Abstract
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.
Highlights
The amazing progress in the field of ultracold Bose and Fermi atoms has provided a versatile tool for a highly controlled investigation of the properties of quantum systems
The main idea behind universality is that two-body interactions in a dilute Fermi or Bose gas can be described by a single parameter [33], namely the s-wave scattering length a, as the mean interparticle distance is large compared to the range of the interaction potential and its details are not important
In the following we study the zero-temperature phase diagram of particles interacting via inverse square interactions and interpret the system properties in relation to the Bose system at unitarity
Summary
The amazing progress in the field of ultracold Bose and Fermi atoms has provided a versatile tool for a highly controlled investigation of the properties of quantum systems. The main idea behind universality is that two-body interactions in a dilute Fermi or Bose gas can be described by a single parameter [33], namely the s-wave scattering length a, as the mean interparticle distance is large compared to the range of the interaction potential and its details are not important. The inverse-square potential is a famous example of exactly-solvable many body quantum systems in one dimension (see the book [48] and references within) Both the wave function and energy can be explicitly written as a function of the interaction parameter both in homogeneous and trapped geometries [49,50,51,52]. In the following we study the zero-temperature phase diagram of particles interacting via inverse square interactions and interpret the system properties in relation to the Bose system at unitarity
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