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arXiv:0912.4893 · Physical Review A

Ground state of a mixture of two bosonic Calogero-Sutherland gases with strong odd-wave interspecies attraction

Marvin D. Girardeau, G. E. Astrakharchik

Published Apr 2, 2010• 9 citations
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Abstract

A model of two Calogero-Sutherland Bose gases $A$ and $B$ with strong odd-wave $\mathit{AB}$ attractions induced by a $p$-wave $\mathit{AB}$ Feshbach resonance is studied. The ground-state wave function is found analytically by a Bose-Bose duality mapping, which permits one to accurately determine static physical properties by a Monte Carlo method. The condensation of particles or particle pairs (molecules) is tested by analyzing the presence of the off-diagonal long-range order in one- or two- body density matrices. The $p$-wave symmetry of $\mathit{AB}$ interaction makes possible quasicondensation of type $A$ particles at the Fermi momentum of the $B$ component. The zero-temperature phase diagram is drawn in terms of densities and interaction strengths.

DOI
10.1103/physreva.81.043601

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A model of two Calogero-Sutherland Bose gases AAA and BBB with strong odd-wave AB\mathit{AB}AB attractions induced by a ppp-wave AB\mathit{AB}AB Feshbach resonance is studied. The ground-state wave function is found analytically by a Bose-Bose duality mapping, which permits one to accurately determine static physical properties by a Monte Carlo method. The condensation of particles or particle pairs (molecules) is tested by analyzing the presence of the off-diagonal long-range order in one- or two- body density matrices. The ppp-wave symmetry of AB\mathit{AB}AB interaction makes possible quasicondensation of type AAA particles at the Fermi momentum of the BBB component. The zero-temperature phase diagram is drawn in terms of densities and interaction strengths.
A model of two 1D ideal Bose gases A and B with strong odd-wave AB attractions induced by a p-wave AB Feshbach resonance is studied. The model is solved exactly by a Bose-Bose duality mapping, and it is shown that there is no A-component or B-component Bose-Einstein condensation and no AB-pair off-diagonal long-range order (ODLRO), but both AA-pair and BB-pair ODLRO. After generalization by adding even-wave AA and BB repulsions and reducing the strength of the odd-wave AB attraction by Feshbach resonance detuning, a quantum phase transition occurs between a phase with AB contact nodes and one with no such nodes.
Ground-state properties of bosons interacting via inverse square potential (three dimensional Calogero-Sutherland model) are analyzed. A number of quantities scale with the density and can be naturally expressed in units of the Fermi energy and Fermi momentum multiplied by a dimensionless constant (Bertsch parameter). Two analytical approaches are developed: the Bogoliubov theory for weak and the harmonic approximation (HA) for strong interactions. Diffusion Monte Carlo method is used to obtain the ground-state properties in a non-perturbative manner. We report the dependence of the Bertsch parameter on the interaction strength and construct a Padé approximant which fits the numerical data and reproduces correctly the asymptotic limits of weak and strong interactions. We find good agreement with beyond-mean field theory for the energy and the condensate fraction. The pair distribution function and the static structure factor are reported for a number of characteristic interactions. We demonstrate that the system experiences a gas-solid phase transition as a function of the dimensionless interaction strength. A peculiarity of the system is that by changing the density it is not possible to induce the phase transition. We show that the low-lying excitation spectrum contains plasmons in both phases, in agreement with the Bogoliubov and HA theories. Finally, we argue that this model can be interpreted as a realization of the unitary limit of a Bose system with the advantage that the system stays in the genuine ground state contrarily to the metastable state realized in experiments with short-range Bose gases.
