Microscopic pairing theory of a binary Bose mixture with interspecies attractions: bosonic BEC-BCS crossover and ultradilute low-dimensional quantum droplets

Abstract

Ultradilute quantum droplets are intriguing new state of matter, in which the attractive mean-field force can be balanced by the repulsive force from quantum fluctuations to avoid collapse. Here, we present a microscopic theory of ultradilute quantum droplets in three-, one- and two-dimensional two-component Bose-Bose mixtures, by generalizing the conventional Bogoliubov theory to include the bosonic pairing arising from the interspecies attraction. Our pairing theory is fully equivalent to a variational approach and hence gives an upper bound for the energy of quantum droplets. In three dimensions, we predict the existence of a strongly interacting Bose droplet at the crossover from Bose-Einstein condensates (BEC) to Bardeen--Cooper--Schrieffer (BCS) superfluids and map out the bosonic BEC-BCS crossover phase diagram. In one dimension, we find that the energy of the one-dimensional Bose droplet calculated by the pairing theory is in an excellent agreement with the latest diffusion Monte Carlo simulation {[}Phys. Rev. Lett. \textbf{122}, 105302 (2019){]}, for nearly all the interaction strengths at which quantum droplets exist. In two dimensions, we show that Bose droplets disappear and may turn into a soliton-like many-body bound state, when the interspecies attraction exceeds a critical value. Below the threshold, the pairing theory predicts more or less the same results as the Bogoliubov theory derived by Petrov and Astrakharchik {[}Phys. Rev. Lett. \textbf{117}, 100401 (2016){]}. The predicted energies from both theories are higher than the diffusion Monte Carlo results, due to the weak interspecies attraction and the increasingly important role played by the beyond-Bogoliubov-approximation effect in two dimensions.

16 pages, 13 figures; the title is changed due to the significant new 3D results contributed by Jia Wang

References in corpus (13)

• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Quantum liquid droplets in a mixture of Bose-Einstein condensates
• Self-bound droplets of a dilute magnetic quantum liquid
• Quantum-fluctuation-driven crossover from a dilute Bose-Einstein condensate to a macro-droplet in a dipolar quantum fluid
• Transient supersolid properties in an array of dipolar quantum droplets
• Collisions of self-bound quantum droplets
• Quantum Fluctuations in the Superfluid State of the BCS-BEC Crossover
• Equation of state of a superfluid Fermi gas in the BCS-BEC crossover
• Two-dimensional solitons and quantum droplets supported by competing self- and cross-interactions in spin-orbit-coupled condensates
• Universal Properties of Two-Dimensional Boson Droplets
• Ground state energy of the two-dimensional weakly interacting Bose gas: First correction beyond Bogoliubov theory
• Beyond Lee-Huang-Yang description of self-bound Bose mixtures
• Quantum fluctuations in a strongly interacting Bardeen-Cooper-Schrieffer polariton condensate at thermal equilibrium

Cited by in corpus (11)

• Thermal instability, evaporation and thermodynamics of one-dimensional liquids in weakly-interacting Bose-Bose mixtures
• Microscopic derivation of the extended Gross-Pitaevskii equation for quantum droplets in binary Bose mixtures
• Many-body and temperature effects in two-dimensional quantum droplets in Bose-Bose mixtures
• Zero-energy modes of two-component Bose-Bose droplets
• Quantum liquid droplets in Bose mixtures with weak disorder
• Quasi-one-dimensional harmonically trapped quantum droplets
• Ultradilute self-bound quantum droplets in Bose-Bose mixtures at finite temperature
• Biexciton-like quartet condensates in an electron-hole liquid
• The Effective Single-mode model of a Binary Boson Mixture in the Quantum Droplet Region
• Functional renormalization for repulsive Bose-Bose mixtures at zero temperature
• Weakly-interacting Bose-Bose mixtures from the functional renormalisation group