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 a > 0 and a smaller than the inverse Fermi wavevector our results show a molecular regime with repulsive interactions well described by the dimer-dimer scattering length am = 0.6a. The pair correlation functions of parallel and opposite spins are also discussed as a function of the interaction strength. PACS numbers:Recent experiments on two-component ultracold atomic Fermi gases near a Feshbach resonance have opened the possibility of investigating the crossover from a Bose-Einstein condensate (BEC) to a BardeenCooper-Schrieffer (BCS) superfluid. In these systems the strength of the interaction can be varied over a very wide range by magnetically tuning the two-body scattering amplitude. For positive values of the s-wave scattering length a, atoms with different spins are observed to pair into bound molecules which, at low enough temperature, form a Bose condensate [1]. The molecular BEC state is adiabatically converted into an ultracold Fermi gas with a < 0 and k F |a| ≪ 1 [2], where standard BCS theory is expected to apply. In the crossover region the value of |a| can be orders of magnitude larger than the inverse Fermi wave vector k −1 F and one enters a new stronglycorrelated regime known as unitary limit [2,3]. In dilute systems, for which the effective range of the interaction R 0 is much smaller than the mean interparticle distance, k F R 0 ≪ 1, the unitary regime is believed to be universal [4,5]. In this regime, the only relevant energy scale should be given by the energy of the noninteracting Fermi gas,The unitary regime presents a challenge for many-body theoretical approaches because there is not any obvious small parameter to construct a well-posed theory. The first theoretical studies of the BEC-BCS crossover at zero temperature are based on the mean-field BCS equations [6]. More sophisticated approaches take into account the effects of fluctuations [7], or include explicitly the bosonic molecular field [8]. These theories provide a correct description in the deep BCS regime, but are only qualitatively correct in the unitary limit and in the BEC region. In particular, in the BEC regime the dimer-dimer scattering length has been calculated exactly from the solution of the four-body problem, yielding a m = 0.6a [9].Available results for the equation of state in this regime do not describe correctly the repulsive molecule-molecule interactions [10].Quantum Monte Carlo techniques are the best suited tools for treating strongly-correlated systems. These methods have already been applied to ultracold degenerate Fermi gases in a recent work by Carlson et al. [11]. In this study the energy per particle of a dilute Fermi gas in the unitary limit is calculated with the fixed-node Green's function Monte Car...

By using the diffusion Monte Carlo method we calculate the one-and two-body density matrix of an interacting Fermi gas at T = 0 in the BCS-BEC crossover. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of fermionic pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover. PACS numbers:The physics of the crossover from Bardeen-CooperSchrieffer (BCS) superfluids to molecular Bose-Einstein condensates (BEC) in ultracold Fermi gases near a Feshbach resonance is a very exciting field that has recently attracted a lot of interest, both from the experimental [1,2] and the theoretical side [3]. An important experimental achievement is the observation of a condensate of pairs of fermionic atoms on the side of the Feshbach resonance where no stable molecules would exist in vacuum [4,5]. Although the interpretation of the experiment is not straightforward, as it involves an out-of-equilibrium projection technique of fermionic pairs onto bound molecules [6], it is believed that these results strongly support the existence of a superfluid order parameter in the strongly correlated regime on the BCS side of the resonance [5].The occurrence of off-diagonal long-range order (ODLRO) in interacting systems of bosons and fermions was investigated by C.N. Yang in terms of the asymptotic behavior of the one-and two-body density matrix [7]. In the case of a two-component Fermi gas with N ↑ spin-up and N ↓ spin-down particles, the one-body density matrix (OBDM) for spin-up particles, defined asdoes not possess any eigenvalue of order N ↑ . This behavior implies for homogeneous systems the asymptotic condition ρ 1 (rIn the above expression ψ † ↑ (r) (ψ ↑ (r)) denote the creation (annihilation) operator of spin-up particles. The same result holds for spin-down particles. ODLRO may occur instead in the two-body density matrix (TBDM), that is defined asFor an unpolarized gas with N ↑ = N ↓ = N/2, if ρ 2 has an eigenvalue of the order of the total number of particles N , the TBDM can be written as a spectral decomposition separating the largest eigenvalue,2 containing only eigenvalues of order one. The parameter α ≤ 1 in Eq. (3) is interpreted as the condensate fraction of pairs, in a similar way as the condensate fraction of single atoms is derived from the OBDM.The spectral decomposition (3) yields for homogeneous systems the following asymptotic behavior of the TBDMThe complex function ϕ is proportional to the order parameter ψ ↑ (r 1 )ψ ↓ (r 2 ) = αN/2ϕ(|r 1 − r 2 |), whose appearance distinguishes the superfluid state of the Fermi gas. Equation (4) should be contrasted with the behavior of Bose systems with ODLRO, where ρ 1 has an eigenvalue of order N [8], and consequently the largest eigenvalue of ρ 2 is of the order of N 2 . In thi...