Ground-state properties of bosons interacting via inverse square potential (three dimensional Calogero-Sutherland model) are analyzed. A number of quantities scale with the density and can be naturally expressed in units of the Fermi energy and Fermi momentum multiplied by a dimensionless constant (Bertsch parameter). Two analytical approaches are developed: the Bogoliubov theory for weak and the harmonic approximation (HA) for strong interactions. Diffusion Monte Carlo method is used to obtain the ground-state properties in a non-perturbative manner. We report the dependence of the Bertsch parameter on the interaction strength and construct a Padé approximant which fits the numerical data and reproduces correctly the asymptotic limits of weak and strong interactions. We find good agreement with beyond-mean field theory for the energy and the condensate fraction. The pair distribution function and the static structure factor are reported for a number of characteristic interactions. We demonstrate that the system experiences a gas-solid phase transition as a function of the dimensionless interaction strength. A peculiarity of the system is that by changing the density it is not possible to induce the phase transition. We show that the low-lying excitation spectrum contains plasmons in both phases, in agreement with the Bogoliubov and HA theories. Finally, we argue that this model can be interpreted as a realization of the unitary limit of a Bose system with the advantage that the system stays in the genuine ground state contrarily to the metastable state realized in experiments with short-range Bose gases.
The ground-state properties of a two-component Fermi gas with attractive short-range interactions are calculated 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. We calculate the energy per particle, the one- and two-body density matrix as a function of the interaction strength. 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 pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover.
We report results of quantum Monte Carlo calculations of the ground state of dilute Fermi gases with attractive short-range two-body interactions. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the sss-wave scattering length and the Fermi wave vector, akFa{k}_{F}akF​. We report results for the ground-state energy, the pairing gap $\ensuremath{\Delta}$, and the quasiparticle spectrum. In the weak-coupling regime, $1∕a{k}_{F}<\ensuremath{-}1$, we obtain Bardeen-Cooper-Schrieffer (BCS) superfluid and the energy gap $\ensuremath{\Delta}$ is much smaller than the Fermi gas energy EFG{E}_{\mathrm{FG}}EFG​. When a>0a>0a>0, the interaction is strong enough to form bound molecules with energy Emol{E}_{\mathrm{mol}}Emol​. For $1∕a{k}_{F}\ensuremath{\gtrsim}0.5$, we find that weakly interacting composite bosons are formed in the superfluid gas with $\ensuremath{\Delta}$ and gas energy per particle approaching $\ensuremath{\mid}{E}_{\mathrm{mol}}\ensuremath{\mid}∕2$. In this region, we seem to have Bose-Einstein condensation (BEC) of molecules. The behavior of the energy and the gap in the BCS-to-BEC transition region, $\ensuremath{-}0.5<1∕a{k}_{F}<0.5$, is discussed.
We consider a Bose-Fermi mixture with a broad and tunable Feshbach resonance allowing to change continuously the attraction between bosons and fermions from weak to strong coupling. We set up a diagrammatic formalism which includes both the Bose-Fermi tunable attraction and the Bose-Bose repulsion at zero temperature. Remarkably, we find that for boson density smaller than or equal to the fermion density, the boson condensate fraction does not depend on the density imbalance across most of the resonance. In the limit of vanishing boson concentration, we find very good agreement with previous results for the polaron quasi-particle residue obtained in the context of strongly polarized Fermi-Fermi mixtures [1]. We calculate also the boson and fermion chemical potentials and momentum distribution functions and, when the condensate fraction vanishes, we recover the results of our previous works for the normal phase [2,3]. In addition, we calculate the effective masses and Fermi steps for the unpaired and composite fermions. We find that the Fermi step of the unpaired fermions remains pinned to the value given by the Fermi radius of a free Fermi gas across most of the resonance, in agreement with the Luttinger’s theorem [4], until molecules start to form (g≈1). The formation of molecules is signalled by the appearance of a second pole in the boson-fermion propagator, which marks the access to a regime where bosons, fermions and molecules cohexist, and by the presence of a Fermi step for the composite fermions, which is related to the density of molecules. Finally, we find quite a good agreement between our results for the condensate fraction and Quantum Monte Carlo calculations [5].