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Physical Review A

Squeezing and higher-order squeezing in one- and two-photon Jaynes-Cummings models

Christopher C. Gerry, Patrick J. Moyer

Published Dec 1, 1988• 64 citations
Publisher

Abstract

We consider the squeezing of the electromagnetic field resulting form the interaction of light in a coherent state with one- and two-photon Jaynes-Cummings models of the two-level atom. We also consider high-order squeezing in the sense of Hong and Mandel [Phys. Rev. Lett. 54, 323 (1985)] and also of Hillery [Phys. Rev. A 36, 3796 (1987)].

DOI
10.1103/physreva.38.5665

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We consider the squeezing of the electromagnetic field resulting form the interaction of light in a coherent state with one- and two-photon Jaynes-Cummings models of the two-level atom. We also consider high-order squeezing in the sense of Hong and Mandel [Phys. Rev. Lett. 54, 323 (1985)] and also of Hillery [Phys. Rev. A 36, 3796 (1987)].
We consider squeezing of the electromagnetic field resulting from the interaction of the three-level ssV-shaped atom with two modes initially taken in coherent-state representation. We also consider higher-order squeezing in the sense of Hong and Mandel [Phys. Rev. Lett. 54, 323 (1985)] and then in the sense of Hillery [Phys. Rev. A 36, 3796 (1987)]. We calculate the two-mode squeezing proposed in [J. Mod. Opt. 34, 709 (1987)] and the sum squeezing defined by Hillery [Phys. Rev. A 40, 3147 (1989)] for an atom starting initially at its ground state.
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.
The nonlinear Jaynes-Cummings model is investigated for squeezing and higher-order squeezing produced from the interaction of the model with two coherent modes. Squeezing of the matter operators is also considered. Two-mode squeezing and higher-order two-mode squeezing are investigated for the present model. We found that squeezing produced using the concept of two-mode squeezing is more effective than squeezing produced using the single-mode-squeezing concept. It is shown that squeezing of the field can be enhanced for small n\ifmmode\bar\else\textasciimacron\fi{}=0 and m\ifmmode\bar\else\textasciimacron\fi{}=0 when the atom is initially in a coherent superposition state.