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International Journal of Quantum Information

Higher-order squeezing oscillations of the single-mode cavity field interacting with a three-level radiator

V. I. Koroli, S. A. Palistrant, Andrei Nistreanu

Published Dec 1, 2017• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0219749917400123

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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.
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 interaction between the laser cooled and trapped equidistant three-level atom (ion) and the quantized cavity field is investigated. The dipole moment matrix transition elements between the adjacent atomic energy levels d12 and d23 are assumed to be different. This model generalizes the problem of the pair of indistinguishable two-level atoms interacting with the squeezed vacuum which is equivalent to the equidistant three-level atom with equal dipole moment matrix transition elements. The exact analytical solution for the atom-field state-vector is found in the case in which at the initial moment t = 0, the single-mode cavity field is supposed to be in the squeezed vacuum state. With the help of this solution, the quantum-statistical and squeezing properties of the radiation field are studied. The obtained results are compared with those for the single two-level atom model. It should be noted that in the proposed model, the exact periodicity of the squeezing revivals is violated by the analogy with the single two-level atom one. The two limiting cases are analyzed. In the first limiting case in which d12 → d23 the quantum-statistical properties of the single-mode cavity field resemble those for the pair of indistinguishable two-level atoms. In the second one d12 → 0 the quantum-statistical and squeezing features of the proposed model are similar with those for the single two-level atom model.
We study the interaction between a laser-cooled and trapped equidistant three-level atom (ion) and a single-mode cavity field. The dipole moment matrix transition elements between the adjacent atomic energy levels d 12 and d 23 are assumed to be different. This problem generalizes the model of a pair of indistinguishable two-level atoms. An intensity-dependent coupling is assumed between the three-level atom and the radiation field. In this situation, we suppose that at the initial moment the field is in the Holstein–Primakoff SU (1,1) coherent state and obtain the exact analytical solution for the atom–field state vector. 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 model. We observe that the exact periodicity of the squeezing revivals that was observed in the case of the single two-level atom is violated in the model involving the equidistant three-level radiator with different dipole moment matrix transition elements. In other words, the exact periodicity of the physical quantities can be destroyed only when more than two levels of the single-atom model are taken into account. Two limiting cases are considered. In the first case, when d 12 → d 23 , the quantum-statistical and squeezing properties of the single-mode cavity field are similar to those for a pair of indistinguishable two-level atoms. In the second case, when d 12 → 0, the exact periodicity of the squeezing revivals takes place. This limiting case is equivalent to the single two-level atom model.
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.
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.