Biaxial spin-nematic phase of two dimensional disordered rotor models and spin-one bosons in optical lattices

We show that the ground state of disordered rotor models with quadrupolar interactions can exhibit biaxial nematic ordering in the disorder-averaged sense. We present a mean-field analysis of the model and demonstrate that the biaxial phase is stable against small quantum fluctuations. We point out the possibility of experimental realization of such rotor models using ultracold spin-one Bose atoms in a spin-dependent and disordered optical lattice in the limit of a large number of atoms per site and also suggest an imaging experiment to detect the biaxial nematicity in such systems.Comment: revtex file 7 pages, 2 figures, version published in PR

Efficient Toffoli Gates Using Qudits

The simplest decomposition of a Toffoli gate acting on three qubits requires {\em five} 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to six. We show that the number of controlled-sign gates required to implement a Toffoli gate can be reduced to just {\em three} if one of the three quantum systems has a third state that is accessible during the computation, i.e. is actually a qutrit. Such a requirement is not unreasonable or even atypical since we often artificially enforce a qubit structure on multilevel quantums systems (eg. atoms, photonic polarization and spatial modes). We explore the implementation of these techniques in optical quantum processing and show that linear optical circuits could operate with much higher probabilities of success

Quantum computing with neutral atoms

We develop a method to entangle neutral atoms using cold controlled collisions. We analyze this method in two particular set-ups: optical lattices and magnetic micro-traps. Both offer the possibility of performing certain multi-particle operations in parallel. Using this fact, we show how to implement efficient quantum error correction and schemes for fault-tolerant computing.Comment: 21 pages, 19 figure

Atom-photon entanglement generation and distribution

We extend an earlier model by Law {\it et al.} \cite{law} for a cavity QED based single-photon-gun to atom-photon entanglement generation and distribution. We illuminate the importance of a small critical atom number on the fidelity of the proposed operation in the strong coupling limit. Our result points to a promisingly high purity and efficiency using currently available cavity QED parameters, and sheds new light on constructing quantum computing and communication devices with trapped atoms and high Q optical cavities.Comment: 7 fig

Noise in Bose Josephson junctions: Decoherence and phase relaxation

Squeezed states and macroscopic superpositions of coherent states have been predicted to be generated dynamically in Bose Josephson junctions. We solve exactly the quantum dynamics of such a junction in the presence of a classical noise coupled to the population-imbalance number operator (phase noise), accounting for, for example, the experimentally relevant fluctuations of the magnetic field. We calculate the correction to the decay of the visibility induced by the noise in the non-Markovian regime. Furthermore, we predict that such a noise induces an anomalous rate of decoherence among the components of the macroscopic superpositions, which is independent of the total number of atoms, leading to potential interferometric applications.Comment: Fig 2 added; version accepted for publicatio

Matter-wave propagation in optical lattices: geometrical and flat-band effects

The geometry of optical lattices can be engineered allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question readily accessible to atomic systems is related to the speed of propagation of matter-waves as a function of the lattice geometry. To address this issue, we have investigated theoretically the quantum transport of non-interacting and weakly-interacting ultracold fermionic atoms in several 2D optical lattice geometries. We find that the triangular lattice has a higher propagation velocity compared to the square lattice, despite supporting longer paths. The body-centered square lattice has even longer paths, nonetheless the propagation velocity is yet faster. This apparent paradox arises from the mixing of the momentum states which leads to different group velocities in quantum systems. Standard band theory provides an explanation and allows for a systematic way to search and design systems with controllable matter-wave propagation. Moreover, the presence of a flat band such as in a two-leg ladder geometry leads to a dynamical density discontinuity, which contrasts the behavior of mobile and localized atoms in quantum transport. Our predictions are realizable with present experimental capability.Comment: 9 pages, 6 figure