coherent states

These can produce new coherent states and allow us to move around phase space.

The construction of coherent states using group representations described above is not sufficient.

It is possible to define operators to move the coherent states around the phase space.

Moreover, these coherent states may be generalized to quantum groups.

They can also be defined as squeezed coherent states.

This work led to the concept of coherent states and the development of the laser.

Thus, the vectors constitute a family of generalized coherent states.

For application to lasers, the amplification of coherent states are important.

Here, we observe a Bayesian duality typical of coherent states.

However, since they obey a closure relation, any state can be decomposed on the set of coherent states.

The Perelomov construction can be used to define coherent states for any locally compact group.

By definition, the coherent states have the following property:

For example, no two coherent states are orthogonal.

Another very important property of the coherent states becomes very apparent in this formalism.

There is a close link to the theory of (generalized) coherent states in Lie algebras.

Scarcely coherent states themselves, they have little money to spare and little power to project in the rescue of other failing nations.

Vectors defined in this way are called Gilmore-Perelomov coherent states.

The eigenstates of the annihilation operator are called coherent states:

This inequality does not necessarily have to be saturated and a common example of such states are squeezed coherent states.

Although the coherent states can be realized in wide variety of physical systems, they refer mainly to the state of optical light.

A set of vectors satisfying the two properties above is called a family of generalized coherent states.

In this definition of generalized coherent states, no resolution of the identity is postulated.

The Husimi representation can also be found using the formula above for the inner product of two coherent states:

In other words, every mode of the black body is normally distributed in the basis of coherent states.

We present in this section some of the more commonly used types of coherent states, as illustrations of the general structure given above.