We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at T = 0 using the fixed-node diffusion Monte Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. Results on Tan's contact parameter associated with short-range physics are also reported along the BCS-BEC crossover. The study of ultracold atomic Fermi gases has become an active and rich field of research [1]. Important areas of investigation include the BCS-BEC crossover in a superfluid gas with resonantly enhanced interactions, the Chandrasekhar-Clogston instability of the superfluid state when spin polarization is increased, the possible onset of itinerant ferromagnetism in a gas with repulsive interactions [2] and the realization of the Hubbard model for fermions loaded in optical lattices [3].Low dimensional configurations of degenerate Fermi gases have also been the object of experimental and theoretical studies [1,3]. In particular, a two-dimensional (2D) ultracold Fermi gas has been recently realized using a highly anisotropic pancake-shaped potential, and the density profile of the cloud has been measured using in situ imaging [4]. On the theoretical side, the evolution from a superfluid state with large Cooper pairs to one with tight molecules in a 2D system of attractive fermions was first investigated by Miyake [5] and later by Randeria and coworkers [6] aiming to describe high-T c superconductors. More recent studies address the problem of the superfluid transition [7,8], of harmonic trapping [9] and of population and mass imbalance [10]. These studies are in general based on perturbative or mean-field (MF) approaches that are suitable in the regime of weak coupling, but are bound to break down for stronger interactions.In this Letter we provide the first determination using quantum Monte Carlo methods of the equation of state at T = 0 of a homogeneous 2D Fermi gas in the BCS-BEC crossover. We also obtain results for the pairing gap and the contact parameter as a function of the interaction strength. In the strong-coupling regime the emergence of interaction effects involving dimers produce large deviations compared to MF predictions. A similar study carried out in 3D [11] has provided an important benchmark against which experimental determination of the equation of state, using measurements of the dispersion of collective modes [12] or of in situ density profiles [13], have been successfully compared. Hopefully, our results will stimulate more experimental efforts towards the realization of a 2D Fermi gas in the strong-coupling regime by means, for example, of a Feshbach resonance to increase the interaction parameter [4].We consider a homogeneous two-component Fermi gas d...
We investigate the phase diagram of a two-component repulsive Fermi gas at T=0 by means of quantum Monte Carlo simulations. Both purely repulsive and resonant attractive model potentials are considered in order to analyze the limits of the universal regime where the details of interatomic forces can be neglected. The equation of state of both balanced and unbalanced systems is calculated as a function of the interaction strength and the critical density for the onset of ferromagnetism is determined. The energy of the strongly polarized gas is calculated and parametrized in terms of the physical properties of repulsive polarons, which are relevant for the stability of the fully ferromagnetic state. Finally, we analyze the phase diagram in the interaction-polarization plane under the assumption that only phases with homogeneous magnetization can be produced.
