Towards a quantum Monte Carlo–based density functional including finite-range effects: Excitation modes of a K39 quantum droplet

Abstract

Some discrepancies between experimental results on quantum droplets made of a mixture of 39 K atoms in different hyperfine states and their analysis within extended Gross-Pitaevskii theory (which incorporates beyond mean-field corrections) have been recently solved by introducing finite-range effects into the theory. Here we study the influence of these effects on the monopole and quadrupole excitation spectrum of extremely dilute quantum droplets using a density functional built from first-principles quantum Monte Carlo calculations, which can be easily introduced in the existing Gross-Pitaevskii numerical solvers. Our results show differences of up to 20% with those obtained within the extended Gross-Pitaevskii theory, likely providing another way to observe finite-range effects in mixed quantum droplets by measuring their lowest excitation frequencies.

Beyond-mean-field crossover from one dimension to three dimensions in quantum droplets of binary mixtures

“…The realization of quasi-1D droplets in the beyondmean-field crossover from 1D to 3D would allow precise studies of the beyond-mean-field effects in Bose gases. Effects beyond the standard Lee-Huang-Yang energy used in this paper will appear [27], either because of higherorder terms in the density expansion [28], because of finite-range interacting potentials [29,30], or because of temperature effects [31].…”

Dilute quantum liquid in a K-Rb Bose mixture

“…6, the compressibility computed with the MF+LHY approach is shown for a set of values of the scattering length and compared to QMC results. In contrast to 39 K droplets [16], the compressibility of QMCbased functional is higher compared to the MF+LHY, due to relatively smaller values of effective ranges in a K-Rb mixture. Fig.…”

“…with a m = 4πR vdw /Γ(1/4) 2 the mean scattering length and R vdw = 2µC 6 / 2 1/4 /2 the van der Waals length, where µ is the reduced mass. The C 6 coefficients for 41 K and 87 Rb are given, along with the effective ranges derived from (16), in Table II.…”

“…A most natural way to include such effects within the DFT scheme is to use density functionals built from results of first-principles quantum Monte Carlo calculations for the homogeneous phase [15,16]. Importantly, firstprinciples finite-N QMC calculations in the low-density regime show good agreement with the DFT approach [17] only in the vicinity of the gas-liquid transition while, at larger densities, modifications to MF+LHY approach are necessary [18][19][20][21].…”