Simple variational approach for an interacting Fermi trapped gas

Jáuregui, R.; Paredes, R.; Sánchez, G. Toledo

doi:10.1103/physreva.69.013606

Cited by 7 publications

(21 citation statements)

References 18 publications

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“…Notice that in the BCS side of the crossover the interaction energy is very small compared to E IF G , in accordance with previous QMC calculations in homogeneous gases [8,9]. In fact, we have checked that for −k F a < 1 this variational energy coincides with the result obtained using an effective contact interaction [17]. At unitarity and for a > 0, the role of the interaction energy becomes more relevant.…”

supporting

confidence: 91%

“…In fact, we have checked that for −k F a < 1 this variational energy coincides with the result obtained using an effective contact interaction [17]. At unitarity and for a > 0, the role of the interaction energy becomes more relevant.…”

mentioning

confidence: 49%

“…For a closed shell configuration (all single particle states with energies below E F = (M F + 3/2)hω are occupied) this energy is given by [17] …”

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confidence: 99%

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BEC-BCS crossover of a trapped Fermi gas without using the local density approximation

2007

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We perform a variational quantum Monte Carlo simulation of an interacting Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based on the results of two-body calculations for trapped atoms, we propose a family of variational many-body wave functions that takes into account the qualitative different nature of the BCS and BEC regimes as a function of the scattering length. Energies, densities and correlation functions are calculated and compared with previous results for homogeneous gases. Universality tests at the unitarity limit are performed including the verification of the virial relation and the evaluation of the β parameter.PACS numbers: 03.75. Ss, 03.75.Hh, 05.30.Fk The crossover from a low interacting attractive Bardeen-Cooper-Schieffer (BCS) gas to a molecular BoseEinstein condensate (BEC) has been realized experimentally using a mixture of ultracold Fermi atoms in two hyperfine states [1,2,3,4,5]. In dilute Fermi gases, the atomic interactions have a range much smaller than the interparticle separation. Nevertheless, under proper conditions, a magnetic field can be used to tune the attractive potential so that the energy of a pair of scattering atoms is close to that of a molecular bound state (Feshbach resonance). In experiments where the resonance is broad, it can be represented by a single-channel model in which the s-wave scattering length a determines the general features of the ultracold atomic gas. At low enough temperatures, atoms in different hyperfine states pair into bound molecules for positive values of a, forming a molecular BEC that can be adiabatically converted into a degenerate Fermi gas by shifting a to negative values. At resonance (|a| → ∞), the gas acquires universal properties, i. e., they are independent of any feature of the atomic potentials [2,6,7]. This is the so called unitarity limit.The theoretical description of the BEC-BCS crossover is complicated because there is no ad hoc single parameter to control the relevant features in both regimes. A reasonable alternative to infer properties of the system at unitarity has been to consider an homogeneous Fermi gas, and to assume the universality hypothesis according to which the only dominant length is the interparticle separation. Then, the thermodynamic potentials have a universal form specified by only few universal numbers [7]. For instance, the interaction energy is proportional to the Fermi energy via a universal constant β.Quantum Monte Carlo (QMC) techniques support ab initio methods to theoretically test the universality hypothesis. They can be used to approximately solve the many-body Schrödinger equation for a given model of the interaction potential. In previous studies the BEC and BCS regimes have been explored using a fixed-node QMC technique, which is rigorous but also computationally demanding. In particular, the value of β has been predicted considering up to 66 particles [8,9]. Nevertheless, these QMC calcu...

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BEC-BCS crossover of a trapped Fermi gas without using the local density approximation

2007

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“…The variational wave function ψ T for multi-component Fermi gases is written as (see Refs. [21,22,53,65,80,81,82] for Monte Carlo studies of two-component systems and Ref. [35] for a Monte Carlo study of three-component systems)…”

Section: A Variational and Fixed-node Diffusion Montementioning

confidence: 99%

Stability of inhomogeneous multicomponent Fermi gases

et al. 2008

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Two-component equal-mass Fermi gases, in which unlike atoms interact through a short-range two-body potential and like atoms do not interact, are stable even when the interspecies s-wave scattering length becomes infinitely large. Solving the many-body Schrödinger equation within a hyperspherical framework and by Monte Carlo techniques, this paper investigates how the properties of trapped two-component gases change if a third or fourth component are added. If all interspecies scattering lengths are equal and negative, our calculations suggest that both three-and four-component Fermi gases become unstable for a certain critical set of parameters. The relevant length scale associated with the collapse is set by the interspecies scattering length and we argue that the collapse is, similar to the collapse of an attractive trapped Bose gas, a many-body phenomenon. Furthermore, we consider a three-component Fermi gas in which two interspecies scattering lengths are negative while the other interspecies scattering length is zero. In this case, the stability of the Fermi system is predicted to depend appreciably on the range of the underlying two-body potential. We find parameter combinations for which the system appears to become unstable for a finite negative scattering length and parameter combinations for which the system appears to be made up of weakly-bound trimers that consist of one fermion of each species.

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“…As a result much interest has been taken in applying numerical methods, such as quantum Monte Carlo and numerical diagonalization. For systems varying from ∼ 10 to hundreds of particles, quantum Monte Carlo calculations have been carried out to calculate ground state [4][5][6][7][8][9][10][11][12][13] and thermodynamic properties [14][15][16][17][18]. For smaller numbers of trapped atoms, energy spectra have been calculated using a basis set expansion method with correlated Gaussians in coordinate space (for up to six atoms) [8,9] and a stochastic variational approach (for four atoms) [19].…”

Section: Introductionmentioning

confidence: 99%

Separable effective interaction for the trapped Fermi gas: The BEC-BCS crossover

Gilbreth

Alhassid

2012

Phys. Rev. A

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We extend a recently introduced separable interaction for the unitary trapped Fermi gas to all values of the scattering length. We derive closed expressions for the interaction matrix elements and the two-particle eigenvectors and analytically demonstrate the convergence of this interaction to the zero-range two-body pseudopotential for s-wave scattering. We apply this effective interaction to the three-and four-particle systems along the BEC-BCS crossover, and find that their low-lying energies exhibit convergence in the regularization parameter that is much faster than for the conventional renormalized contact interaction. We find similar convergence properties of the three-particle free energy at unitarity.

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Simple variational approach for an interacting Fermi trapped gas

Cited by 7 publications

References 18 publications

BEC-BCS crossover of a trapped Fermi gas without using the local density approximation

BEC-BCS crossover of a trapped Fermi gas without using the local density approximation

Stability of inhomogeneous multicomponent Fermi gases

Separable effective interaction for the trapped Fermi gas: The BEC-BCS crossover

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