Physica Scripta

A new approach to quantum theory of multimode coupled parametric processes

Timur Tlyachev, Alexander Mikhailovich Chebotarev, A. S. Chirkin

Published Mar 1, 2013• 8 citations

Abstract

A new approach is proposed to solve the quantum evolution problem for a system with an arbitrary number of coupled optical parametric processes. Our method is based on the canonical transformations which define the evolution of the system in the Heisenberg picture. This theory overcomes the difficulties arising in the Wei–Norman method. The application of the approach developed is illustrated with the example of generation of a three-mode entangled light field.

DOI: 10.1088/0031-8949/2013/t153/014060

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Physica Scripta

A new approach to quantum theory of multimode coupled parametric processes

Timur Tlyachev, Alexander Mikhailovich Chebotarev, A. S. Chirkin

Published Mar 1, 2013• 8 citations

Publisher

Abstract

DOI: 10.1088/0031-8949/2013/t153/014060

Related papers

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A general approach is considered to find wave function and density operator evolution of the systems including the arbitrary number of coupled optical parametric interactions described by the quadratic Hamiltonian. This approach is based on the time-dependent canonical transformations that define the evolution of the system in the Heisenberg picture or in the interaction picture. An application is illustrated with four-frequency entangled light fields, which can be produced at the nonlinear optical interactions in vapors and solid states. The process includes one non-degenerate parametric down-conversion followed by two parametric up-conversions occurring in the field of the same classical pumping wave.A general approach is considered to find wave function and density operator evolution of the systems including the arbitrary number of coupled optical parametric interactions described by the quadratic Hamiltonian. This approach is based on the time-dependent canonical transformations that define the evolution of the system in the Heisenberg picture or in the interaction picture. An application is illustrated with four-frequency entangled light fields, which can be produced at the nonlinear optical interactions in vapors and solid states. The process includes one non-degenerate parametric down-conversion followed by two parametric up-conversions occurring in the field of the same classical pumping wave.

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Laser Physics LettersSep 7, 20162 citations

{\text{Al}}_{y}{\text{O}}_{x}/{\text{Al}}_{0.5}{\text{Ga}}_{0.5}\text{As}

ridge waveguide is discussed to illustrate the application of the formalism.

For the process of non-degenerate parametric decay in an optical resonator, in which a quantum with energy

\hbar {{{{\omega }}}_{3}}

decays into two quanta with energies

\hbar {{{{\omega }}}_{2}}

and

\hbar {{{{\omega }}}_{1}}

, where

\hbar {{{{\omega }}}_{3}} = \hbar {{{{\omega }}}_{2}} + \hbar {{{{\omega }}}_{1}}

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.