The liquid and crystal phases of a single-component Fermi gas with dipolar interactions are investigated using quantum Monte Carlo methods in two spatial dimensions and at zero temperature. The dipoles are oriented by an external field perpendicular to the plane of motion, resulting in a purely repulsive 1/r(3) interaction. In the liquid phase we calculate the equation of state as a function of the interaction strength and other relevant properties characterizing the Fermi-liquid behavior: effective mass, discontinuity at the Fermi surface, and pair correlation function. In the high density regime we calculate the equation of state of the Wigner crystal phase and the critical density of the liquid to solid quantum phase transition. Close to the freezing density we also search for the existence of a stripe phase, but such a phase is never found to be energetically favorable.

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A one-dimensional world is very unusual as there is an interplay between quantum statistics and geometry, and a strong short-range repulsion between atoms mimics Fermi exclusion principle, fermionizing the system. Instead, a system with a large number of components with a single atom in each, on the opposite acquires many bosonic properties. We study the ground-state properties of a multicomponent repulsive Fermi gas trapped in a harmonic trap by a fixed-node diffusion Monte Carlo method. The interaction between all components is considered to be the same. We investigate how the energetic properties (energy, contact) and correlation functions (density profile and momentum distribution) evolve as the number of components is changed. It is shown that the system fermionizes in the limit of strong interactions. Analytical expressions are derived in the limit of weak interactions within the local density approximation for an arbitrary number of components and for one plus one particle using an exact solution.fermions with a single atom in each component should have similar energetic properties as a single component Bose gas consisting of N c atoms [15]. Recently a six-component mixture of one-dimensional fermions was realized in LENS group [16]. The measured frequency of the breathing mode approaches that of a Bose system as N c is increased from 1 to 6. It was observed that the momentum distribution increases its width as the number of components is increased, keeping the number of atoms in each spin component fixed.The Bethe ansatz theory is well suited for finding the energetic properties in a homogeneous geometry, predicting the equation of state for the case of N c = 2 components [17,18] and an arbitrary N c [19,20]. Unfortunately the Bethe ansatz method is not applicable in the presence of an external potential. The use of LDA is generally good for energy but misses two-body correlations. Instead, quantum Monte Carlo methods can be efficiently used to tackle the problem. Recently, lattice and path integral Monte Carlo algorithms were successfully used to study the properties of trapped bosons [21], trapped fermions with attraction [22] and fermions in a box with periodic boundary [23]. The properties of a balanced two-component Fermi gas in a harmonic trap were studied by means of the coupled-cluster method [24]. The lattice Hubbard model and its continuum limit for trapped two component gas was studied by the DMRG method [25]. The limit of strong interactions is special and allows different approaches. The three-particle system can be studied analytically in this regime [26]. Multicomponent gases were analyzed in the same regime using a spin-chain model in Ref. [27], resulting in an effective Hamiltonian description for that regime. The spin-chain model permitted the study of the effect of population imbalance on the momentum distribution in a two-component trapped system [28]. For bosonic systems the regime of strong repulsion corresponds to the vicinity of the Tonks-Girardeau limit and the system can be mappe...

We investigate the BCS-BEC crossover in a bilayer system of fermionic dipoles at zero temperature using the fixed-node diffusion Monte Carlo technique. The dipoles are confined on two parallel planes separated by a distance λ and are aligned perpendicular to the planes by an external field. The interlayer pairing, which is responsible for the superfluid behavior of the system, crosses from a weak-to a strong-coupling regime by reducing the separation distance λ. For a fixed in-plane density equal in the two layers, we calculate the ground-state energy, the chemical potential, the pairing gap, and the quasiparticle dispersion as a function of the interlayer separation. At large λ one recovers the ground-state energy of a single layer of fermions, and at small λ one recovers that of a single layer of composite bosons with twice the particle mass and the dipole moment. The superfluid gap varies from the exponentially small BCS result to half of the large two-body binding energy in the Bose-Einstein condensate (BEC) regime of strong interlayer pairing. Results are compared with the predictions of the simplest mean-field theory valid in the low-density limit, and deviations are observed both in the BCS regime, where in-plane repulsions are important, and in the BEC regime, where the mean-field approach fails to describe the physics of composite dipolar bosons.