Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations

A remarkable feature of typical ground states of strongly-correlated many-body systems is that the entanglement entropy is not an extensive quantity. In one dimension, there exists a proof that a finite correlation length sets a constant upper-bound on the entanglement entropy, called the area law. However, the known bound exists only in a hypothetical limit, rendering its physical relevance highly questionable. In this paper, we give a simple proof of the area law for entanglement entropy in one dimension under the condition of exponentially decaying correlations. Our proof dramatically reduces the previously known bound on the entanglement entropy, bringing it, for the first time, into a realistic regime. The proof is composed of several simple and straightforward steps based on elementary quantum information tools. We discuss the underlying physical picture, based on a renormalization-like construction underpinning the proof, which transforms the entanglement entropy of a continuous region into a sum of mutual informations in different length scales and the entanglement entropy at the boundary

Addressing individual atoms in optical lattices with standing-wave driving fields

A scheme for addressing individual atoms in one- or two-dimensional optical lattices loaded with one atom per site is proposed. The scheme is based on position-dependent atomic population transfer induced by several standing-wave driving fields. This allows various operations important in quantum information processing, such as manipulation and measurement of any single atom, two-qubit operations between any pair of adjacent atoms, and patterned loading of the lattice with one atom per every nth site for arbitrary n. The proposed scheme is robust against considerable imperfections and actually within reach of current technology.Comment: 4 pages, 3 figures; minor revision

Two-dimensional imaging of gauge fields in optical lattices

We propose a scheme to generate an arbitrary Abelian vector potential for atoms trapped in a two-dimensional optical lattice. By making the optical lattice potential dependent on the atomic state, we transform the problem into that of a two-dimensional imaging. It is shown that an arbitrarily fine pattern of the gauge field in the lattice can be realized without need of diffraction-limited imaging.Comment: 4 pages, 3 figure

Generation of Atomic Cluster States through the Cavity Input-Output Process

We propose a scheme to implement a two-qubit controlled-phase gate for single atomic qubits, which works in principle with nearly ideal success probability and fidelity. Our scheme is based on the cavity input-output process and the single photon polarization measurement. We show that, even with the practical imperfections such as atomic spontaneous emission, weak atom-cavity coupling, violation of the Lamb-Dicke condition, cavity photon loss, and detection inefficiency, the proposed gate is feasible for generation of a cluster state in that it meets the scalability criterion and it operates in a conclusive manner. We demonstrate a simple and efficient process to generate a cluster state with our high probabilistic entangling gate

Boundary effect and quantum phases in spin chains

Boundary effect is a widespread idea in many-body theories. However, it is more of a conceptual notion than a rigorously defined physical quantity. One can quantify the boundary effect by comparing two ground states of the same physical model, which differ only slightly in system size. Here, we analyze the quantity, which we call a boundary effect function, for an XXZ spin-1/2 model using density matrix renormalization group calculations. We find that three quantum phases of the model manifest as different functional forms of the boundary effect function. As a result, the quantum phase transition of the model is associated with a nonanalytic change of the boundary effect function. This work thus provides and concretizes a novel perspective on the relationship between bulk and boundary properties of ground states.Comment: 9 pages, 3 figure