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Computational Methods in Science and Technology

Computer Simulations of Entanglement Dynamics for Nonlinear System

W. Leoński, A. Kowalewska-Kudłaszyk, Adam Miranowicz

Published Aug 14, 2025• 1 citation
Publisher

Abstract

In this paper we discuss the simulation method allowing modeling of quantum unitary dynamics. In particular, we discuss the model of two nonlinear oscillators (nonlinear coupler) excited by an external field as an example of systems exhibiting a possibility of entanglement generation. We show that Bell-like states are generated proving that the numerical method applied can be used as tools of quantum-mechanical simulations leading to interesting results.

DOI
10.12921/cmst.2010.16.02.169-172

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In this paper we discuss the simulation method allowing modeling of quantum unitary dynamics. In particular, we discuss the model of two nonlinear oscillators (nonlinear coupler) excited by an external field as an example of systems exhibiting a possibility of entanglement generation. We show that Bell-like states are generated proving that the numerical method applied can be used as tools of quantum-mechanical simulations leading to interesting results.
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.
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 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.
The nonlinear coupler, which consists of two nonlinear oscillators linearly coupled together and one or two of these oscillators excited by external coherent fields, is investigated. We show that evolution of the nonlinear coupler is possible closed in a finite set of n-photon Fock states and can create Bell-like states. Especially, the entropy of entanglement and the Bell-like states vary dramatically with the different initial conditions are discussed. These results are compared with that obtained previously in the literature.
We discuss a system comprising two nonlinear (Kerr-like) oscillators coupled mutually by a nonlinear interaction. The system is excited by an external coherent field that is resonant to the frequency of one of the oscillators. We show that the coupler evolution can be closed within a finite set of nnn-photon states, analogously as in the nonlinear quantum scissors model. Moreover, for this type of evolution our system can be treated as a Bell-like state generator. Thanks to the nonlinear nature of both oscillators and their internal coupling, these states can be generated even if the system exhibits its energy dissipating nature, contrary to systems with linear couplings.
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.