What is coherent states?

Coherent states are quantum states that are used to describe the closest approximation to classical states in quantum mechanics. They are often considered to be the most classical-like states in quantum mechanics, as they have properties that resemble classical waves or particles.

Some key features of coherent states include:

• They are eigenstates of the annihilation operator, which means that they are the states that are most easily destroyed by the annihilation operator.
• They have a minimum uncertainty product, meaning that their position and momentum uncertainties are at their lowest possible value.
• They exhibit well-defined phase properties, as their wave function has a fixed phase relationship between position and momentum.

Coherent states are often used in quantum optics, quantum information theory, and quantum computing due to their classical-like properties and ease of manipulation. They are also commonly used in the study of quantum mechanical systems and in the description of harmonic oscillators.

Overall, coherent states play a crucial role in bridging the gap between classical and quantum physics, and are a valuable tool in understanding and describing quantum systems.