Bright and Dark periods in the Entanglement Dynamics of Interacting Qubits in Contact with the Environment

Interaction among the qubits are basis to many quantum logic operations. We report how such inter-qubit interactions can lead to new features, in the form of bright and dark periods in the entanglement dynamics of two qubits subject to environmental perturbations. These features are seen to be precursors to the well known phenomenon of sudden death of entanglement [Yu & Eberly, Phys. Rev. Lett. {\bf 93}, 140404 (2004)] for noninteracting qubits. Further we find that the generation of bright and dark periods are generic and occur for wide varieties of the models of environment. We present explicit results for two popular models.Comment: New published version, corrected figure

Strong Topological Rigidity of Non-Compact Orientable Surfaces

We show that if a homotopy equivalence between two non-compact orientable (finite or infinite-type) surfaces is proper, then it is properly homotopic to a homeomorphism, provided surfaces are neither the plane nor the punctured plane. Thus all non-compact orientable surfaces, except the plane and the punctured plane, are topologically rigid in a strong sense.Comment: 22 pages, 8 figures. Everything has been revised drastically. The current version contains a much stronger statement than the previous one: The non-zero degree assumption of the main theorem of the earlier version follows from the main theorem of the current version, provided the punctured plane is also omitted from the hypothesis. Comments Welcome

Quantum interference effects in an ensemble of 229^{229}Th nuclei interacting with coherent light

As a unique feature, the $^{229}$Th nucleus has an isomeric transition in the vacuum ultraviolet that can be accessed by optical lasers. The interference effects occurring in the interaction between coherent optical light and an ensemble of $^{229}$Th nuclei are investigated theoretically. We consider the scenario of nuclei doped in vacuum ultraviolet-vacuum ultraviolet transparent crystals and take into account the effect of different doping sites and therefore different lattice fields that broaden the nuclear transition width. This effect is shown to come in interplay with interference effects due to the hyperfine splitting of the ground and isomeric nuclear states. We investigate possible experimentally available situations involving two-, three- and four-level schemes of quadrupole sublevels of the ground and isomeric nuclear states coupling to one or two coherent fields. Specific configurations which offer clear signatures of the isomer excitation advantageous for the more precise experimental determination of the transition energy are identified. Furthermore, it is shown that population trapping into the isomeric state can be achieved. This paves the way for further nuclear quantum optics applications with $^{229}$Th such as nuclear coherent control.Comment: 14 papes, 13 figure

Quantum correlations and violation of Bell inequality induced by External Field in a two photon radiative cascade

We study the polarization dependent second order correlation of a pair of photons emitted in a four level radiative cascade driven by an external field. It is found that the quantum correlations of the emitted photons, degraded by the energy splitting of the intermediate levels in the radiative cascade can be efficiently revived by a far detuned external field. The physics of this revival is linked to an induced stark shift and the formation of dressed states in the system by the non-resonant external field. Further, we investigated the competition between the effect of the coherent external field and incoherent dephasing of the intermediate levels. We found that the degradation of quantum correlations due to the incoherent dephasing can be content for small dephasing with the external field. We also studied the non-locality of the correlations by evaluating the Bell's inequality in the linear polarization basis for the radiative cascade. We find that the Bell parameter decreases rapidly with increase in the intermediate level energy splitting or incoherent dephasing rate to the extent that there is no violation. However, the presence of an external field leads to control over the degrading mechanisms and preservation of nonlocal correlation among the photons. This in turn can induce, violation of Bell's inequality in the radiative cascade for arbitrary intermediate level splitting and small incoherent dephasing