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Indian Journal of Physics

Higher-order squeezing oscillations in Jaynes–Cummings model of a pair of cold atoms

N. A. Enaki, V. I. Koroli, Sergiu Bazgan, Andrei Nistreanu, C. H. Raymond Ooi

Published Feb 12, 2015• 1 citation
Publisher

Abstract

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 $$\langle n_v\rangle =0$$ . 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 $$t=0$$ , 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 $$t=0$$ , pair of atoms is supposed to be in the first excited state $$\vert e_1\rangle $$ 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 $$\vert \xi \vert $$ 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.

DOI
10.1007/s12648-015-0658-z

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We study the two-photon interaction between a three-level equidistant radiator (atom, molecule) with different dipole transitions and the single-mode cavity field. It is supposed that the three-level radiator is laser cooled and trapped into the ground vibrational state, in which the vibrational quantum number [Formula: see text]. In the proposed two-photon Jaynes–Cummings model (JCM) of a three-level atom at the initial moment [Formula: see text], the quantized cavity field is prepared in the squeezed vacuum state and the three-level radiator in the first excited state [Formula: see text]. By using the exact analytical solution for the state-vector of the coupled atom-field system, the amplitude-squared squeezing of the quantized cavity field is examined as a function of the [Formula: see text] and [Formula: see text] parameters. In this situation, higher-order squeezing has the tendency towards oscillations, but the exact periodicity of these oscillations is violated by the analogy with the second-order squeezing.
The interaction between the pair of cold two-level atoms and the single-mode cavity field is investigated. The two-level atoms in the pair are supposed to be indistinguishable. This problem generalizes the two-photon Jaynes-Cummings model of a single two-level atom interacting with the squeezed vacuum. The model of the pair of indistinguishable two-level atoms is equivalent to the problem of the equidistant three-level radiator with equal dipole moment matrix transition elements between the adjacent energy levels. Supposing that at the initial moment the field is in the squeezed vacuum state we obtain the exact analytical solution for the atom-field state-vector. By using this solution the quantum-statistical and squeezing properties of the radiation field are investigated. The obtained results are compared with those for the single two-level atom system. We observe that in the model of the pair of cold two-level atoms the exact periodicity of the squeezing revivals is violated by the analogy with the single two-level atom one.
We study the interaction between the single-mode electromagnetic field and the pair of indistinguishable two-level atoms via the intensity-dependent coupling. This problem is equivalent to the equidistant three-level atom with equal dipole moment matrix transition elements between the adjacent levels. The exact analytical solution for the tom-field state- vector is obtained assuming that at the initial moment the field is in the Holstein-Primakoff SU (1,1) coherent state. The quantum-statistical and squeezing properties of the field are investigated. The obtained results are compared with those for the single two-level atom. It is observed that the exact periodicity of the field squeezing that takes place in the case of the single two-level atom is violated in the case of the pair of cold atoms. In other words, the exact periodicity of the physical quantities can be destroyed only if the radiation field interacts with a system of more than one two-level atom.
An exactly solvable generalization of the intensity-dependent Jaynes-Cummings model to the case of N 0 atoms is introduced together with its solution. The quantum dynamics of the model including the squeezing properties of the su (1,1) Perelomov and Glauber coherent states is investigated. The cases of one and two atoms present in the cavity are analysed in detail. These two cases are compared in the situation when the atomic subsystem is initially prepared in the ground state, the Dicke state and the state of thermal equilibrium.
We study the interaction between a single-mode electromagnetic field and a pair of indistinguishable two-level atoms via the intensity-dependent coupling. This problem is equivalent to the equidistant three-level atom with equal dipole moment matrix transition elements between the adjacent levels. The exact analytical solution for the atom–field state-vector is obtained assuming that at the initial moment the field is in the Holstein–Primakoff SU (1,1) coherent state. The quantum statistical and squeezing properties of the field are investigated. The results obtained are compared with those for the single two-level atom obtained by Buzek. We observe that the exact periodicity of the field squeezing that takes place in the case of the single two-level atom is violated in the case of the pair of cold atoms. That is, the exact periodicity of the physical quantities can be destroyed only if the radiation field interacts with a system of more than one two-level atom.
We have assumed that atoms are placed in given positions of the standing wave of cavity. Based on modern optical achievements it is possible to localize a small number of emitters (atoms, ions, molecules and even nuclei) in various geometrical systems like optical cavities, quantum dots, optical lattices and dielectric or disordered media. It is supposed that at initial moment t = 0 pair of atoms is prepared in superposition of ground state |g⟩, first excited |e1⟩, second |e2⟩ and third excited |e3⟩ states and quantized cavity field in coherent state |ξ⟩. By using exact analytical solution for statevector of the coupled atom-field system found with the help of Schrodinger equation quantum-statistical properties of the quantized cavity field are examined as a function of the |ξ| parameter. Exact analytical solutions for the atomic population inversion ⟨Sz⟩, mean photon number ⟨n⟩ and their fluctuations σ are obtained by using this solution. In this situation quantum statistics of cavity field has the tendency towards oscillations, but exact periodicity of these oscillations is violated by the analogy with the micromaser model [2] and two-photon JCM of a threelevel atom [3].