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Journal of Contemporary Physics (Armenian Academy of Sciences)

Entangled Field States in the Process of Nondegenerate Parametric Decay in an Optical Cavity

S. T. Gevorgyan, M. S. Gevorgyan

Published Mar 1, 2023• 2 citations
Publisher

Abstract

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.

DOI
10.1134/s1068337223010115

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arXiv:quant-ph/0309203•Sep 29, 2003•0 citations
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 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 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 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.
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
We explore in detail the possibility of generation of continuous-variable (CV) entangled states of light fields with well-localized phases. We show that such quantum states, called entangled self-phase locked states, can be generated in nondegenerate optical parametric oscillator (NOPO) based on a type-II phase-matched down-conversion combined with polarization mixer in a cavity. A quantum theory of this device, recently realized in the experiment, is developed for both sub-threshold and above-threshold operational regimes. We show that the system providing relative phase coherence between two generated modes also exhibits different types of quantum correlations between photon numbers and phases of these modes. We quantify the entanglement as two-mode squeezing and show that CV entanglement is realized for both unitary, non-dissipative dynamics and for dissipative NOPO in the entire range of pump field intensities.