SU(N) Fermions in a One-Dimensional Harmonic Trap

We conduct a theoretical study of SU(N) fermions confined by a one-dimensional harmonic potential. Firstly, we introduce a new numerical approach for solving the trapped interacting few-body problem, by which one may obtain accurate energy spectra across the full range of interaction strengths. In the strong-coupling limit, we map the SU(N) Hamiltonian to a spin-chain model. We then show that an existing, extremely accurate ansatz - derived for a Heisenberg SU(2) spin chain - is extendable to these N-component systems. Lastly, we consider balanced SU(N) Fermi gases that have an equal number of particles in each spin state for N=2, 3, 4. In the weak- and strong-coupling regimes, we find that the ground-state energies rapidly converge to their expected values in the thermodynamic limit with increasing atom number. This suggests that the many-body energetics of N-component fermions may be accurately inferred from the corresponding few-body systems of N distinguishable particles.Comment: 15 pages, 6 figure

Frustrated orbital Feshbach resonances in a Fermi gas

The orbital Feshbach resonance (OFR) is a novel scheme for magnetically tuning the interactions in closed-shell fermionic atoms. Remarkably, unlike the Feshbach resonances in alkali atoms, the open and closed channels of the OFR are only very weakly detuned in energy. This leads to a unique effect whereby a medium in the closed channel can Pauli block, or frustrate, the two-body scattering processes. Here, we theoretically investigate the impact of frustration in the few- and many-body limits of the experimentally accessible three-dimensional $^{173}$Yb system. We find that by adding a closed-channel atom to the two-body problem, the binding energy of the ground state is significantly suppressed, and by introducing a closed-channel Fermi sea to the many-body problem, we can drive the system towards weaker fermion pairing. These results are potentially relevant to superconductivity in solid-state multiband materials, as well as to the current and continuing exploration of unconventional Fermi-gas superfluids near the OFR.Comment: 14 pages, 6 figure

Pairing in spin polarized two-species fermionic mixtures with mass asymmetry

We discuss on the pairing mechanism of fermions with mismatch in their fermi momenta due to a mass asymmetry. Using a variational ansatz for the ground state we also discuss the BCS -BEC crossover of this system. It is shown that the breached pairing solution with a single fermi surface is stable in the BEC regime. We also include the temperatures effect on the fermion pairing within an approximation that is valid for temperatures much below the critical temperature.Comment: 8 pages and 6 figures, few typos corrected, version to appear in EPJ

Asymmetric Fermi superfluid with different atomic species in a harmonic trap

We study the dilute fermion gas with pairing between two species and unequal concentrations in a harmonic trap using the mean field theory and the local density approximation. We found that the system can exhibit a superfluid shell structure sandwiched by the normal fermions. This superfluid shell structure occurs if the mass ratio is larger then certain critical value which increases from the weak-coupling BCS region to the strong-coupling BEC side. In the strong coupling BEC regime, the radii of superfluid phase are less sensitive to the mass ratios and are similar to the case of pairing with equal masses. However, the lighter leftover fermions are easier to mix with the superfluid core than the heavier ones. A partially polarized superfluid can be found if the majority fermions are lighter, whereas phase separation is still found if they are heavier.Comment: 12 pages, 7 figure

p-wave phase shift and scattering length of 6^6Li

We have calculated the p-wave phase shifts and scattering length of $^6$Li. For this we solve the $p$ partial wave Schr\"odinger equation and analyze the validity of adopting the semiclassical solution to evaluate the constant factors in the solution. Unlike in the $s$ wave case, the semiclassical solution does not provide unique value of the constants. We suggest an approximate analytic solution, which provides reliable results in special cases. Further more, we also use the variable phase method to evaluate the phase shifts. The p-wave scattering lengths of $^{132}$Cs and $^{134}$Cs are calculated to validate the schemes followed. Based on our calculations, the value of the $p$ wave scattering length of $^6$Li is $-45a_o$.Comment: 10 figure

Control of CydB and GltA1 Expression by the SenX3 RegX3 Two Component Regulatory System of Mycobacterium tuberculosis

Two component regulatory systems are used widely by bacteria to coordinate changes in global gene expression profiles in response to environmental signals. The SenX3-RegX3 two component system of Mycobacterium tuberculosis has previously been shown to play a role in virulence and phosphate-responsive control of gene expression. We demonstrate that expression of SenX3-RegX3 is controlled in response to growth conditions, although the absolute changes are small. Global gene expression profiling of a RegX3 deletion strain and wild-type strain in different culture conditions (static, microaerobic, anaerobic), as well as in an over-expressing strain identified a number of genes with changed expression patterns. Among those were genes previously identified as differentially regulated in aerobic culture, including ald (encoding alanine dehydrogenase) cyd,encoding a subunit of the cytochrome D ubiquinol oxidase, and gltA1, encoding a citrate synthase. Promoter activity in the upstream regions of both cydB and gltA1 was altered in the RegX3 deletion strain. DNA-binding assays confirmed that RegX3 binds to the promoter regions of ald, cydB and gltA1 in a phosphorylation-dependent manner. Taken together these data suggest a direct role for the SenX-RegX3 system in modulating expression of aerobic respiration, in addition to its role during phosphate limitation

The BCS Functional for General Pair Interactions

The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.Comment: Revised Version. To appear in Commun. Math. Phys