Dilute dipolar quantum droplets beyond the extended Gross-Pitaevskii equation

Abstract

Dipolar quantum droplets are exotic quantum objects that are self-bound due to the subtle balance of attraction, repulsion and quantum correlations. Here we present a systematic study of the critical atom number of these self-bound droplets, comparing the experimental results with extended mean-field Gross-Pitaevskii equation (eGPE) and quantum Monte-Carlo simulations of the dilute system. The respective theoretical predictions differ, questioning the validity of the current theoretical state-of-the-art description of quantum droplets within the eGPE framework and indicating that correlations in the system are significant. Furthermore, we show that our system can serve as a sensitive testing ground for many-body theories in the near future.

Theory for self-bound states of dipolar Bose-Einstein condensates

“…Moreover, the coherent nature of the EGPE ground state implies that the particle number distribution (PND) is of Poissonian type, which for large particle numbers, is symmetric around the mean. This, however, is inconsistent with the asymmetric PND observed in experiments [5,6].…”

“…Since the observation of the stable liquid droplets in dipolar condensates in the mean-field collapse regime [1,2], this novel quantum phase has received increasing attention in the community. To date, there has been rapid experimental progress in the exploration of the fundamental properties of these quantum droplets, such as their stabilization mechanism [2,3], collective excitations [2,4], self-bound states [5,6], striped states [7], and metastable states with supersolid characteristics [8][9][10]. Aside from dipolar systems, liquid droplets have also been observed in attractive bosonic mixtures [11][12][13].…”

“…To the first order, quantum fluctuations can be incorporated into the Gross-Pitavskii equation (GPE) through the Lee-Huang-Yang (LHY) correction to the condensate energy [15], leading to the so-called extended Gross-Pitaevskii equation (EGPE) [16][17][18][19]. Although the EGPE has successfully explained many experimental observations, it still shows many discrepancies as well [6]. In fact, the EGPE is affected by an intrinsic flaw when applied to the droplet state, since the LHY correction requires the collective excitation upon the coherent ground state to be stable, which is not ensured in this case.…”

The low-energy Goldstone mode in a trapped dipolar supersolid

“…For the presented measurements the magnetic field is orientated along theŷdirection. Subsequently, we tune the contact interaction from the background scattering length a bg = 140(20) a 0 42-44 to approximately 112 a 0 by ramping the magnetic field closer to the double Feshbach resonances near 5.1 G 8,45,46 . To reach the droplet region, the magnetic field is further linearly ramped to the final scattering length in the range of 90 a 0 and 105 a 0 in 30 ms. We then let the samples evolve for 15 ms in order to allow the quantum droplet arrays to form and equilibrate.…”

“…As an indicator of the phase coherence, we show the ratio of the first minimum in the density compared to the central droplet peak density as an indicator of the overlap between the droplets 46 of the calculated density profile of the ground state in red. As in the experiment, three regions are identified and the coherent region locates between 94 a 0 and 97 a 0 , shifting ∼3 a 0 from the experimentally obtained phase diagram.…”