TY - JOUR

T1 - The minimum-uncertainty squeezed states for atoms and photons in a cavity

AU - Kryuchkov, Sergey I.

AU - Suslov, Sergei

AU - Vega-Guzmán, José M.

PY - 2013/5/28

Y1 - 2013/5/28

N2 - 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.

AB - 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.

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U2 - 10.1088/0953-4075/46/10/104007

DO - 10.1088/0953-4075/46/10/104007

M3 - Article

AN - SCOPUS:84878149287

SN - 0953-4075

VL - 46

JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

IS - 10

M1 - 104007

ER -