This chapter generalizes quasiprobabilities based on coherent states to ones based on squeezed states. Especially, the representation of an operator as a diagonal mixture of squeezed states defines an analogue of the Glauber-Sudarshan P-function. The new quasiprobabilities can be useful tools in describing processes the intrinsic quantum nature of which forbids the existence of the familiar P-function. The chapter illustrates the concepts for a linearized model of subharmonic generation. It is important to express the coherent-state based Q function in terms of its squeezed-state based generalization. The chapter illustrates the squeezed-state techniques for a simple dynamical model of subharmonic generation. It confines to the subthreshold regime where the oscillation, to be down converted, can be treated parametrically.This chapter generalizes quasiprobabilities based on coherent states to ones based on squeezed states. Especially, the representation of an operator as a diagonal mixture of squeezed states defines an analogue of the Glauber-Sudarshan P-function. The new quasiprobabilities can be useful tools in describing processes the intrinsic quantum nature of which forbids the existence of the familiar P-function. The chapter illustrates the concepts for a linearized model of subharmonic generation. It is important to express the coherent-state based Q function in terms of its squeezed-state based generalization. The chapter illustrates the squeezed-state techniques for a simple dynamical model of subharmonic generation. It confines to the subthreshold regime where the oscillation, to be down converted, can be treated parametrically.

CRC Press eBooksAug 12, 20200 citations

Generalized squeezed states

Kevin Zelaya, Sanjib Dey, Véronique Hussin

arXiv:1810.02947Physics Letters AOct 5, 201830 citations

Squeezed States: Basic Principles

P. L. Knight, Vladimír Bužek

Springer series on atomic, optical, and plasma physicsJan 1, 200414 citations

Analysis of a multiphoton Jaynes-Cummings model with squeezed inputs

Tariq Maqbool, M. S. K. Razmi

An m-photon Jaynes-Cummings model is analyzed assuming the field to be initially in the squeezed vacuum state or in a more general squeezed state. Collapses and revivals of the Rabi oscillations in the atomic population inversion appear for a general squeezed input, but not for a squeezed vacuum input. The second-order coherence function is found to exhibit collapses and revivals for large initial average photon numbers. With a low-intensity input field and large m, one can achieve nearly steady-state squeezing.An m-photon Jaynes-Cummings model is analyzed assuming the field to be initially in the squeezed vacuum state or in a more general squeezed state. Collapses and revivals of the Rabi oscillations in the atomic population inversion appear for a general squeezed input, but not for a squeezed vacuum input. The second-order coherence function is found to exhibit collapses and revivals for large initial average photon numbers. With a low-intensity input field and large m, one can achieve nearly steady-state squeezing.

Physical Review ANov 1, 199114 citations

Extended two-parameter squeezed states

Xiang‐Bin Wang, L. C. Kwek, C. H. Oh

Physics Letters AAug 1, 19996 citations

Transfer of correlations from squeezed states of radiation to atoms in a generalized Jaynes-Cummings model

Donita Cohen, Y. Ben-Aryeh, A. Mann

The correlations between two atoms in a generalized two-mode Jaynes-Cummings model (JCM), in the presence of a two-mode squeezed state, are studied. It is found that for a small amount of initial squeezing the correlations go back and forth between the radiation and the atoms. For large initial squeezing the atoms are found to be highly correlated at all times, while the squeezing of the radiation is destroyed as a function of time. In addition, the squeezing of the field is studied in the two-mode JCM and is compared to the one-mode squeezing that is obtained for the ordinary JCM. It is found that in the two-mode model the squeezing is preserved for longer times under the condition that ${\mathit{g}}_{1}$ and ${\mathit{g}}_{2}$ (the two coupling constants) are almost equal.The correlations between two atoms in a generalized two-mode Jaynes-Cummings model (JCM), in the presence of a two-mode squeezed state, are studied. It is found that for a small amount of initial squeezing the correlations go back and forth between the radiation and the atoms. For large initial squeezing the atoms are found to be highly correlated at all times, while the squeezing of the radiation is destroyed as a function of time. In addition, the squeezing of the field is studied in the two-mode JCM and is compared to the one-mode squeezing that is obtained for the ordinary JCM. It is found that in the two-mode model the squeezing is preserved for longer times under the condition that ${\mathit{g}}_{1}$ and ${\mathit{g}}_{2}$ (the two coupling constants) are almost equal.

Physical Review AMar 1, 199411 citations

{\mathit{g}}_{1}

and

{\mathit{g}}_{2}

(the two coupling constants) are almost equal.