at temperatures of a few micro-Kelvin.

Quantum Leap

Quantum mechanical systems, such as electrons in an atom, can transition between energy states by absorbing or emitting energy in the form of a photon. This "quantum leap" has made its way into our everyday language. Incidentally, it is only thanks to the laws of quantum mechanics, such as the uncertainty principle, that we can explain why atoms exist. According to classical physics, electrons would crash into atomic nuclei, resulting in no stable matter. In this sense, everything we touch is "quantum mechanics at your fingertips."

quantum leap
Image: Illustration quantum leap, an electron in an atom atom can only absorb or emit photons. Picture: Ruth Bründler, UZH

 

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More on: Cantilever

https://www.nature.com/articles/nature08967

When we consider systems in which quantum mechanical effects play a role, we often think of individual atoms or their components: electrons. Mechanical systems such as pendulums or cantilevers seem very far removed from the realm governed by quantum physics. However, even such systems can be brought into the quantum realm, particularly if they are made small and carefully decoupled from their surroundings, as well as being cooled very well. It can then be demonstrated that the energy of the mechanical modes is quantised, and that the system can be brought into its lowest mechanical mode — the ground state. In this state, the motion of a cantilever (an oscillating plate) is no longer clearly defined as in the macroscopic world. We cannot visualise the oscillation as a temporal evolution of the cantilever's velocity and position. According to Heisenberg's uncertainty principle, the position and velocity of the cantilever cannot be determined simultaneously. This is also associated with a finite ground state energy, meaning that the cantilever does not 'stand perfectly still' even at absolute zero temperature.

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