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Proceedings of NAS RA Physics

Запутанные состояния поля в процессе невырожденного параметрического распада в оптическом резонаторе

Институт физических исследований НАН Армении, Аштарак, Армения, М. С. Геворгян, М. С. Геворгян, М. С.

Published Mar 3, 2023• 0 citations
Publisher

Abstract

For the process of non-degenerate parametric decay in an optical cavity, where a photon with energy ћ3 decays into two photons with energies ћ2 and ћ1, where ћ3 = ћ2 + ћ1, the possibility of formation of entangled field states in terms of photon number variables between interacting modes of the optical system is investigated. It is shown that strongly entangled states are obtained between the modes with frequencies 2 and 1 in the case of strong coupling between interacting modes. In the case of weak and very strong coupling between these modes, relatively weak entangled states are formed. In the case of weak coupling, these modes are localized in entangled vacuum states with low values of quantum entropy. For modes with frequencies 3 and 1 entangled states are formed only in the case of strong coupling.

DOI
10.54503/0002-3035-2023-58.1-75

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For the process of non-degenerate parametric decay in an optical cavity, where a photon with energy ћ3 decays into two photons with energies ћ2 and ћ1, where ћ3 = ћ2 + ћ1, the possibility of formation of entangled field states in terms of photon number variables between interacting modes of the optical system is investigated. It is shown that strongly entangled states are obtained between the modes with frequencies 2 and 1 in the case of strong coupling between interacting modes. In the case of weak and very strong coupling between these modes, relatively weak entangled states are formed. In the case of weak coupling, these modes are localized in entangled vacuum states with low values of quantum entropy. For modes with frequencies 3 and 1 entangled states are formed only in the case of strong coupling.
For the process of nondegenerate parametric decay in an optical cavity, where a photon with energy ħω3 decays into two photons with energies ħω2 and ħω1 , where ħω3 = ħω2 +ħω1, the possibility of forming entangled field states of the interacting modes of the optical system based on the variable of quadrature amplitudes is studied. It is shown that strongly entangled states are obtained between the modes with the frequencies ω2 and ω1 in the case of a very strong coupling of the interacting modes. Weakly entangled states are formed in the case of strong coupling between modes, and no entanglement of these modes occurs in the case of weak coupling. Entangled states by the variable of quadrature amplitude do not form for the modes with frequencies ω3 and ω1 , in the optical system.
Abstract For the process of non-degenerate parametric decay in an optical cavity, where a photon with energy ћω3 decays into two photons with energies ћω2 and ћω1, where ћω3 = ћω2 + ћω1, the possibility of formation of entangled field states in terms of photon number variables between interacting modes of the optical system is investigated. Strong entangled states are shown between the modes with frequencies ω2 and ω1 in the case of strong coupling between interacting modes. In the case of weak and very strong coupling between these modes, relatively weak entangled states are formed. In the case of weak coupling, these modes are localized in entangled vacuum states with low values of quantum entropy. For modes with frequencies ω3 and ω1etangled states are formed only in the case of strong coupling.
For the process of nondegenerate parametric decay in an optical cavity in which a photon with energy ℏω3\hbar {{{{\omega }}}_{3}}ℏω3​ decays into two photons with energies ℏω2\hbar {{{{\omega }}}_{2}}ℏω2​ and ℏω1\hbar {{{{\omega }}}_{1}}ℏω1​ , where ℏω3=ℏω2+ℏω1,\hbar {{{{\omega }}}_{3}} = \hbar {{{{\omega }}}_{2}} + \hbar {{{{\omega }}}_{1}},ℏω3​=ℏω2​+ℏω1​, the possibility of forming entangled field states of the interacting modes of the optical system based on the variable of quadrature amplitudes is studied. It is shown that strongly entangled states are obtained between the modes with the frequencies ω2{{{{\omega }}}_{2}}ω2​ and ω1{{{{\omega }}}_{1}}ω1​ in the case of a very strong coupling of the interacting modes. Weakly entangled states are formed in the case of strong coupling between modes, and no entanglement of these modes occurs in the case of weak coupling. In the optical system, the entangled states by the variable of quadrature amplitude do not form for the modes with frequencies ω3{{{{\omega }}}_{3}}ω3​ and ω1{{{{\omega }}}_{1}}ω1​ .
For the process of non-degenerate parametric decay in an optical resonator, in which a quantum with energy ℏω3\hbar {{{{\omega }}}_{3}}ℏω3​ decays into two quanta with energies ℏω2\hbar {{{{\omega }}}_{2}}ℏω2​ and ℏω1\hbar {{{{\omega }}}_{1}}ℏω1​ , where ℏω3=ℏω2+ℏω1\hbar {{{{\omega }}}_{3}} = \hbar {{{{\omega }}}_{2}} + \hbar {{{{\omega }}}_{1}}ℏω3​=ℏω2​+ℏω1​ is the possibility of forming entangled states of the field by variables of the number of photons between interacting modes of the optical system is investigated. For this purpose, we investigated the dynamics of normalized correlation functions of fluctuations of the number of photons of interacting modes using a Monte–Carlo method. It is shown that in the stationary interaction limit, the value of these correlation functions strongly depends on the value of the coupling coefficient between the modes. It is shown that strong entanglement of the state of three interacting field modes is obtained in the case of weak coupling between the modes. In the case of extreme coupling between them, the value of the correlation function of fluctuations of the number of photons of the field modes tends to unity, because of which entanglement between the states of the modes disappears.
The quantum dynamics of the number of photons, of the quantum entropy, and the Wigner functions of field interacting modes are studied for the process of non-degenerate parametric decay in an optical cavity, where a quantum with energy ℏω3\hbar {{\omega }_{3}}ℏω3​ decays into two photons with energies ℏω2\hbar {{\omega }_{2}}ℏω2​ and ℏω1\hbar {{\omega }_{1}}ℏω1​ ( ℏω3=ℏω2+ℏω1\hbar {{\omega }_{3}} = \hbar {{\omega }_{2}} + \hbar {{\omega }_{1}}ℏω3​=ℏω2​+ℏω1​ ). It is shown that the mode with frequency ω3{{\omega }_{3}}ω3​ can localize in a squeezed state in the region of very strong coupling between the interacting modes, and the modes with frequencies ω1{{\omega }_{1}}ω1​ and ω2{{\omega }_{2}}ω2​ localize in states that are statistical mixtures of Fock states regardless of the value of the coupling coefficient
In this article, we have given the size of the coupling constant, a system of quantum electro-dynamics in weak coupling regime, strong and very strong case our analysis and simulation. Also by choosing the type of quantum system and the electrical field of the electromagnetic wave, the size of Rabi frequency to the extent that we are less than excited states and photons in the cavity decay rate is. In this case, the interaction between the quantum system and electromagnetic field coupling regime is weak. It is one of the properties of quantum light emitting modes of the cavity modes can be in resonance with each other, resulting in a sudden increase in the spontaneous emission rate, causing a sharp peak in the density of the spontaneous emission spectrum. The nature of this regime leads to appropriate in light production applications, such as it is possible to increase efficiency, reduce the threshold lasers emitting light in alignment with the vertical cavity structure light emitting diodes noted. Also property is listed under the regime of entangled photons is used in the production of instant. While this research, the rotating wave approximation is used in this context, survival and annihilation operators of photons Sinusoidal behavior.