Minimum uncertainties and squeezed states of radiation (A)

Yatindra Kumar, Yashraj Jha, Namrata Shukla

Sergey Kryuchkov, Sergeĭ K. Suslov, José M. Vega-Guzmán

We describe a multi-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of the corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions and the corresponding photon statistics are discussed. Some applications to quantum optics, cavity quantum electrodynamics and superfocusing in channelling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.

Khalid Zaheer, Muhammad Suhail Zubairy

Kasivishwanathan Sundar

Sergey Kryuchkov, Sergeĭ K. Suslov, José M. Vega-Guzmán

We describe a six-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions. The corresponding photons statistics are discussed and some applications to quantum optics, cavity quantum electrodynamics, and superfocusing in channeling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.

Y. Ben-Aryeh

It is shown that there are certain quantum limits to angular momentum minimum-uncertainty (MU) obtained by polarization squeezing Hamiltonians, beyond which the MU cannot be realized. The analysis is made for two cases: (a) when a strong coherent state is in one mode and a squeezed vacuum is in the other mode. (b) For the interference between two optical modes which are amplitude squeezed, with equal squeezing and intensities’ magnitudes.