Generation of excited coherent states for a charged particle in a uniform magnetic field

We introduce excited coherent states, $β , α ; n ≔ a † n β , α$⁠, where n is an integer and states $β , α$ denote the coherent states of a charged particle in a uniform magnetic field. States $β , α$ minimize the Schrödinger-Robertson uncertainty relation while having the nonclassical properties. It has been shown that the resolution of identity condition is realized with respect to an appropriate measure on the complex plane. Some of the nonclassical features such as sub-Poissonian statistics and quadrature squeezing of these states are investigated. Our results are compared with similar Agarwal’s type photon added coherent states (PACSs) and it is shown that, while photon-counting statistics of $β , α , n$ are the same as PACSs, their squeezing properties are different. It is also shown that for large values of $β$⁠, while they are squeezed, they minimize the uncertainty condition. Additionally, it has been demonstrated that by changing the magnitude of the external magnetic field, B_ext, the squeezing effect is transferred from one component to another. Finally, a new scheme is proposed to generate states $β , α ; n$ in cavities.