This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as 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.

/pdf/many-body-physics-with-ultracold-gases-552s10zfdn.pdf

Many-Body Physics with Ultracold Gases

Experiments with ultracold quantum gases provide a platform for creating many-body systems that can be well controlled and whose parameters can be tuned over a wide range. These properties put these systems in an ideal position for simulating problems that are out of reach for classical computers. This review surveys key advances in this field and discusses the possibilities offered by this approach to quantum simulation.

/pdf/quantum-simulations-with-ultracold-quantum-gases-46hfprb333.pdf

Quantum simulations with ultracold quantum gases

One of Feynman's early applications of path integrals was to superfluid $^{4}\mathrm{He}$. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of interacting classical "ring polymer." Using this mapping, one can generalize Monte Carlo simulation techniques commonly used for classical systems to simulate boson systems. In this review, the author introduces this picture of a boson superfluid and shows how superfluidity and Bose condensation manifest themselves. He shows the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution. Major aspects of computational techniques developed for a boson superfluid are discussed: the construction of more accurate approximate density matrices to reduce the number of points on the path integral, sampling techniques to move through the space of exchanges and paths quickly, and the construction of estimators for various properties such as the energy, the momentum distribution, the superfluid density, and the exchange frequency in a quantum crystal. Finally the path-integral Monte Carlo method is compared to other quantum Monte Carlo methods.

Path integrals in the theory of condensed helium

The physics of quantum degenerate atomic 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 that 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 broad 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, on 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 nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.

/pdf/theory-of-ultracold-atomic-fermi-gases-3ed32dmdoj.pdf

Theory of ultracold atomic Fermi gases

Results of room-temperature Raman scattering studies of ultrathin graphitic films supported on Si (100)/SiO2 substrates are reported. The results are significantly different from those known for graphite. Spectra were collected using 514.5 nm radiation on films containing from n = 1 to 20 graphene layers, as determined by atomic force microscopy. Both the first- and second-order Raman spectra show unique signatures of the number of layers in the film. The nGL film analogue of the Raman G-band in graphite exhibits a Lorentzian line shape whose center frequency shifts linearly relative to graphite as ∼1/n (for n = 1 ωG ≈ 1587 cm-1). Three weak bands, identified with disorder-induced first-order scattering, are observed at ∼1350, 1450, and 1500 cm-1. The ∼1500 cm-1 band is weak but relatively sharp and exhibits an interesting n-dependence. In general, the intensity of these D-bands decreases dramatically with increasing n. Three second-order bands are also observed (∼2450, ∼2700, and 3248 cm-1). They are ana...

Raman Scattering from High-Frequency Phonons in Supported n-Graphene Layer Films

We calculate the equation of state of a two-component Fermi gas with attractive short-range interspecies interactions using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value $a$ of the $s$-wave scattering length of the two-body potential. For $ag0$ and $a$ smaller than the inverse Fermi wave vector our results show a molecular regime with repulsive interactions well described by the dimer-dimer scattering length ${a}_{m}=0.6a$. The pair correlation functions of parallel and opposite spins are also discussed as a function of the interaction strength.

Equation of State of a Fermi Gas in the BEC-BCS Crossover: A Quantum Monte Carlo Study

By means of a quadratic diffusion Monte Carlo method we have performed a comparative analysis between the Aziz potential and a revised version of it. The results demonstrate that the revised version produces a better description of the equation of state for liquid [sup 4]He. In spite of the improvement in the description of derivative magnitudes of the energy, as the pressure or the compressibility, the energy per particle which comes from this revised potential is lower than the experimental one. The inclusion of three-body interactions, which give a repulsive contribution to the potential energy, makes it feasible that the calculated energy comes close to the experimental result.

Monte Carlo analysis of an interatomic potential for He.

We consider a homogeneous 1D Bose gas with contact interactions and a large attractive coupling constant. This system can be realized in tight waveguides by exploiting a confinement induced resonance of the effective 1D scattering amplitude. By using the diffusion Monte Carlo method we show that, for small densities, the gaslike state is well described by a gas of hard rods. The critical density for cluster formation is estimated using the variational Monte Carlo method. The behavior of the correlation functions and of the frequency of the lowest breathing mode for harmonically trapped systems shows that the gas is more strongly correlated than in the Tonks-Girardeau regime.

Beyond the Tonks-Girardeau gas: strongly correlated regime in quasi-one-dimensional Bose gases.

A Monte Carlo algorithm for computing quantum-mechanical expectation values of coordinate operators in many-body problems is presented The algorithm, which relies on the forward walking method, fits naturally in a Green's function Monte Carlo calculation, ie, it does not require side walks or a bilinear sampling method Our method evidences stability regions large enough to accurately sample unbiased pure expectation values The proposed algorithm yields accurate results when it is applied to test problems such as the hydrogen atom and the hydrogen molecule An excellent description of several properties of a fully many-body problem such as liquid $^{4}\mathrm{He}$ at zero temperature is achieved

Unbiased estimators in quantum Monte Carlo methods: Application to liquid 4 He

We use a diffusion Monte Carlo method to calculate the lowest-energy state of a uniform gas of bosons interacting through different model potentials, both strictly repulsive and with an attractive well. We explicitly verify that at low density the energy per particle follows a universal behavior fixed by the gas parameter ${\mathrm{na}}^{3}.$ In the regime of densities typical for experiments in trapped Bose-condensed gases, the corrections to the mean-field energy greatly exceed the differences due to the details of the potential.

Joaquim Casulleras

Papers

Equation of State of a Fermi Gas in the BEC-BCS Crossover: A Quantum Monte Carlo Study

Monte Carlo analysis of an interatomic potential for He.

Beyond the Tonks-Girardeau gas: strongly correlated regime in quasi-one-dimensional Bose gases.

Unbiased estimators in quantum Monte Carlo methods: Application to liquid 4 He

Ground state of a homogeneous Bose gas: A diffusion Monte Carlo calculation