Two-Level Systems

Have you ever wondered what the simplest example from the wonderful world of quantum mechanics is? If so, meet the two-level system! In plain terms, it is a model that describes a system of two levels and a way to control the system. A natural question to ask is if this simple model has any relevance in the real world. It may surprise you that the answer to that question is a resounding ‘Yes!’.

From Magnetic Resonance Imaging (MRI) to controlling the electronic state of an atom with a laser, the manifestations of the two-level system are indeed numerous.

An excellent example is Magnetic Resonance Imaging (MRI) which is a widely used technique in the medical industry to perform non-invasive imaging of e.g. the brain. Tissue contains a lot of H2O, ie. water molecules. A large set of coils produces a strong magnetic field that can be used to control the orientation of the hydrogen (H) atoms in the patient’s body. Each independent atom is then either aligned or anti-aligned with the field. These states constitute the two levels in our system. It is also possible for the atom to be in a superposition state of being aligned and anti-aligned - a hallmark of quantum mechanics!

This interactive demo application gives you an intuitive real-time control over the manipulation of the most fundamental quantum systems. You are tasked with steering the system from an initial state into a target state - exactly like in our flagship game, Quantum Moves! Although the physics behind the two-level system and Quantum Moves is essentially the same, the two-level system exhibits a very neat property: all possible states can be represented as an arrow on a sphere. The matter of controlling the initial state to a target state then corresponds to rotating an initial arrow into a target arrow. Sounds easy? Give it a try!