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Liquid Quantum Bose-Fermi droplets

Tomasz Karpiuk, Debraj Rakshit, Mirosław Brewczyk, Mariusz Gajda

Published Dec 31, 2017• 0 citations
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Abstract

We study stability of a zero temperature mixture of attractively interacting degenerate bosons and spin-polarized fermions in the absence of confinement. We demonstrate that higher order corrections to the standard mean field energy of the system can lead to a formation of liquid droplets -- self-bound incompressible systems in a three-dimensional space. In addition to the quantum Lee-Huang-Yang correction to the boson-boson interaction energy, a higher order term in the Bose-Fermi coupling constant is crucial for stabilization of the system. We study a stability region of droplets for three different mixtures of species with different mass ratios, namely: $^{41}$K$\,$-$^{40}$K, $^{87}$Rb$\,$-$^{40}$K, and $^{133}$Cs$\,$-$^{6}$Li as a function of the ratio of Bose-Fermi to Bose-Bose scattering length. The stability analysis is supported by a numerical simulations of droplet formation dynamics starting with a trapped system which is subsequently released from the trap. Our results indicate that Bose-Fermi droplets can be realized experimentally.

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We study stability of a zero temperature mixture of attractively interacting degenerate bosons and spin-polarized fermions in the absence of confinement. We demonstrate that higher order corrections to the standard mean field energy of the system can lead to a formation of liquid droplets -- self-bound incompressible systems in a three-dimensional space. In addition to the quantum Lee-Huang-Yang correction to the boson-boson interaction energy, a higher order term in the Bose-Fermi coupling constant is crucial for stabilization of the system. We study a stability region of droplets for three different mixtures of species with different mass ratios, namely: 41^{41}41K \,-40^{40}40K, 87^{87}87Rb \,-40^{40}40K, and 133^{133}133Cs \,-6^{6}6Li as a function of the ratio of Bose-Fermi to Bose-Bose scattering length. The stability analysis is supported by a numerical simulations of droplet formation dynamics starting with a trapped system which is subsequently released from the trap. Our results indicate that Bose-Fermi droplets can be realized experimentally.
We study the stability of a zero temperature mixture of attractively interacting degenerate bosons and spin-polarized fermions in the absence of confinement. We demonstrate that higher order corrections to the standard mean-field energy can lead to a formation of Bose-Fermi liquid droplets – self-bound systems in three-dimensional space. The stability analysis of the homogeneous case is supported by numerical simulations of finite systems by explicit inclusion of surface effects. We discuss the experimental feasibility of formation of quantum droplets and indicate the main obstacle – inelastic three-body collisions.
Abstract We study weakly interacting mixtures of ultracold atoms composed of bosonic and fermionic species in 2D and 1D. When interactions between particles are appropriately tuned, self-bound quantum liquids can be formed. We show that while formation of these droplets in 2D is due to the higher order correction terms contributing to the total energy and originating in quantum fluctuations, in 1D geometry the quantum fluctuations have a negligible role on formation of the self-bound systems. The leading mean-field interactions are then sufficient for droplet formation in 1D. We analyze energetic stability for 2D and 1D systems and predict values of equilibrium densities of droplets.
We study liquid quantum droplets in a mixture of two-component Bose-Einstein condensates under variable confinement introduced along one or two spatial dimensions. Although the atom-atom scattering has a three-dimensional character, discreteness of the available modes in the reduced dimension(s) strongly influences the zero-point energy, which for a weakly interacting three-dimensional system is given by the Lee-Huang-Yang term. Here, we generalize the result of Lee, Huang, and Yang and calculate the higher order corrections to the mean-field energy for a single component Bose-Einstein condensate under condition of a tight confinement in one or two spatial directions. We apply our results to the two-component mixture of bosonic species under conditions favorable for the creation of quantum liquid droplets, which constitute a perfect playground for studies of the beyond mean-field effects. Our findings allow one to analyze the properties of quantum droplets at the dimensional crossover and provide demanding conditions for accessing quasilow dimensions. They also pave a way for experimental exploration of this state of matter in reduced dimensions.
We study the canonical problem of a Fermi gas interacting with a weakly repulsive Bose-Einstein condensate at zero temperature. To explore the quantum phases across the full range of boson-fermion interactions, we construct a versatile variational Ansatz that incorporates pair correlations and correctly captures the different polaron limits. Remarkably, we find that self-bound quantum droplets can exist in the strongly interacting regime, preempting the formation of boson-fermion dimers, when the Fermi pressure is balanced by the resonant boson-fermion attraction. This scenario can be achieved in experimentally available Bose-Fermi mixtures for a range of boson-fermion mass ratios in the vicinity of equal masses. We furthermore show that a larger fermion density instead yields phase separation between a Bose-Fermi mixture and excess fermions, as well as behavior reminiscent of a liquid-gas critical point. Our results suggest that first-order quantum phase transitions play a crucial role in the phase diagram of Bose-Fermi mixtures.
Abstract The static and dynamic properties of self-bound quantum droplets in a one-dimensional Bose-Bose mixture are discussed in the spirit of the Hartree–Fock-Bogoliubov theory. This latter enables us to provide beyond the Lee-Huang-Yang (LHY) quantum corrections to the equation of state at both zero and finite temperatures. In the uniform case our results for the ground-state energy and the critical temperature are confirmed through comparison with Quantum Monte-Carlo simulation and with available theoretical results. The density profiles are supported by numerical simulations of the generalized Gross-Pitaevskii equation which selfconsistently includes higher-order terms originating from the normal and anomalous fluctuations under the local density approximation. We show that the density exhibits a dip near its center in the flat-top plateau region for large interspecies interactions. We exemplify the impact of the beyond LHY corrections on the spatiotemporal evolution of the self-bound droplet in the presence of excitation induced by periodic density modulation. It is found that higher-order corrections may lead to the formation of a train of small droplets. We then extend our study for the case of inhomogeneous droplets in quasi one-dimensional Bose mixtures.
Using numerical methods, we study the formation of self-bound quantum Bose-Fermi droplets at nonzero temperatures. We describe an attractive atomic Bose-Fermi mixture using quantum hydrodynamics enriched by beyond-mean-field corrections and thermal fluctuations, together with a simplified self-consistent Hartree-Fock model. With these models, we determine that low-temperature droplets with finite lifetimes can exist in free space when the attraction between bosons and fermions is sufficiently strong. Additionally, Bose-Fermi droplets at nonzero temperatures can exist in a box potential in equilibrium with bosonic and fermionic vapor. We discuss the properties of Bose-Fermi droplets at nonzero temperatures in terms of the initial condensate fraction, total atom number, and interspecies attraction strength.