Resummation of fermionic in-medium ladder diagrams to all orders

A system of fermions with a short-range interaction proportional to the scattering length $a$ is studied at finite density. At any order $a^n$, we evaluate the complete contributions to the energy per particle $\bar E(k_f)$ arising from combined (multiple) particle-particle and hole-hole rescatterings in the medium. This novel result is achieved by simply decomposing the particle-hole propagator into the vacuum propagator plus a medium-insertion and correcting for certain symmetry factors in the $(n-1)$-th power of the in-medium loop. Known results for the low-density expansion up to and including order $a^4$ are accurately reproduced. The emerging series in $a k_f$ can be summed to all orders in the form of a double-integral over an arctangent function. In that representation the unitary limit $a\to \infty$ can be taken and one obtains the value $\xi= 0.5067$ for the universal Bertsch parameter. We discuss also applications to the equation of state of neutron matter at low densities and mention further extensions of the resummation method.Comment: 12 pages, 7 figures, submitted to Nuclear Physics

Theory of ultracold Fermi gases

The physics of quantum degenerate Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions which play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems interactions are characterized by a single parameter, the s-wave scattering length, whose value can be tuned using an external magnetic field near a Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, of the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to non-perturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare the theoretical predictions with the available experimental results.Comment: Revised and abridged version accepted for publication in Rev. Mod. Phys.: 63 pages, 36 figure

Chemical reactivity of ultracold polar molecules: investigation of H + HCl and H + DCl collisions

Quantum scattering calculations are reported for the H+HCl(v,j=0) and H+DCl(v,j=0) collisions for vibrational levels v=0-2 of the diatoms. Calculations were performed for incident kinetic energies in the range 10-7 to 10-1 eV, for total angular momentum J=0 and s-wave scattering in the entrance channel of the collisions. Cross sections and rate coefficients are characterized by resonance structures due to quasibound states associated with the formation of the H...HCl and H...DCl van der Waals complexes in the incident channel. For the H+HCl(v,j=0) collision for v=1,2, reactive scattering leading to H_2 formation is found to dominate over non-reactive vibrational quenching in the ultracold regime. Vibrational excitation of HCl from v=0 to v=2 increases the zero-temperature limiting rate coefficient by about 8 orders of magnitude.Comment: 9 pages, 6 figures, submitted to Euro. Phys. J. topical issue on "Ultracold Polar Molecules: Formation and Collisions

Adiabatic Phase Diagram of an Ultracold Atomic Fermi Gas with a Feshbach Resonance

We determine the adiabatic phase diagram of a resonantly-coupled system of Fermi atoms and Bose molecules confined in the harmonic trap by using the local density approximation. The adiabatic phase diagram shows the fermionic condensate fraction composed of condensed molecules and Cooper pair atoms. The key idea of our work is conservation of entropy through the adiabatic process, extending the study of Williams et al. [Williams et al., New J. Phys. 6, 123 (2004)] for an ideal gas mixture to include the resonant interaction in a mean-field theory. We also calculate the molecular conversion efficiency as a function of initial temperature. Our work helps to understand recent experiments on the BCS-BEC crossover, in terms of the initial temperature measured before a sweep of the magnetic field.Comment: 13 pages, 8 figures. In press, "Journal of the Physical Society of Japan", Vol.76, No.

Feynman diagrams versus Fermi-gas Feynman emulator

Precise understanding of strongly interacting fermions, from electrons in modern materials to nuclear matter, presents a major goal in modern physics. However, the theoretical description of interacting Fermi systems is usually plagued by the intricate quantum statistics at play. Here we present a cross-validation between a new theoretical approach, Bold Diagrammatic Monte Carlo (BDMC), and precision experiments on ultra-cold atoms. Specifically, we compute and measure with unprecedented accuracy the normal-state equation of state of the unitary gas, a prototypical example of a strongly correlated fermionic system. Excellent agreement demonstrates that a series of Feynman diagrams can be controllably resummed in a non-perturbative regime using BDMC. This opens the door to the solution of some of the most challenging problems across many areas of physics

Hydrodynamic Modes in a Trapped Strongly Interacting Fermi Gases of Atoms

The zero-temperature properties of a dilute two-component Fermi gas in the BCS-BEC crossover are investigated. On the basis of a generalization of the variational Schwinger method, we construct approximate semi-analytical formulae for collective frequencies of the radial and the axial breathing modes of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. It is shown that the method gives nearly exact solutions.Comment: 11 page

Many-Body Physics with Ultracold Gases

This article reviews recent experimental and theoretical progress on many-body phenomena in dilute, ultracold gases. Its focus are effects beyond standard weak-coupling descriptions, like the Mott-Hubbard-transition in optical lattices, strongly interacting gases in one and two dimensions or lowest Landau level physics in quasi two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near Feshbach resonances in the BCS-BEC crossover.Comment: revised version, accepted for publication in Rev. Mod. Phy

Variational Monte Carlo analysis of the Hubbard model with a confining potential: one-dimensional fermionic optical lattice systems

We investigate the one-dimensional Hubbard model with a confining potential, which may describe cold fermionic atoms trapped in an optical lattice. Combining the variational Monte Carlo simulations with the new stochastic reconfiguration scheme proposed by Sorella, we present an efficient method to systematically treat the ground state properties of the confined system with a site-dependent potential. By taking into account intersite correlations as well as site-dependent on-site correlations, we are able to describe the coexistence of the metallic and Mott insulating regions, which is consistent with other numerical results. Several possible improvements of the trial states are also addressed.Comment: 7 pages, 15 figures; removed unnecessary graphs (p.8-p.32 in the old version are removed

Collisionally inhomogeneous Bose-Einstein condensates in double-well potentials

In this work, we consider quasi-one-dimensional Bose-Einstein condensates (BECs), with spatially varying collisional interactions, trapped in double well potentials. In particular, we study a setup in which such a 'collisionally inhomogeneous' BEC has the same (attractive-attractive or repulsive-repulsive) or different (attractive-repulsive) type of interparticle interactions. Our analysis is based on the continuation of the symmetric ground state and anti-symmetric first excited state of the noninteracting (linear) limit into their nonlinear counterparts. The collisional inhomogeneity produces a saddle-node bifurcation scenario between two additional solution branches; as the inhomogeneity becomes stronger, the turning point of the saddle-node tends to infinity and eventually only the two original branches remain present, which is completely different from the standard double-well phenomenology. Finally, one of these branches changes its monotonicity as a function of the chemical potential, a feature especially prominent, when the sign of the nonlinearity changes between the two wells. Our theoretical predictions, are in excellent agreement with the numerical results.Comment: 14 pages, 12 figures, Physica D, in pres

Bosons and Fermions near Feshbach resonances

Near Feshbach resonances, $n|a|^3\gg 1$, systems of Bose and Fermi particles become strongly interacting/dense. In this unitary limit both bosons and fermions have very different properties than in a dilute gas, e.g., the energy per particle approach a value $\hbar^2n^{2/3}/m$ times an universal many-body constant. Calculations based upon an approximate Jastrow wave function can quantitatively describe recent measurements of trapped Bose and Fermi atoms near Feshbach resonances. The pairing gap between attractive fermions also scales as $\Delta\sim\hbar^2n^{2/3}/m$ near Feshbach resonances and is a large fraction of the Fermi energy - promising for observing BCS superfluidity in traps. Pairing undergoes several transitions depending on interaction strength and the number of particles in the trap and can also be compared to pairing in nuclei.Comment: Revised version extended to include recent molecular BEC-BCS result