Quantum dilute droplets of dipolar bosons at finite temperature

Abstract

We systematically study the properties of dipolar Bose gases with two-and three-body contact interactions at finite temperature using the Hartree-Fock-Bogoliubov-Popov approximation. In uniform case, we obtain an exciting new extension of the seminal Lee-Huang-Yang corrected equation of state that depends explicitly on the thermal fluctuations and on the coupling constant of the three-body interaction. We investigate, on the other hand, the effects of thermal fluctuations on the occurrence and stability of a droplet state in a Bose-Einstein condensate with strong dipole-dipole interactions. We find that at finite temperature, the droplet phase appears as a narrow peak surrounded by a broader thermal halo. We show that the number of particles inside the droplet decays with increasing temperature.

Dipolar Bose gas with three-body interactions at finite temperature

“…It is worth stressing that the omission of the long-range exchange term does not preclude the stability of the system [10,12,13,46,[48][49][50].…”

“…Form = 0, Eq. (1) reduces to the HFB-Popov equation [10,11,46] which is gapless theory. Form =ñ = 0, it reduces to standard GP equation that describes dipolar Bose gases only at zero temperature.…”

“…The quasi-particle amplitudes u k (r), v k (r) satisfy the generalized nonlocal Bogoliubov-de-Gennes (BdG) equations [46]: (2) and (3) describe the collective excitations of the system. The normal and the anomalous one-body density matrices can be obtained employing the transfor-…”

“…It is straightforward to check that the condensate wavefunction Φ(r) = ψ (r) , witĥ ψ(r) being the Bose field operator, satisfies the generalized Gross-Pitaevskii (GP) equation [46] ih ∂Φ(r, t) ∂t…”

“…For instance, it has been argued that TBI play a crucial role in the stablization of the supersolid state in 2D dipolar bosons [42] and in the quantum droplet state in 3D BEC with strong DDI [43][44][45][46].…”