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Physica Scripta

Emergence of stationary entanglement in a dissipative kicked linear chain of three qubits

Pablo Carlos López Vázquez, Andrés García, Gilberto Sánchez‐González

Published Nov 14, 2017• 1 citation

Abstract

Abstract We describe the features of the non-equilibrium stationary states reached by a kicked linear chain made of three qubits in contact with a zero temperature dissipative environment and report the emergence of stationary entanglement between a pair of qubits of the linear chain when periodic kicks are applied simultaneously to this pair of qubits. In our scheme, the steady entanglement emerges as a result of the collective action of dissipation and kicks. We explore in this paper some of the conditions under which stationary entanglement emerges. Furthermore, the application of periodic kicks as the driven mechanism, allows us to calculate in a simple way, some of the thermodynamical properties of the non-equilibrium steady states and study their relation to the emergence of entanglement.

DOI: 10.1088/1402-4896/aa923d

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Abstract We describe the features of the non-equilibrium stationary states reached by a kicked linear chain made of three qubits in contact with a zero temperature dissipative environment and report the emergence of stationary entanglement between a pair of qubits of the linear chain when periodic kicks are applied simultaneously to this pair of qubits. In our scheme, the steady entanglement emerges as a result of the collective action of dissipation and kicks. We explore in this paper some of the conditions under which stationary entanglement emerges. Furthermore, the application of periodic kicks as the driven mechanism, allows us to calculate in a simple way, some of the thermodynamical properties of the non-equilibrium steady states and study their relation to the emergence of entanglement.

We consider a model of two qubits, which interact through a Rotating Wave Approximation (RWA) potential; while the first qubit is incoherently pumped to its excited state, the second qubit loses its excitations by contact to a zero-temperature bath. We show that purely dissipative effects (and the help of the qubit-qubit interaction) can produce entangled stationary states. The steady state entanglement is significant when the interaction constant, and the pumping and dissipation rates are of the same order of magnitude. In this toy model, the entanglement of the system exists only when the two thermal baths are on and the qubits are coupled; if we turn off either the pumping or the dissipation these correlations disappear. We calculate and compare two quantifiers of non-classical correlations: the quantum discord [3] and the entanglement of formation, in the steady state. We find an analytical form for the conditions for which the steady-state qubit-qubit entanglement attains its maximum value Css..

We study two two-level atomic quantum systems (qubits) placed close to a body held at a temperature different from that of the surrounding walls. While at thermal equilibrium the two-qubit dynamics is characterized by non-entangled steady thermal states, we show that the absence of thermal equilibrium may bring to the generation of entangled steady states. Remarkably, this entanglement emerges from the two-qubit dissipative dynamic itself, without any further external action on the two qubits, suggesting a new protocol to create and protect entanglement which is intrinsically robust to environmental effects.

We study an ensemble of two-level quantum systems (qubits) interacting with a common electromagnetic field in the proximity of a dielectric slab whose temperature is held different from that of some far surrounding walls. We show that the dissipative dynamics of the qubits driven by this stationary and out of thermal equilibrium field allows the production of steady many-body entangled states, different from the case at thermal equilibrium where steady states are always nonentangled. By studying up to ten qubits, we point out the role of symmetry in the entanglement production, which is exalted in the case of permutationally invariant configurations. In the case of three qubits, we find a strong dependence of tripartite entanglement on the spatial disposition of the qubits, and in the case of six qubits we find several highly entangled bipartitions where entanglement can, remarkably, survive for large qubit-qubit distances up to $100\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$.

The dynamics of simple qubit systems in a chain configuration coupled at both ends to separate bosonic baths at different temperatures is studied. An exact analytical solution of the master equation in the Born-Markov approximation for the reduced density matrix of the qubit system is constructed. The unique non-equilibrium stationary state for the long time behavior of the reduced density matrix in obtained. Dynamical and steady state properties of the concurrence between the first and the last spin are studied.

In recent years it has been found that quantum systems can posses entanglement in equilibrium thermal states provided temperature is low enough. In the present work we explore a possibility of having entanglement in nonequilibrium stationary states. We show analytically that, in a simple one-dimensional spin chain, there is entanglement even at the highest attainable energies; that is, starting from an equilibrium state at infinite temperature, a sufficiently strong driving can induce entanglement, even in the thermodynamic limit. We also show that dissipative dephasing, on the other hand, destroys entanglement.