The ground-state phase diagram of a two-dimensional Bose system with dipole-dipole interactions is studied by means of quantum Monte Carlo technique. Our calculation predicts a quantum phase transition from gas to solid phase when the density increases. In the gas phase the condensate fraction is calculated as a function of the density. Using Feynman approximation, the collective excitation branch is studied and appearance of a roton minimum is observed. Results of the static structure factor at both sides of the gas-solid phase are also presented. The Lindeman ratio at the transition point comes to be γ = 0.230(6). The condensate fraction in the gas phase is estimated as a function of the density.The chromium atom has exceptionally large permanent dipole moment and recent realization of Bose-Einstein condensation of 52 Cr[1] has stimulated great interest in properties of dipolar systems at low temperatures. It was observed[2] that dipolar forces lead to anisotropic deformation during expansion of the condensate. In the experiments [1,2], the dipolar forces were competing with short-range scattering. The latter, in principle, can be removed by tuning the s-wave scattering length to zero by Feshbach resonance [3]. This would lead to an essentially pure system of dipoles. On the other hand, lowdimensional systems can be realized by making the confinement in one (or two) directions so tight, that no excitations of the levels of the tight confinement are possible and the system is dynamically two-(or one-) dimensional.A major development has also been done in the present years towards the realization of excitons at temperatures close to the Bose-Einstein condensation temperature [4]. An exciton is much more stable if the electron is spatially separated from the hole (spatially separated excitons). Such an exciton can be modeled as a dipole. If the excitons are in two coupled quantum wells they can be treated effectively as two-dimensional if the size of an exciton is small compared to the mean distance between excitons.One might expect to find a phase transition from gas phase to a crystal one at large density. As the condensate fraction is small at the transition point, perturbative theories, like Gross-Pitaevskii [5] or Bogoliubov [6,7] approaches, will fail to describe accurately this transition. One has to use ab initio numerical methods to address this quantum many-body problem. Recently a trapped system of two-dimensional dipoles has been studied by Path Integral Monte Carlo method [8] and mesoscopic analog of crystallization has been found. Trapped dipoles with s-wave scattering were investigated [9]. So far, there have been no full quantum microscopic computations of the properties of a homogeneous system of dipoles.The Hamiltonian of a homogeneous system of N bosonic dipoles has the formwhere M is the dipole mass and r i , i = 1, N are the positions of dipoles. The expression for the coupling constant C dd depends on the nature of the dipole-dipole interaction. Two possible physical realizations of a twodim...

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 new potential produces a better description of the equation of state for liquid 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 new 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.

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 follow a universal behavior fixed by the gas parameter 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.02.70. Lq, 05.30.Jp, 03.75.Fi The achievement of Bose-Einstein condensation (BEC) in magnetically trapped atomic vapours [1] has revived interest in the theoretical study of Bose gases. Mean-field methods provide us with relatively simple predictions both for the equilibrium properties of these systems (energy per particle, density profiles, condensate fraction) and for the dynamic behavior (frequency of collective excitations, interference effects), which have been found in close agreement with experiments (for a review see Ref.[2]). In fact, the atomic clouds realized in experiments are very dilute, the average distance between particles being significantly larger than the range of interatomic forces, and mean-field approaches are well suited. However, the investigation of effects beyond mean-field theory is an important task, which would make these systems even more interesting from the point of view of many-body physics. Theoretical studies of these effects have already been proposed, either by analytic inclusion of fluctuations around mean-field [3,4] or through numerical calculations based on quantum Monte Carlo methods [5] and, more recently, also on correlated basis function approaches [6]. All these investigations are based on the idea that, for the values of density relevant in experiments, the details of the interatomic potential can be neglected and one can safely use the hard-sphere model in numerical simulations, and the expansion in powers of the gas parameter na 3 , fixed by the number density n and the s-wave scattering length a, in analytic corrections beyond mean-field. The main motivation of the present work is to verify the validity of this approach. By using a diffusion Monte Carlo (DMC) method we calculate the ground-state energy of a system of bosons interacting through different two-body model potentials. We explicitly show that for the values of the gas parameter reached in magnetic traps (na 3 ≃ 1E-5 -1E-4) the behavior is universal and fixed by na 3 and that the corrections to the mean-field energy are much larger than the differences due to the details of the interatomic potential.The ground state of a homogeneous dilute Bose gas was intensively studied in the 50's and early 60's. One of the main results of this investigation is that the ground-state energy can be expanded in powers of √ na 3 . In units of h 2 /2ma 2 the energy per particle takes the formThe first term corresponds to the mean-field prediction and was already calculated by Bogoliubov [7]. The corrections...

