There are many different models that we can use to describe how particles interact with each other in the quantum world. We can also refer to these models as systems. A system is a set of parts that form a complex whole and has order to it.One of these systems is a two-level or two-state system. This system is sometimes abbreviated as a TLS.

A simple way of picturing this type of system is a coin. A coin is a single object with two sides to it. In the quantum world, the two sides of the coin would have two possible quantum states. A quantum state is a state of a quantized system that is described by a set of quantum numbers. A quantum number is a number that expresses the value of some property of a particle which occurs in the quanta

There are several examples of these systems in the quantum world:

Spin. Spin is one of the four basic quantum numbers. It is the intrinsic angular momentum It defines the spin given to a particle. For the two level system, spin can exists as counter clockwise and clockwise. It can have a value of either +1/2 or -1/2. There is a special name given to these type of particles. They are called fermions. Fermions obey the Pauli Exclusion Principle. This means that no two particles in the same energy level have the same properties or states. Think about the coin, it has a head on one side and a building(or eagle) on the other side.. There are no two same images per coin. This is the same with spin as a two-level system. One particle has a -1/2 spin while the other particle has a +1/2 spin. Protons, neutron, electron, neutrinos, and quarks are all fermions.

The transition of an atom from an excited state to a ground state . This is not necessarily a quantum system.Because photons are involved, this can be classified as a quantum system and be called an “atom-light” interaction. Using the coin, you have the excited state on one side and the ground state on the other side. The excited state is where the atom jumps to when energy is added. The ground state is the lowest energy level of the atom.

There are two processes that happen between the ground state and the excited state. These processes are absorption and emission. Absorption happens when the atom absorbs a photon . this causes the atom to become excited. Emission happens when the atom falls to ground state and releases a photon. There are actually two types of emission. There is stimulated emission and spontaneous emission. An example of spontaneous emission would be radioactive decay. An example of stimulated emission is a laser.

The difference between the two types of emission is that stimulated emission requires an induced electromagnetic field. This means that an electromagnetic field has to be introduced to the system to cause emission . Spontaneous emission, on the other hand, occurs naturally. With our coin, we can imagine that the coin has been forced to spin or is infinitely flipping, this action demonstrates how absorption and emission are constantly occurring.

The ammonia molecule. The nitrogen of ammonia has two molecular states. These states are “up “and “down”. Once again, on one side of the coin, you have “up” and on the other, you have “down”.These two states are non-degenerate. When something is non-degenerate, it does not have the same quantum energy level. In this situation, when excitation of the molecule happens, vibration is caused by the absorption and re-emission of photons.

This is similar to tossing a slinky back and forth in your hand.This quantum phenomena allows the ammonia molecule to have its pyramidal shape and allows ammonia to be used a source for a special type of a laser called a “maser”.MASER stands for Microwave Amplification of Stimulated Emission of Radiation.

The qubit. The qubit is used in quantum computing. Like the bit that is used in regular computing, the qubit is the unit of quantum information used in quantum computing. Unlike the bit, the qubit can have a 0 and 1 at the same time. A common example of the two states used in the qubit is polarization. On one side of the coin, there is vertical polarization and on the other, horizontal polarization. You have the value of 0 and perhaps horizontal polarization. While, on the other side, you have the value of 1 and vertical polarization.

The qubit reveals an interesting property about our quantum coin. This property is called superposition. This basically means that two states are existing at the same time. This is also called entanglement. Entanglement is when collective properties are shared. In this case, the collective or common property is polarization; vertical and horizontal.

The doublet. Doublets are spectral lines of an ionized gas that have been split into two lines under the influence of a magnetic field. The doublet would have +1/2 on one side of the coin and -1/2 on the other side of the coin. The doublet reveals another unique feature about our quantum coin. This feature is called rotational symmetry. This means that , regardless of how you rotate the coin, the value is still .

The concept of the two-level or two-state quantum system is being studied more as researchers seek to refine the idea of quantum computing. Though there are systems other than the qubit. The other systems have helped researchers understand how to manipulate and develop the qubit.