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Physical Review A

Higher-order squeezing for the quantized light field:Kth-power amplitude squeezing

Si-de Du, Chang-De Gong

Published Sep 1, 1993• 19 citations
Publisher

Abstract

Kth-power amplitude squeezing (KPAS) is introduced and examined in the nonlinear-harmonic-oscillator model and the Jaynes-Cummings model with an intensity coupling. We discover that, in these two cases, the long-time behavior of KPAS (k\ensuremath{\le}4) for the strong initial field periodically displays a collapse-revival-valley and squeezed collapse-revival phenomenon, respectively. For a nonclassical state, the relation between KPAS and ordinary squeezing, Hong-Mandel squeezing, and antibunching is investigated. The results show that KPAS is another intrinsic and independent nonclassical effect inequivalent to the last three.

DOI
10.1103/physreva.48.2198

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Kth-power amplitude squeezing (KPAS) is introduced and examined in the nonlinear-harmonic-oscillator model and the Jaynes-Cummings model with an intensity coupling. We discover that, in these two cases, the long-time behavior of KPAS (k\ensuremath{\le}4) for the strong initial field periodically displays a collapse-revival-valley and squeezed collapse-revival phenomenon, respectively. For a nonclassical state, the relation between KPAS and ordinary squeezing, Hong-Mandel squeezing, and antibunching is investigated. The results show that KPAS is another intrinsic and independent nonclassical effect inequivalent to the last three.
We have defined a new nonclassical effect: amplitude kth-power squeezing. We have analyzed the squeezing properties of the k-photon coherent states as defined by D'Ariano, Rasetti, and Vadacchio [Phys. Rev. D 32, 1034 (1985)]; Katriel et al. [Phys. Rev. D 34, 332 (1986)]; and D'Ariano and Sterpi [Phys. Rev. A 39, 1810 (1989)]. It has been shown that, due to the interaction with the nonlinear nonabsorbing medium modeled as an anharmonic oscillator, these states become amplitude kth power squeezed.
An analysis of the amplitude-squared squeezing is presented for the lossless anharmonic-oscillator, Jaynes-Cummings, and intensity-dependent coupling Jaynes-Cummings models using coherent and squeezed inputs. Periodic revivals of the amplitude-squared squeezing are shown to exist in the anharmonic-oscillator and intensity-dependent coupling Jaynes-Cummings models for any value of the initial average photon number n\ifmmode\bar\else\textasciimacron\fi{}. The Jaynes-Cummings model, on the other hand, displays this characteristic for small n\ifmmode\bar\else\textasciimacron\fi{} only. The effect of the squeezing angle on the amplitude-squared squeezing is studied. A comparison with the normal-order squeezing is presented.
We study interaction between a pair of indistinguishable two-level atoms and the single-mode cavity field. It is supposed that the pair of two-level atoms is laser cooled and trapped into the ground vibrational state, in which vibrational quantum number ⟨nv⟩=0\langle n_v\rangle =0⟨nv​⟩=0 . Two Jaynes–Cummings models are investigated. One is the Jaynes–Cummings model with intensity-dependent coupling and the another is the two-photon Jaynes–Cummings model of a pair of indistinguishable two-level atoms. It should be noted that in the present model, at initial moment t=0t=0t=0 , in intensity-dependent Jaynes–Cummings model the cavity field is prepared in Holstein–Primakoff SU(1,1) CS, while in two-photon Jaynes–Cummings model it is prepared in the squeezed vacuum state. Moreover, at initial moment t=0t=0t=0 , pair of atoms is supposed to be in the first excited state ∣e1⟩\vert e_1\rangle ∣e1​⟩ in both models. By using exact analytical solutions for state-vectors of the coupled atom-field systems amplitude-squared squeezing of the quantized cavity field is examined as a function of the ∣ξ∣\vert \xi \vert ∣ξ∣ parameter. In this situation, in both models higher-order squeezing has the tendency towards oscillations, but exact periodicity of these oscillations is violated by the analogy with the second-order squeezing.