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arXiv:1309.3635 · Computational Methods in Science and Technology

Computer Simulation of Two-Mode Nonlinear Quantum Scissors

Thi Dung Nguyen, W. Leoński, Van Cao Long

Published Jul 31, 2013• 6 citations
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Abstract

We present a simulation method allowing for modeling of quantum dynamics of nonlinear quantum scissors' (NQS) systems.We concentrate on the two-mode model involving two mutually interacting nonlinear quantum oscillators (Kerr nonlinear coupler) excited by a series of ultra-short external coherent pulses.We show that despite the simplicity of the method one can obtain non-trivial results.In particular, we discuss and compare two cases of kicked nonlinear coupler, showing that the quantum evolution of the system remains closed within a two-qubit Hilbert space and can lead to maximally entangled states generation.

DOI
10.12921/cmst.2013.19.03.175-181

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We present a simulation method allowing for modeling of quantum dynamics of nonlinear quantum scissors' (NQS) systems.We concentrate on the two-mode model involving two mutually interacting nonlinear quantum oscillators (Kerr nonlinear coupler) excited by a series of ultra-short external coherent pulses.We show that despite the simplicity of the method one can obtain non-trivial results.In particular, we discuss and compare two cases of kicked nonlinear coupler, showing that the quantum evolution of the system remains closed within a two-qubit Hilbert space and can lead to maximally entangled states generation.
We consider a nonlinear coupler with two Kerr-like oscillators mutually coupled by continuous linear interaction and excited by a series of ultrashort external pulses. We show that the system behaves like nonlinear quantum scissors . It evolves in such a way that it can be treated as a qubit–qubit system. We derive analytic formulas for the probabilities of the states involved in the system's evolution and show that they differ from those already discussed in the literature and corresponding to the continuously excited models. Moreover, for the model discussed here, maximally entangled Bell states can be generated with high efficiency.
We study a model with two nonlinear oscillators (Kerr-like nonlinear coupler) pumped by two external coherent fields as a nonlinear quantum scissor (NQS). Using the numerical simulation method introduced before for quantum state engineering in NQS of such type, we obtain the wave function describing the evolution of the system as a combination of n-photon states. Considered NQS generates a truncation of optical states that leads to achieve two-qubit states due to the nonlinear properties of oscillators and their interaction. In particular, evolution of the system generates maximally entangled states as so-called Bell-like states. We will show that a proper choice of initial conditions for such evolution implies the increase of efficiency of entanglement creation process. We consider our model for both damping and without damping cases.
We discuss a model comprising two coupled nonlinear oscillators (Kerr-like nonlinear coupler) with one of them pumped by an external coherent excitation. Applying the method of nonlinear quantum scissors we show that the quantum evolution of the coupler can be closed within a finite set of n -photon Fock states. Moreover, we show that the system is able to generate Bell-like states and, as a consequence, the coupler discussed behaves as a two-qubit system. We also analyse the effects of dissipation on entanglement of formation parametrized by concurrence.
We discuss the simulation method allowing modeling of quantum unitary dynamics for quantum nonlinear scissors systems. In particular, we consider the model of two nonlinear oscillators (Ker-like coupler) excited by an external field. We show that the time-evolution of the system is closed within a finite set of n-photo states and the Bell-like states are generated. Thus, we prove that the numerical method applied can be used as tools of quantum-mechanical simulations leading to the interesting results.
Schemes for optical-state truncation of two cavity modes are analysed. The systems, referred to as the nonlinear quantum scissors devices, comprise two coupled nonlinear oscillators (Kerr nonlinear coupler) with one or two of them pumped by external classical fields. It is shown that the quantum evolution of the pumped couplers can be closed in a two-qubit Hilbert space spanned by vacuum and single-photon states only. Thus, the pumped couplers can behave as a two-qubit system. Analysis of time evolution of the quantum entanglement shows that Bell states can be generated. A possible implementation of the couplers is suggested in a pumped double-ring cavity with resonantly enhanced Kerr nonlinearities in an electromagnetically-induced transparency scheme. The fragility of the generated states and their entanglement due to the standard dissipation and phase damping are discussed by numerically solving two types of master equations.
The study described in this paper focuses on a model featuring two nonlinear oscillators, which are stimulated by two external coherent fields, and are referred to as a nonlinear quantum scissors (NQS). To analyze the system's evolution, the NQS method for quantum state engineering was applied, leading to the discovery of a wave function that comprises a composite of n-photon states. Through the implementation of NQS, the system's optical states undergo a truncation process, resulting in the production of two-qubit states that can be achieved due to the oscillators' nonlinear characteristics and their interaction. As the system evolves, maximally entangled states referred to as Belllike states are created.