Entanglement and entropy engineering of atomic two-qubit mixed states

Abstract

We propose and analyze a number of schemes to deterministically entangle pairs of atoms through their interaction with quantum-correlated reservoirs. These reservoirs are created using sources of squeezed light, such as the degenerate or non-degenerate parametric amplifier, or by means of quantum-reservoir engineering [1]. The atoms become entangled when the phase-sensitive correlations present in the reservoir transfer to the atoms [2]. In a succession of models, we consider pairs of atoms that are either in free space, or trapped in one or more high-finesse optical micro-cavities. For atoms in a cavity QED situation, a variety of possible atomic level schemes are investigated, in which coherent driving lasers and the quantized cavity mode are used to initiate Raman transitions between two meta-stable atomic ground states. In particular, we find a 4-level atomic configuration for an atom in a cavity, which, in the appropriate limits, is shown to interact with a single squeezed cavity mode in a manner that is entirely analogous to the interaction of a single atom in free space with a broadband squeezed vacuum. For each system we find the reduced master equation for the atomic ground states and investigate the dynamics of this master equation using the entropy-entanglement plane. Under appropriate conditions, we find that the atoms may be modelled as a pair of two-level systems (qubits) for which the amplitude and phase coupling to the quantum reservoir are independently adjustable. Using local unitary transformations and appropriate manipulation of the amplitude and phase decay rates, we can then generate non-maximally entangled mixed states covering the full range of the Linear Entropy-Entanglement of Formation plane. The most promising scheme we have developed uses quantum-reservoir engineering to entangle two 5-level atoms trapped in a single optical cavity. An effective squeezed reservoir is created without the need for non-classical sources of light. The deleterious effects of spontaneous emission from the excited atomic states during the Raman transition are investigated for this model. Even in the presence of spontaneous emission we can generate states covering a broad region of the Linear Entropy-Entanglement of Formation plane, including areas above the line corresponding to the Werner states.