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arXiv:1406.0414 · Journal of the Optical Society of America B

Nonlinear coupler operating on Werner-like states—entanglement creation, its enhancement, and preservation

A. Kowalewska-Kudłaszyk, W. Leoński

Published May 9, 2014• 11 citations
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Abstract

We discuss a model of two nonlinear Kerr-like oscillators, mutually coupled and excited by parametric process. We show that the system’s evolution, starting from Werner-like states, remains closed within a small set of two-mode n-photon states and that a pure two-qubit entangled state can be generated. For some initial Werner-like states, delayed entanglement generation can be observed. We investigate the influence of two damping mechanisms on the system’s evolution. We show that, for both cases, entanglement can survive despite the presence of damping, and that the effects of sudden entanglement death and its rebirth can appear in the system.

DOI
10.1364/josab.31.001290

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We discuss a model of two nonlinear Kerr-like oscillators, mutually coupled and excited by parametric process. We show that the system’s evolution, starting from Werner-like states, remains closed within a small set of two-mode n-photon states and that a pure two-qubit entangled state can be generated. For some initial Werner-like states, delayed entanglement generation can be observed. We investigate the influence of two damping mechanisms on the system’s evolution. We show that, for both cases, entanglement can survive despite the presence of damping, and that the effects of sudden entanglement death and its rebirth can appear in the system.
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.
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.
Two nonlinear Kerr oscillators mutually coupled by parametric pumping are studied as a source of states entangled in photon numbers. Temporal evolution of entanglement quantified by negativity shows the effects of sudden death and birth of entanglement. Entanglement is preserved even in asymptotic states under certain conditions. The role of reservoirs at finite temperature in entanglement evolution is elucidated. Relation between generation of entangled states and violation of Cauchy-Schwartz inequality for oscillator intensities is found.
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 analyze the entanglement dynamics in a nonlinear Kerr-like coupler interacting with external environment. Whenever the reservoir is in a thermal vacuum state, the entanglement (measured by concurrence for a two-qubit system) exhibits regular oscillations of decreasing amplitude. In contrast, for thermal reservoirs we can observe dark periods in concurrence oscillations (which can be called a sudden death of the entanglement) and the entanglement rebuild (which can be named the sudden birth of entanglement). We show that these features can be observed when we deal with two-qubit system as well as qubit-qutrit system.