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arXiv:1104.4889 · Physical Review A

Photon-number entangled states generated in Kerr media with optical parametric pumping

A. Kowalewska-Kudłaszyk, W. Leoński, Jan Peřina

Published May 26, 2011• 52 citations
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Abstract

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.

DOI
10.1103/physreva.83.052326

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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.
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 investigate the evolution of initial entangled two-atom in cavity with single-mode light field. Using the method of negative eigenvalue of partially transposed matrix we analysis the evolution of the entanglement of the two-atom in a field of number state and Kerr-media environment and find that entanglement sudden death phenomenon occurs in the number of particles field. When the atoms interact with the Kerr medium, we obtain that the phenomenon of sudden death can be eliminated in the particle-number field, and the entanglement of two-atom oscillates around a high-value.
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.
Motivated by the proposal for quantification of Bell nonlocality Phys. Rev. A 92, 030101 (2015), and the concept of ICPS symmetric states Phys. Rev. A 95, 042333 (2017), we present applications of those tools in the case of the physical system, namely photon-number entangled states generated in Kerr media with optical parametric pumping Prog. Opt. 41, 361 (2000).We start from the projection of a density matrix of the considered physical system to the family of ICPS states.For each step of the considered time evolution, we subsequently calculate both the negativity and negativity of projections to examine the lower bound of entanglement versus the actual one.Then we use those projections to calculate the lower bound of nonlocality for the volume of violation.
We consider time-evolution of the disentanglement process of once generated entangled qubit pair as a result of the phase variation of the pumping field. As a source of maximally entangled states we use the nonlinear coupler (two oscillators with Kerr-like nonlinearities) with nonlinear internal interactions. The coupler prepared in a maximally entangled state interacts afterwards with external reservoir of thermal character and pumping field as well. We show that the fact of the coupling with additional state (which can create additional entanglement with one of the 2-qubit system's previously entangled states) is an origin of interesting entanglement decay behaviour. We can observe shortening of both: entanglement death-time and entanglement birth caused by changing the phase of an external driving field.