Coherent states In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state that has dynamics most closely resembling the oscillatory behavior of a classical harmo ...

are quasi-classical states that may be defined in different ways, for instance as

eigenstates In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system re ...

of the annihilation operator :

a, \alpha\rangle=\alpha, \alpha\rangle

, or as a displacement from the

vacuum A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...

, \alpha\rangle=D(\alpha), 0\rangle

, where

D(\alpha)=\exp(\alpha a^-\alpha^* a)

is the Sudarshan- Glauber

displacement operator In the quantum mechanics study of optical phase space, the displacement operator for one mode is the shift operator in quantum optics, :\hat(\alpha)=\exp \left ( \alpha \hat^\dagger - \alpha^\ast \hat \right ) , where \alpha is the amount of disp ...

. One may think of a non-linear coherent state by generalizing the annihilation operator: :

A=af(a^a)

, and then using any of the above definitions by exchanging

a

A

. The above definition is also known as an

f

-deformed annihilation operator.V. I. Man'ko, G. Marmo, F. Zaccaria and E. C. G. Sudarshan, Proceedings of the IV Wigner Symposium, eds. N. Atakishiyev, T. Seligman and K. B. Wolf (World Scientific, Singapore, 1996), p. 421

References

Quantum states {{quantum-stub