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Steady-state entanglement in bipartite systems under the influence of non-Markovian environments

Joachim Fischbach

Published Jan 1, 2016• 0 citations
Publisher

Abstract

In this thesis, we examine steady-state entanglement in bipartite systems. In the uprising field of quantum technologies, entanglement is a vital resource. In general, environmental effects are thought to be detrimental for entanglement. Counterintuitively, the interaction with an environment can also generate entanglement in special situations. The idea to prepare entanglement dissipatively in the steady-state by exploiting this interaction poses an alternative approach for creating entanglement. We focus on the influence of non-Markovian environments on the steady-state entanglement in this thesis. Amongst other things, we show how a dissipative ancilla system can be used to increase the entanglement in the steady-state of a bipartite system.

DOI
10.18725/oparu-4116

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In this thesis, we examine steady-state entanglement in bipartite systems. In the uprising field of quantum technologies, entanglement is a vital resource. In general, environmental effects are thought to be detrimental for entanglement. Counterintuitively, the interaction with an environment can also generate entanglement in special situations. The idea to prepare entanglement dissipatively in the steady-state by exploiting this interaction poses an alternative approach for creating entanglement. We focus on the influence of non-Markovian environments on the steady-state entanglement in this thesis. Amongst other things, we show how a dissipative ancilla system can be used to increase the entanglement in the steady-state of a bipartite system.
We investigate how to enhance entanglement in the steady state of interacting two-level systems. The steady state is reached by spontaneous decay of the individual systems. When we additionally couple them to a dissipative two-level ancilla with variable eigenfrequency and coupling strength, we observe a considerable enhancement effect in the entanglement of this steady state. Moreover, we see that the increased entanglement is directly connected to the selection of certain excited states via the environment disturbing the ancilla. This effect could be used in dissipative state preparation schemes, and as a test-bed for decoherence models.
We examine the entanglement of two atoms induced by an external quantum system. Both two-level atoms are coupled to a third two-level system by dipole interaction, and the third system is under the influence of a certain environment. We examine different types of environments and show that the steady-state bipartite entanglement can be achieved. We show that a strongly fluctuating environment is more preferable because the transmission of quantum fluctuations to the atomic system creates and supports steady-state entanglement with a higher amount of concurrence than a nonfluctuating environment or an environment with strong classical fluctuations. Copyright © 2005 by MAIK "Nauka/Interperiodica" (Russia).
We analyze the steady state entanglement generated in a coherently coupled dimer system subject to dephasing noise as a function of the degree of Markovianity of the evolution. By keeping fixed the effective noise strength while varying the memory time of the environment, we demonstrate that non-Markovianity is an essential, quantifiable resource that may support the formation of steady state entanglement whereas purely Markovian dynamics governed by Lindblad master equations lead to separable steady states. This result illustrates possible mechanisms leading to long-lived entanglement in purely decohering, possibly local, environments. We present a feasible experimental demonstration of this noise assisted phenomenon using a system of trapped ions.
The thesis is contributed to the study of the decoherence dynamics of dissipative qubit systems. We reveal the profound impact of the formation of a bound state between the qubit and its local environment on the decoherence dynamics of qubit system in non-Markovian regime. We find that the decoherence can be suppressed greatly under the non-Markovian dynamics when the bound state is formed. Consequently, the entanglement can be partially preserved in the steady state. A criterion on this decoherence/disentanglement suppression is given explicitly. It can give a useful guideline on the decoherence control in experiment. We also find that the entanglement can be stably distributed among all components and particularly it always satisfies an identity. Our unified treatment includes the previous results in the literatures as special cases. The result reveals the profound nature of the entanglement and should have significant implications for quantum information processing.
We study the entanglement dynamics of an open quantum system composed of two identical two-level subsystems in a common stationary environment undergoing Markovian dissipation, with the help of a set of physical parameters defined with the collective transition coefficients of the system. We then systematically investigate the steady-state entanglement of such a system and obtain the necessary and sufficient condition for steady-state entanglement when it is initial-state dependent. We also show in particular conditions for steady-state entanglement in some circumstances and propose in general a conjecture for the necessary and sufficient condition when it is independent of the initial state.
An entangled bipartite Gaussian state is coupled to two thermal reservoirs, one for each particle, and a linear interaction is allowed between the two particles. The reservoirs are assumed to have different dynamics and to be coupled to their particles with different coupling strengths. This allows for a realistic situation where a bipartite state may be shared between two parties who 'keep' their part in different environments. The difference in temperature between the bath creates a non-equilibrium situation that we study via the steady state of the system. We find that the steady state does not exist for all values of the system parameters, and offer an explanation for this behaviour.