We compute the zero-temperature dynamical structure factor of one-dimensional liquid 4 He by means of state-of-the-art quantum Monte Carlo and analytic continuation techniques. By increasing the density, the dynamical structure factor reveals a transition from a highly compressible critical liquid to a quasisolid regime. In the low-energy limit, the dynamical structure factor can be described by the quantum hydrodynamic Luttinger-liquid theory, with a Luttinger parameter spanning all possible values by increasing the density. At higher energies, our approach provides quantitative results beyond the Luttinger-liquid theory. In particular, as the density increases, the interplay between dimensionality and interaction makes the dynamical structure factor manifest a pseudo-particle-hole continuum typical of fermionic systems. At the low-energy boundary of such a region and moderate densities, we find consistency, within statistical uncertainties, with predictions of a power-law structure by the recently developed nonlinear Luttinger-liquid theory. In the quasisolid regime, we observe a novel behavior at intermediate momenta, which can be described by new analytical relations that we derive for the hard-rods model. DOI: 10.1103/PhysRevLett.116.135302 One-dimensional (1D) quantum systems exhibit some of the most diverse and fascinating phenomena of condensed matter physics [1][2][3]. Among the most spectacular signatures of the interplay between quantum fluctuations, interaction and reduced dimensionality, are the breakdown of ordered phases in the presence of short-range interactions [4] and the loosened distinction between Bose and Fermi behavior [5]. The study of quasi-1D quantum systems is a very active research field, aroused by the experimental investigation of electronic transport properties [6][7][8][9][10], by the fabrication of long 1D arrays of Josephson junctions [11], and recently corroborated by the availability of ultracold atomic gases in highly anisotropic traps and optical lattices [2,[12][13][14], as well as by experiments on confined He atoms [15][16][17][18][19].The low-energy properties of a wide class of Bose and Fermi 1D quantum systems [1,20] are notoriously captured by the phenomenological Tomonaga-Luttinger-liquid (TLL) theory [21][22][23], characterized by collective phononlike excitations. This theory introduces two conjugate Bose fields ϕðxÞ and θðxÞ describing, respectively, the density and phase fluctuations of the field operator ψðxÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ρ þ ∂ x ϕðxÞ p e iθðxÞ , where ρ is the average density. Those fields are described by the exactly solvable lowenergy effective Hamiltonian:Although, in general, the TLL parameter K L and the sound velocity c are independent quantities (notably in lattice models), for Galilean-invariant systems c ¼ v F =K L [23], v F ¼ ℏk F =m being the Fermi velocity and k F ¼ πρ the Fermi wave vector of a 1D ideal Fermi gas (IFG), and K L is thus related to the compressibility κ S by mK 2 L ¼ ℏ 2 π 2...
We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion component. We focus on the case where the boson density nB is smaller than the fermion density nF , for which a first-order quantum phase transition is found from a state with condensed bosons immersed in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired fermions. We obtain the equation of state and the phase diagram, and we find that the region of phase separation shrinks to zero for vanishing nB.PACS numbers: 67.85. Pq, 03.75.Ss, 03.75.Hh Let us consider a system of bosons and spinless fermions with a tunable short-range boson-fermion (BF) attraction. For weak attraction, at sufficiently low temperature the bosons condense, while the fermions fill a Fermi sphere, and the BF interaction can be treated with perturbative methods [1,2]. For sufficiently strong attraction, bosons and fermions pair into molecules. In particular, for a fermion density n F larger than the boson density n B , one expects all the bosons to pair with fermions. The boson condensate is then absent in such a regime, and the system should be described as a weakly interacting Fermi-Fermi mixture, one component consisting of molecules, with density n M = n B , and the other component of unpaired fermions, with densityHow does the system evolve at zero temperature between the two above physical regimes? Several scenarios could be imagined in principle: (i) a continuous quantum phase transition, with the condensate fraction vanishing smoothly at a certain critical value of the BF coupling; (ii) a first-order quantum phase transition, with phase separation between a condensed phase and a molecular phase without condensate; (iii) the collapse of the system in the intermediate coupling region, with no stable state connecting the two different regimes.The above question has been the object of increasing attention recently, especially in the field of ultracold trapped gases, where the interaction can be tuned by using Feshbach resonances [3]. In particular, for "broad" resonances, a Bose-Fermi mixture can be accurately described by a minimal set of parameters: the scattering lengths a BB and a BF describing, respectively, the bosonboson (BB) and boson-fermion interaction, the boson and fermion densities n B and n F , and their masses m B and m F (the short-range fermion-fermion interaction being negligible, due to Pauli exclusion).Initial experiments [4,5] with ultracold Bose-Fermi mixtures supported the collapse scenario, with the instability occurring already for moderate BF coupling. However, only a limited region of the parameter space was explored (e.g., a boson number N B considerably greater than the fermion number N F and nonresonant values of the scattering lengths). 12] mixtures, in the latter case observing lifetimes of the order of 100ms, sufficient for the setup of m...
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