Quantum control of spin-correlations in ultracold lattice gases

We demonstrate that it is possible to prepare a lattice gas of ultracold atoms with a desired non-classical spin-correlation function using atom-light interaction of the kind routinely employed in quantum spin polarization spectroscopy. Our method is based on quantum non-demolition (QND) measurement and feedback, and allows in particular to create on demand exponentially or algebraically decaying correlations, as well as a certain degree of multi-partite entanglement.Comment: 2 figure

Separable approximations of density matrices of composite quantum systems

We investigate optimal separable approximations (decompositions) of states rho of bipartite quantum systems A and B of arbitrary dimensions MxN following the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261 (1998)]. Such approximations allow to represent in an optimal way any density operator as a sum of a separable state and an entangled state of a certain form. For two qubit systems (M=N=2) the best separable approximation has a form of a mixture of a separable state and a projector onto a pure entangled state. We formulate a necessary condition that the pure state in the best separable approximation is not maximally entangled. We demonstrate that the weight of the entangled state in the best separable approximation in arbitrary dimensions provides a good entanglement measure. We prove in general for arbitrary M and N that the best separable approximation corresponds to a mixture of a separable and an entangled state which are both unique. We develop also a theory of optimal separable approximations for states with positive partial transpose (PPT states). Such approximations allow to decompose any density operator with positive partial transpose as a sum of a separable state and an entangled PPT state. We discuss procedures of constructing such decompositions.Comment: 12 pages, 2 figure

Generalized spin squeezing inequalities in NN qubit systems: theory and experiment

We present detailed derivations, various improvements and application to concrete experimental data of spin squeezing inequalities formulated recently by some of us [Phys. Rev. Lett. {\bf 95}, 120502 (2005)]. These inequalities generalize the concept of the spin squeezing parameter, and provide necessary and sufficient conditions for genuine 2-, or 3- qubit entanglement for symmetric states, and sufficient entanglement condition for general $N$-qubit states. We apply our method to theoretical study of Dicke states, and, in particular, to $W$-states of $N$ qubits. Then, we analyze the recently experimentally generated 7- and 8-ion $W$-states [Nature {\bf 438}, 643 (2005)]. We also present some novel details concerning this experiment. Finally, we improve criteria for detection of genuine tripartite entanglement based on entanglement witnesses.Comment: Final versio

Three level atom optics in dipole traps and waveguides

An analogy is explored between a setup of three atomic traps coupled via tunneling and an internal atomic three-level system interacting with two laser fields. Within this scenario we describe a STIRAP like process which allows to move an atom between the ground states of two trapping potentials and analyze its robustness. This analogy is extended to other robust and coherent transport schemes and to systems of more than a single atom. Finally it is applied to manipulate external degrees of freedom of atomic wave packets propagating in waveguides.Comment: 14 pages, 6 figures; submitted to special issue 'Quantum Control of Light and Matter' of Optics Communication

Entangled symmetric states of N qubits with all positive partial transpositions

From both theoretical and experimental points of view symmetric states constitute an important class of multipartite states. Still, entanglement properties of these states, in particular those with positive partial transposition (PPT), lack a systematic study. Aiming at filling in this gap, we have recently affirmatively answered the open question of existence of four-qubit entangled symmetric states with positive partial transposition and thoroughly characterized entanglement properties of such states [J. Tura et al., Phys. Rev. A 85, 060302(R) (2012)] With the present contribution we continue on characterizing PPT entangled symmetric states. On the one hand, we present all the results of our previous work in a detailed way. On the other hand, we generalize them to systems consisting of arbitrary number of qubits. In particular, we provide criteria for separability of such states formulated in terms of their ranks. Interestingly, for most of the cases, the symmetric states are either separable or typically separable. Then, edge states in these systems are studied, showing in particular that to characterize generic PPT entangled states with four and five qubits, it is enough to study only those that assume few (respectively, two and three) specific configurations of ranks. Finally, we numerically search for extremal PPT entangled states in such systems consisting of up to 23 qubits. One can clearly notice regularity behind the ranks of such extremal states, and, in particular, for systems composed of odd number of qubits we find a single configuration of ranks for which there are extremal states.Comment: 16 pages, typos corrected, some other improvements, extension of arXiv:1203.371

Edge Transport in 2D Cold Atom Optical Lattices

We theoretically study the observable response of edge currents in two dimensional cold atom optical lattices. As an example we use Gutzwiller mean-field theory to relate persistent edge currents surrounding a Mott insulator in a slowly rotating trapped Bose-Hubbard system to time of flight measurements. We briefly discuss an application, the detection of Chern number using edge currents of a topologically ordered optical lattice insulator

High-order harmonic generation from inhomogeneous fields

We present theoretical studies of high-order harmonic generation (HHG) produced by non-homogeneous fields as resulting from the illumination of plasmonic nanostructures with a short laser pulse. We show that both the inhomogeneity of the local fields and the confinement of the electron movement play an important role in the HHG process and lead to the generation of even harmonics and a significantly increased cutoff, more pronounced for the longer wavelengths cases studied. In order to understand and characterize the new HHG features we employ two different approaches: the numerical solution of the time dependent Schr\"odinger equation (TDSE) and the semiclassical approach known as Strong Field Approximation (SFA). Both approaches predict comparable results and show the new features, but using the semiclassical arguments behind the SFA and time-frequency analysis tools, we are able to fully understand the reasons of the cutoff extension.Comment: 25 pages, 12 figure