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arXiv:quant-ph/0611090 · Physical Review A

Decoherence-free subspace and entanglement by interaction with a common squeezed bath

Douglas F. Mundarain, Miguel Orszag

Published Apr 30, 2007• 35 citations
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Abstract

In this work we find explicitly the decoherence-free subspace (DFS) for a two two-level system in a common squeezed vacuum bath. We also find an orthogonal basis for the DFS composed of a symmetrical and an antisymmetrical (under particle permutation) entangled state. For any initial symmetrical state, the master equation has one stationary state which is the symmetrical entangled decoherence-free state. In this way, one can generate entanglement via a common squeezed bath of the two systems. If the initial state does not have a definite parity, the stationary state depends strongly on the initial conditions of the system and it is a statistical mixture of states which belong to DFS. We also study the effect of the coupling between the two-level systems on the DFS.

DOI
10.1103/physreva.75.040303

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In this work we find explicitly the decoherence-free subspace (DFS) for a two two-level system in a common squeezed vacuum bath. We also find an orthogonal basis for the DFS composed of a symmetrical and an antisymmetrical (under particle permutation) entangled state. For any initial symmetrical state, the master equation has one stationary state which is the symmetrical entangled decoherence-free state. In this way, one can generate entanglement via a common squeezed bath of the two systems. If the initial state does not have a definite parity, the stationary state depends strongly on the initial conditions of the system and it is a statistical mixture of states which belong to DFS. We also study the effect of the coupling between the two-level systems on the DFS.
We study the non-Markovian entanglement dynamics of two qubits in a common squeezed bath. We see a remarkable difference between the non-Markovian entanglement dynamics and its Markovian counterpart. We show that a non-Markovian decoherence-free state is also decoherence free in the Markovian regime, but all the Markovian decoherence-free states are not necessarily decoherence free in the non-Markovian domain. We extend our calculation from a squeezed vacuum bath to a squeezed thermal bath, where we see the effect of finite bath temperatures on the entanglement dynamics.
In this work, decoherence of a system from an entangled state is studied theoretically by computing the time-dependent probability amplitude with which the system remains in that state. The system is composed of, in addition to vacuum, identical two-level atoms that interact indirectly with each other through photons and have a uniform distribution in the vacuum. Under the assumption that in the initial entangled state only one atom is allowed to be in the excited state, a general expression for the probability amplitude is obtained and applied to two specific entangled states, one symmetric and one antisymmetric, to demonstrate that the system decoheres from these two states at the same rate under certain conditions.
We investigate the entanglement dynamics of two modes in a common squeezed thermal environment by means of the characteristic function method and the logarithmic negativity. When the two modes are prepared initially in separable squeezed states, we find that the external environment can not only induce but also enhance the two-mode entanglement if their initial squeezing parameters are suitably chosen. When the two modes are initially in a two-mode squeezed vacuum state, we find that whether the initial entanglement is degraded or increased depends strongly on the difference between the squeezing parameters of the considered bath and of a quantum state. Finally, we give a condition of all two-mode entangled Gaussian states to be the decoherence-free state in a given squeezed bath.
We investigate the properties of quantum entanglement of two-mode squeezed states interacting with symmetric linear baths with general gain and loss parameters. By explicitly solving for $\ensuremath{\rho}$ from the master equation, we determine analytical expressions of eigenvalues and eigenvectors of ${\ensuremath{\rho}}^{{T}_{A}}$ (the partial transposition of density matrix $\ensuremath{\rho}$). In Fock space, ${\ensuremath{\rho}}^{{T}_{A}}$ is shown to maintain a block diagonal structure as the system evolves. In addition, we discover that the decoherence induced by the baths would break the degeneracy of ${\ensuremath{\rho}}^{{T}_{A}}$, and leads to a set of eigenvectors for the construction of entanglement witness operators. Such eigenvectors are shown to be time independent, which is a signature of robust entanglement of two-mode squeezed states in the presence of noise.
"or many years the entangled systems have been associated to the quantum world, while the separable systems with the classical world. Recently quantum discord showed that some separable states posses quantum correlation even when the entanglement is zero. In this work, we compare different features of quantum discord and entanglement of formation for two qubits in a common squeezed reservoir. We relate the quantum correlations with the “distance” of our initial condition from the decoherence free subspace where the system is not affected by environment. While for some initial conditions, the entanglement presents sudden death and revival, quantum discord does not. Still, is not clear the relation between these two measurements of “quantumness”."