We investigate the phenomenon of Bose-Einstein condensation and superfluidity in a Bose gas at zero temperature with disorder. By using the Diffusion Monte-Carlo method we calculate the superfluid and the condensate fraction of the system as a function of density and strength of disorder. In the regime of weak disorder we find agreement with the analytical results obtained within the Bogoliubov model. For strong disorder the system enters an unusual regime where the superfluid fraction is smaller than the condensate fraction.PACS numbers: 03.75.Fi, 05.30.Fk, 67.40.Db The study of disordered Bose systems has attracted in the recent past considerable attention both theoretically and experimentally. The problem of boson localization, the superfluid-insulator transition and the nature of elementary excitations in the presence of disorder have been the object of several theoretical investigations [1] and Monte-Carlo numerical simulations [2,3], both based on Hubbard or equivalent models on a lattice. More recently, the problem of Bose systems with disorder has also been addressed in the continuum. On the one hand, the dilute Bose gas with disorder has been studied within the Bogoliubov model [4][5][6]. On the other, Path Integral Monte-Carlo (PIMC) techniques have been applied to the study of the elementary excitations in liquid 4 He [7] and the transition temperature of a hard-sphere Bose gas [8], in the presence of randomly distributed static impurities. Disordered Bose systems are produced experimentally in liquid 4 He adsorbed in porous media, such as Vycor or silica gels (aerogel, xerogel). The suppression of superfluidity and the critical behavior at the phase transition have been investigated in these systems in a classic series of experiments [9], and the elementary excitations of liquid 4 He in Vycor have been recently studied using neutron inelastic scattering [10]. Furthermore, the recent achievement of Bose-Einstein condensation (BEC) in alkali vapours has sparked an even larger interest in the physics of degenerate Bose gases and their macroscopic quantum properties, such as long-range order and superfluid behavior (for a review see [11]).In this Letter we investigate the effects of disorder on BEC and superfluidity in a Bose gas at zero temperature. As a model for disorder a uniform random distribution of static impurities is assumed. This choice provides us with a reasonable model for 4 He adsorbed in porous media and might also be relevant for trapped Bose condensates in the presence of heavy impurities. In addition, the quenched-impurity model allows us to derive analytical results in the weak-disorder regime and can be implemented in a quantum Monte Carlo simulation.The present work is divided in two parts. In the first part, following the analysis of Ref.[4], the properties of the system are investigated within the Bogoliubov approximation. Results for the effects of disorder on the ground-state energy, superfluid density and condensate fraction are discussed. In the second part, we resort to the...

The phase diagram of the first layer of 4He adsorbed on a single graphene sheet has been calculated by a series of diffusion Monte Carlo calculations including corrugation effects. Since the number of C-He interactions is smaller than in graphite, the binding energy of 4He atoms to graphene is reduced approximately 13.4 K per helium atom. Our results indicate that the phase diagram is qualitatively similar to that of helium on top of graphite. A two-dimensional liquid film on graphene is predicted to be metastable with respect to the commensurate solid but the difference in energy between both phases is very small, opening the possibility of such a liquid film to be experimentally observed.

Quantum crystals abound in the whole range of solid-state species. Below a certain threshold temperature the physical behavior of rare gases ( 4 He and Ne), molecular solids (H 2 and CH 4 ), and some ionic (LiH), covalent (graphite), and metallic (Li) crystals can be only explained in terms of quantum nuclear effects (QNE). A detailed comprehension of the nature of quantum solids is critical for achieving progress in a number of fundamental and applied scientific fields like, for instance, planetary sciences, hydrogen storage, nuclear energy, quantum computing, and nanoelectronics. This review describes the current physical understanding of quantum crystals formed by atoms and small molecules, as well as the wide palette of simulation techniques that are used to investigate them. Relevant aspects in these materials such as phase transformations, structural properties, elasticity, crystalline defects and the effects of reduced dimensionality, are discussed thoroughly. An introduction to quantum Monte Carlo techniques, which in the present context are the simulation methods of choice, and other quantum simulation approaches (e. g., path-integral molecular dynamics and quantum thermal baths) is provided. The overarching objective of this article is twofold. First, to clarify in which crystals and physical situations the disregard of QNE may incur in important bias and erroneous interpretations. And second, to promote the study and appreciation of QNE, a topic that traditionally has been treated in the context of condensed matter physics, within the broad and interdisciplinary areas of materials science.