Effective Hamiltonian for fermions in an optical lattice across Feshbach resonance

We derive the Hamiltonian for cold fermionic atoms in an optical lattice across a broad Feshbach resonance, taking into account of both multiband occupations and neighboring-site collisions. Under typical configurations, the resulting Hamiltonian can be dramatically simplified to an effective single-band model, which describes a new type of resonance between the local dressed molecules and the valence bond states of fermionic atoms at neighboring sites. On different sides of such a resonance, the effective Hamiltonian is reduced to either a t-J model for the fermionic atoms or an XXZ model for the dressed molecules. The parameters in these models are experimentally tunable in the full range, which allows for observation of various phase transitions.Comment: 5 pages, 2 figure

Oscillating Superfluidity of Bosons in Optical Lattices

We follow up on a recent suggestion by C. Orzel et. al., Science, 291, 2386 (2001), whereby bosons in an optical lattice would be subjected to a sudden parameter change from the Mott to the superfluid phase. We analyze the Bose Hubbard model with a modified coherent states path integral which can escribe - both - phases. The saddle point theory yields collective oscillations of the uniform superfluid order parameter. These would be seen in time resolved interference patterns made by the released gas. We calculate the collective oscillation's damping rate by phason pair emission. In two dimensions the overdamped region largely overlaps with the quantum critical region. Measurements of critical dynamics on the Mott side are proposed.Comment: 4 pages 1 eps figures; Final version as appears in PRL. Added discussion on spontaneous generation of vortice

Valence-bond-solid order in antiferromagnets with spin-lattice coupling

We propose that a valence-bond-solid (VBS) order can be stabilized in certain two-dimensional antiferromagnets due to spin-lattice coupling. In contrast to the VBS state of the Affleck-Kennedy-Lieb-Tesaki (AKLT) type in which the spin $2S$ and the lattice coordination $z$ must be commensurate, the spin-lattice coupling-induced VBS state can occur when $2S$ is not an integer multiple of $z$. As a concrete example, S=2 spins on the triangular network with $z=6$ is discussed. Within the Schwinger boson mean-field theory it is shown that the ground state is given by the $\sqrt{3}\times\sqrt{3}$ modulation of the valence bond amplitudes for sufficiently strong spin-lattice coupling. Using the corresponding AKLT wave function, we work out the excitation spectrum for this state within the single-mode approximation. The calculated spectrum should provide a new type of collective mode which is distinct from the spin wave excitations of the magnetically ordered ground state

Control of gradient-driven instabilities using shear Alfv\'en beat waves

A new technique for manipulation and control of gradient-driven instabilities through nonlinear interaction with Alfv\'en waves in a laboratory plasma is presented. A narrow field-aligned density depletion is created in the Large Plasma Device (LAPD), resulting in coherent unstable fluctuations on the periphery of the depletion. Two independent kinetic Alfv\'en waves are launched along the depletion at separate frequencies, creating a nonlinear beat-wave response at or near the frequency of the original instability. When the beat-wave has sufficient amplitude, the original unstable mode is suppressed, leaving only the beat-wave response at a different frequency, generally at lower amplitude.Comment: Submitted for Publication in Physical Review Letters. Revision 2 reflects changes suggested by referees for PRL submission. One figure removed, several major changes to another figure, and a number of major and minor changes to the tex

Dissipation-induced d-Wave Pairing of Fermionic Atoms in an Optical Lattice

We show how dissipative dynamics can give rise to pairing for two-component fermions on a lattice. In particular, we construct a "parent" Liouvillian operator so that a BCS-type state of a given symmetry, e.g. a d-wave state, is reached for arbitrary initial states in the absence of conservative forces. The system-bath couplings describe single-particle, number conserving and quasi-local processes. The pairing mechanism crucially relies on Fermi statistics. We show how such Liouvillians can be realized via reservoir engineering with cold atoms representing a driven dissipative dynamics.Comment: 5 pages, 3 figures. Replaced with the published versio

