Cooling Fermions in an Optical Lattice by Adiabatic Demagnetization

The Fermi-Hubbard model describes ultracold fermions in an optical lattice and exhibits antiferromagnetic long-ranged order below the N\'{e}el temperature. However, reaching this temperature in the lab has remained an elusive goal. In other atomic systems, such as trapped ions, low temperatures have been successfully obtained by adiabatic demagnetization, in which a strong effective magnetic field is applied to a spin-polarized system, and the magnetic field is adiabatically reduced to zero. Unfortunately, applying this approach to the Fermi-Hubbard model encounters a fundamental obstacle: the $SU(2)$ symmetry introduces many level crossings that prevent the system from reaching the ground state, even in principle. However, by breaking the $SU(2)$ symmetry with a spin-dependent tunneling, we show that adiabatic demagnetization can achieve low temperature states. Using density matrix renormalization group (DMRG) calculations in one dimension, we numerically find that demagnetization protocols successfully reach low temperature states of a spin-anisotropic Hubbard model, and we discuss how to optimize this protocol for experimental viability. By subsequently ramping spin-dependent tunnelings to spin-independent tunnelings, we expect that our protocol can be employed to produce low-temperature states of the Fermi-Hubbard Model.Comment: References adde

Bosonic molecules in a lattice: unusual fluid phase from multichannel interactions

We show that multichannel interactions significantly alter the phase diagram of ultracold bosonic molecules in an optical lattice. Most prominently, an unusual fluid region intervenes between the conventional superfluid and the Mott insulator. In it, number fluctuations remain but phase coherence is suppressed by a significant factor. This factor can be made arbitrarily large, at least in a two-site configuration. We calculate the phase diagram using complementary methods, including Gutzwiller mean-field and density matrix renormalization group (DMRG) calculations. Although we focus on bosonic molecules without dipolar interactions, we expect multichannel interactions to remain important for dipolar interacting and fermionic molecules.Comment: 6 pages incl. refs, 4 figure

Ultracold nonreactive molecules in an optical lattice: connecting chemistry to many-body physics

We derive effective lattice models for ultracold bosonic or fermionic nonreactive molecules (NRMs) in an optical lattice, analogous to the Hubbard model that describes ultracold atoms in a lattice. In stark contrast to the Hubbard model, which is commonly assumed to accurately describe NRMs, we find that the single on-site interaction parameter $U$ is replaced by a multi-channel interaction, whose properties we elucidate. The complex, multi-channel collisional physics is unrelated to dipolar interactions, and so occurs even in the absence of an electric field or for homonuclear molecules. We find a crossover between coherent few-channel models and fully incoherent single-channel models as the lattice depth is increased. We show that the effective model parameters can be determined in lattice modulation experiments, which consequently measure molecular collision dynamics with a vastly sharper energy resolution than experiments in an ultracold gas.Comment: 4 pages+refs, 3 figures; 2.5 pages+1 figure Supplemental Materia

Microscopic derivation of multi-channel Hubbard models for ultracold nonreactive molecules in an optical lattice

Recent experimental advances in the cooling and manipulation of bialkali dimer molecules have enabled the production of gases of ultracold molecules that are not chemically reactive. It has been presumed in the literature that in the absence of an electric field the low-energy scattering of such nonreactive molecules (NRMs) will be similar to atoms, in which a single $s$-wave scattering length governs the collisional physics. However, in Ref. [1], it was argued that the short-range collisional physics of NRMs is much more complex than for atoms, and that this leads to a many-body description in terms of a multi-channel Hubbard model. In this work, we show that this multi-channel Hubbard model description of NRMs in an optical lattice is robust against the approximations employed in Ref. [1] to estimate its parameters. We do so via an exact, albeit formal, derivation of a multi-channel resonance model for two NRMs from an ab initio description of the molecules in terms of their constituent atoms. We discuss the regularization of this two-body multi-channel resonance model in the presence of a harmonic trap, and how its solutions form the basis for the many-body model of Ref. [1]. We also generalize the derivation of the effective lattice model to include multiple internal states (e.g., rotational or hyperfine). We end with an outlook to future research.Comment: 19 pages, 4 figure

Regulation of Dendritic Protein Synthesis by Miniature Synaptic Events

We examined dendritic protein synthesis after a prolonged blockade of action potentials alone and after a blockade of both action potentials and miniature excitatory synaptic events (minis). Relative to controls, dendrites exposed to a prolonged blockade of action potentials showed diminished protein synthesis. Dendrites in which both action potentials and minis were blocked showed enhanced protein synthesis, suggesting that minis inhibit dendritic translation. When minis were acutely blocked or stimulated, an immediate increase or decrease, respectively, in dendritic translation was observed. Taken together, these results reveal a role for miniature synaptic events in the acute regulation of dendritic protein synthesis in neurons

Hubbard parameters for programmable tweezer arrays

The experimental realization of Fermi-Hubbard tweezer arrays opens a new stage for engineering fermionic matter, where programmable lattice geometries and Hubbard model parameters are combined with single-site imaging. In order to use these versatile experimental Fermi-Hubbard models as quantum simulators, it is crucial to know the Hubbard parameters describing them. Here we develop methods to calculate the Hubbard model parameters of arbitrary two-dimensional lattice geometries: the tunneling $t$, on-site potential $V$, and interaction $U$, for multiple bands and for both fermions and bosons. We show several examples. One notable finding is that a finite array of equally strong and separated individual tweezer potentials actually sums to give a non-periodic total potential and thus spatially non-uniform Hubbard parameters. We demonstrate procedures to find trap configurations that equalize these parameters. More generally, these procedures solve the inverse problem of calculating Hubbard parameters: given desired Hubbard parameters, find trap configurations to realize them. These methods will be critical tools for using tunnel-coupled tweezer arrays.Comment: 14 pages, 8 figure

Balancing Pastoral and Plantation Forestry Options in New Zealand and the Role of Agroforestry

Pastoral agriculture and forestry enterprises are key features of New Zealand’s landscape and are very important economically. They are competing landuses, particularly on moderate to steep hill country. Agroforestry involving spaced trees of Pinus radiata on pasture was developed in the 1970s to provide dual incomes from livestock enterprises and the later tree crop. In contrast, wide-spaced trees of predominantly Populus and Salix spp. are planted mainly for erosion control. Characteristics of pastoralism and plantation forestry are reviewed, including trends in conversions between these landuses. Roles, challenges and opportunities with wide-spaced trees are presented, together with current and future research initiatives. Pastoralism and forestry will continue to compete strongly for hill country sites and at present there is an increasing trend of converting previously forested areas to pasture, particularly in the central North Island. Agroforestry involving Pinus radiata has virtually ceased because of adverse effects on wood quality, pasture production and animal performance. There are millions of wide-spaced trees of Populus and Salix spp. on hill country and their planting is expected to continue unabated because they are the most practical and efficient means of enabling pastoralism on erodible slopes and they provide multiple ecosystem services. The species have significant advantages compared to other woody species but many older trees have grown very large because they have received negligible or no silviculture. This is an increasing problem, requiring development and implementation of appropriate management strategies. There is growing interest by landowners in the environmental outcomes of spaced-tree plantings