Nazarii Sudak

Phase space description of quantum optics

A classical particle has a definite position and momentum and is therefore represented as a point in phase space. When there is a set of particles, the probability of finding a particle in a certain small volume of phase space is given by the probability distribution function. This is not true for a quantum particle due to the uncertainty principle. Instead, one can introduce a quasi-probability distribution, which is not required to satisfy all the properties of a normal probability distribution function. For example, the Wigner function becomes negative for states that have no classical counterparts, so it can be used to identify non-classical states. Connection to other quasiprobability functions such as Glauber's-Sudarashan P function and Husimi Q function will also be shown.