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...

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...

We consider a homogeneous 1D Bose gas with contact interactions and 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 a variational ansatz for the many-body wavefunction, we show that for small densities the gas-like state is stable and the corresponding equation of state is well described by a gas of hard rods. By calculating the compressibility of the system, we provide an estimate of the critical density at which the gas-like state becomes unstable against cluster formation. Within the hard-rod model we calculate the one-body density matrix and the static structure factor of the gas. The results show that in this regime the system is more strongly correlated than a Tonks-Girardeau gas. The frequency of the lowest breathing mode for harmonically trapped systems is also discussed as a function of the interaction strength. PACS numbers:The study of quasi-1D Bose gases in the quantumdegenerate regime has become a very active area of research. The role of correlations and of quantum fluctuations is greatly enhanced by the reduced dimensionality and 1D quantum gases constitute well suited systems to study beyond mean-field effects [1]. Among these, particularly intriguing is the fermionization of a 1D Bose gas in the strongly repulsive Tonks-Girardeau (TG) regime, where the system behaves as if it consisted of noninteracting spinless fermions [2]. The Bose-Fermi mapping of the TG gas is a peculiar aspect of the universal low-energy properties which are exhibited by bosonic and fermionic gapless 1D quantum systems and are described by the Luttinger liquid model [3]. The concept of Luttinger liquid plays a central role in condensed matter physics and the prospect of a clean testing for its physical implications using ultracold gases confined in highly elongated traps is fascinating [4,5].Bosonic gases in 1D configurations have been realized experimentally. Complete freezing of the transverse degrees of freedom and fully 1D kinematics has been reached for systems prepared in a deep 2D optical lattice [6,7]. The strongly interacting regime has been achieved by adding a longitudinal periodic potential and the transition from a 1D superfluid to a Mott insulator has been observed [8]. A different technique to increase the strength of the interactions, which is largely employed in both bosonic and fermionic 3D systems [9] but has not yet been applied to 1D configurations, consists in the use of a Feshbach resonance. With this method one can tune the effective 1D coupling constant g 1D to essentially any value, including ±∞, by exploiting a confinement induced resonance [10]. For large and positive values of g 1D the system is a TG gas of point-like impenetrable bosons. On the contrary, if g 1D is large and negative, we will show that a new gas-like regime is entered (super-Tonks) where the hard-core repulsion between particles becomes of finite range and correlations are stronger than in the TG...

A Monte Carlo algorithm for computing quantum mechanical expectation values of coordinate operators in many body problems is presented. The algorithm, that relies on the forward walking method, fits naturally in a Green's Function Monte Carlo calculation, i.e., 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 as the hydrogen atom and the hydrogen molecule. An excellent description of several properties of a fully many body problem as liquid 4 He at zero temperature is achieved. 02.70.Lq, 67.40.Db Typeset using REVT E X

High order actions proposed by Chin have been used for the first time in path integral Monte Carlo simulations. Contrarily to the Takahashi-Imada action, which is accurate to fourth order only for the trace, the Chin action is fully fourth order, with the additional advantage that the leading fourth and sixth order error coefficients are finely tunable. By optimizing two free parameters entering in the new action we show that the time step error dependence achieved is best fitted with a sixth order law. The computational effort per bead is increased but the total number of beads is greatly reduced, and the efficiency improvement with respect to the primitive approximation is approximately a factor of ten. The Chin action is tested in a one-dimensional harmonic oscillator, a H 2 drop, and bulk liquid 4 He. In all cases a sixth-order law is obtained with values of the number of beads that compare well with the pair action approximation in the stringent test of superfluid 4 He.