The Kagome Antiferromagnet: A Schwinger-Boson Mean-Field Theory Study

The Heisenberg antiferromagnet on the Kagom\'{e} lattice is studied in the framework of Schwinger-boson mean-field theory. Two solutions with different symmetries are presented. One solution gives a conventional quantum state with $\mathbf{q}=0$ order for all spin values. Another gives a gapped spin liquid state for spin $S=1/2$ and a mixed state with both $\mathbf{q}=0$ and $\sqrt{3}\times \sqrt{3}$ orders for spin $S>1/2$. We emphasize that the mixed state exhibits two sets of peaks in the static spin structure factor. And for the case of spin $S=1/2$, the gap value we obtained is consistent with the previous numerical calculations by other means. We also discuss the thermodynamic quantities such as the specific heat and magnetic susceptibility at low temperatures and show that our result is in a good agreement with the Mermin-Wagner theorem.Comment: 9 pages, 5 figure

A Path Intergal Approach to Current

Discontinuous initial wave functions or wave functions with discontintuous derivative and with bounded support arise in a natural way in various situations in physics, in particular in measurement theory. The propagation of such initial wave functions is not well described by the Schr\"odinger current which vanishes on the boundary of the support of the wave function. This propagation gives rise to a uni-directional current at the boundary of the support. We use path integrals to define current and uni-directional current and give a direct derivation of the expression for current from the path integral formulation for both diffusion and quantum mechanics. Furthermore, we give an explicit asymptotic expression for the short time propagation of initial wave function with compact support for both the cases of discontinuous derivative and discontinuous wave function. We show that in the former case the probability propagated across the boundary of the support in time $\Delta t$ is $O(\Delta t^{3/2})$ and the initial uni-directional current is $O(\Delta t^{1/2})$. This recovers the Zeno effect for continuous detection of a particle in a given domain. For the latter case the probability propagated across the boundary of the support in time $\Delta t$ is $O(\Delta t^{1/2})$ and the initial uni-directional current is $O(\Delta t^{-1/2})$. This is an anti-Zeno effect. However, the probability propagated across a point located at a finite distance from the boundary of the support is $O(\Delta t)$. This gives a decay law.Comment: 17 pages, Late

Relativistic deformed mean-field calculation of binding energy differences of mirror nuclei

Binding energy differences of mirror nuclei for A=15, 17, 27, 29, 31, 33, 39 and 41 are calculated in the framework of relativistic deformed mean-field theory. The spatial components of the vector meson fields and the photon are fully taken into account in a self-consistent manner. The calculated binding energy differences are systematically smaller than the experimental values and lend support to the existency of the Okamoto--Nolen-Schiffer anomaly found decades ago in nonrelativistic calculations. For the majority of the nuclei studied, however, the results are such that the anomaly is significantly smaller than the one obtained within state-of-the-art nonrelativistic calculations.Comment: 13 pages, REVTeX, no figure

Exploring Contractor Renormalization: Tests on the 2-D Heisenberg Antiferromagnet and Some New Perspectives

Contractor Renormalization (CORE) is a numerical renormalization method for Hamiltonian systems that has found applications in particle and condensed matter physics. There have been few studies, however, on further understanding of what exactly it does and its convergence properties. The current work has two main objectives. First, we wish to investigate the convergence of the cluster expansion for a two-dimensional Heisenberg Antiferromagnet(HAF). This is important because the linked cluster expansion used to evaluate this formula non-perturbatively is not controlled by a small parameter. Here we present a study of three different blocking schemes which reveals some surprises and in particular, leads us to suggest a scheme for defining successive terms in the cluster expansion. Our second goal is to present some new perspectives on CORE in light of recent developments to make it accessible to more researchers, including those in Quantum Information Science. We make some comparison to entanglement-based approaches and discuss how it may be possible to improve or generalize the method.Comment: Completely revised version accepted by Phy Rev B; 13 pages with added material on entropy in COR