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arXiv:cond-mat/9902131 · Physical Review Letters

Dilute Quantum Droplets

Aurel Bulgac

Published Jul 16, 2002• 217 citations
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Abstract

In the limit when the two-body scattering length a is negative and much larger than the effective two-body interaction radius the contribution to the ground state energy due to the three-body correlations is given by the Efimov effect. For particular values of the diluteness parameter rho/a/(3) the three-body contribution can become the dominant term of the energy density functional. Under these conditions both Bose-Einstein and Fermi-Dirac systems could become self-bound and either boson droplets or fermion "designer nuclei" of various sizes and densities could be manufactured.

DOI
10.1103/physrevlett.89.050402

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In the limit when the two-body scattering length a is negative and much larger than the effective two-body interaction radius the contribution to the ground state energy due to the three-body correlations is given by the Efimov effect. For particular values of the diluteness parameter rho/a/(3) the three-body contribution can become the dominant term of the energy density functional. Under these conditions both Bose-Einstein and Fermi-Dirac systems could become self-bound and either boson droplets or fermion "designer nuclei" of various sizes and densities could be manufactured.
In the limit when the two-body scattering length aaa is negative and much larger than the effective two-body interaction radius the contribution to the ground state energy due to the three-body correlations is given by the Efimov effect. For particular values of the diluteness parameter ρ∣a∣3\rho |a|^3ρ∣a∣3 the three-body contribution can become the dominant term of the energy density functional. Under these conditions both Bose-Einstein and Fermi-Dirac systems could become self-bound and either boson droplets or fermion ``designer nuclei'' of various sizes and densities could be manufactured.
We study a dilute Bose gas of atoms whose scattering length a is large compared to the range of their interaction. We calculate the energy density E of a homogeneous Bose-Einstein condensate (BEC) to second order in the low-density expansion, expressing it in terms of a and a second parameter Lambda* that determines the low-energy observables in the three-body sector. The second-order correction to E has a small imaginary part that reflects the instability due to three-body recombination. In the case of a trapped BEC with large negative a, we calculate the coefficient of the three-body mean-field term in E in terms of a and Lambda*. It can be very large if there is an Efimov state near threshold.
Small weakly bound droplets determine a number of properties of ultracold Bose and Fermi gases. For example, Efimov trimers near the atom-atom-atom and atom-dimer thresholds lead to enhanced losses from bosonic clouds. Generalizations to four- and higher-body systems have also been considered. Moreover, Efimov trimers have been predicted to play a role in the Bose polaron with large boson-impurity scattering length. Motivated by these considerations, the present work provides a detailed theoretical analysis of weakly bound NNN-body clusters consisting of $N\ensuremath{-}1$ identical bosons (denoted by ``B'') of mass mmm that interact with a single distinguishable impurity particle (denoted by ``X'') of mass MMM. The system properties are analyzed as a function of the mass ratio $\ensuremath{\kappa}$ (values from $\ensuremath{\kappa}=1$ to 50 are considered), where $\ensuremath{\kappa}$ is equal to m/Mm/Mm/M, and the two-body sss-wave scattering length aBX{a}_{\text{BX}}aBX​ between the bosons and the impurity. To reach the universal Efimov regime in which the size of the BBX trimer as well as those of larger clusters is much larger than the length scales of the underlying interaction model, three different approaches are considered: resonance states are determined in the absence of BB and BBX interactions, bound states are determined in the presence of repulsive three-body boson-boson-impurity interactions, and bound states are determined in the presence of repulsive two-body boson-boson interactions. The universal regime, in which the details of the underlying interaction model become irrelevant, is identified.
A many-body system of fermion atoms with a model interaction characterized by the scattering length a is considered. We treat both a and the density as parameters assuming that the system can be created artificially in a trap. If a is negative the system becomes strongly correlated at densities ρ ∼ |a | −3, provided the scattering length is the dominant parameter of the problem. It means that we consider |a | to be much bigger than the radius of the interaction or any other relevant parameter of the system. The density ρc1 at which the compressibility vanishes is defined by ρc1 ∼ |a | −3. Thus, a system composed of fermion atoms with the scattering length a → − ∞ is completely unstable at low densities, inevitably collapsing until the repulsive core stops the density growth. As a result, any Fermi system possesses the equilibrium density and energy if the bare particle-particle interaction is sufficiently strong to make a negative and to be the dominant parameter. This behavior can be realized in a trap. Our results show that a low density neutron matter can have the equilibrium density. PACS numbers: 05.30.Fk, 24.10.Cn, 71.10.Ca Key Words: trapped Fermi gases; effective interaction