Microscopic derivation of the extended Gross-Pitaevskii equation for quantum droplets in binary Bose mixtures
arXiv:2006.05769 · doi:10.1103/PhysRevA.102.043302
Abstract
An ultradilute quantum droplet is a self-bound liquid-like state recently observed in ultracold Bose-Einstein condensates. In all previous theoretical studies, it is described by a phenomenological low-energy effective theory, termed as the extended Gross\textendash Pitaevskii equation. Here, we microscopically derive the Gross\textendash Pitaevskii equation for the condensate and also for a pairing field in an inhomogeneous quantum droplet realized by Bose-Bose mixtures with attractive inter-species interaction. We show that the inclusion of the pairing field is essential, in order to have a consistent description of the droplet state. We clarify that, the extended Gross\textendash Pitaevskii equation used earlier should be understood as the equation of motion for the pairing field, rather than the condensate. The fluctuations of the pairing field give rise to low-energy collective excitations of the droplet. We also present the Bogoliubov equations for gapless phonon modes and gapped modes due to pairing in real space, which characterizes single-particle-like excitations of the droplet. The equations of motion derived in this work for the condensate and the pairing field serve an ideal starting point to understand the structure and collective excitations of non-uniform ultradilute quantum droplets in on-going cold-atom experiments.
arXiv comment6 pages, no figures; title changed; to appear in Physical Review A as a Regular Article
References in corpus (34)
- Theory of Bose-Einstein condensation in trapped gases
- Quantum Mechanical Stabilization of a Collapsing Bose-Bose Mixture
- Quantum liquid droplets in a mixture of Bose-Einstein condensates
- Observation of quantum droplets in a strongly dipolar Bose gas
- Self-bound quantum droplets in atomic mixtures
- 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
- Conserving and Gapless Approximations for an Inhomogeneous Bose Gas at Finite Temperatures
- Ultradilute low-dimensional liquids
- Bright soliton to quantum droplet transition in a mixture of Bose-Einstein condensates
- Observation of Quantum Droplets in a Heteronuclear Bosonic Mixture
- Finite temperature excitations of a trapped Bose gas
- Collisions of self-bound quantum droplets
- Quantum Fluctuations in the Superfluid State of the BCS-BEC Crossover
- Ground-state properties and elementary excitations of quantum droplets in dipolar Bose-Einstein condensates
- Self-bound dipolar droplet: a localized matter-wave in free space
- Equation of state of a superfluid Fermi gas in the BCS-BEC crossover
- Collective Excitations of a One-Dimensional Quantum Droplet
- Two-dimensional solitons and quantum droplets supported by competing self- and cross-interactions in spin-orbit-coupled condensates
- Dilute dipolar quantum droplets beyond the extended Gross-Pitaevskii equation
- Collective excitations of self-bound droplets of a dipolar quantum fluid
- The liquid state of one-dimensional Bose mixtures: a quantum Monte-Carlo study
- Universality in ultradilute liquid Bose-Bose mixtures
- Consistent theory of self-bound quantum droplets with bosonic pairing
- Equation of state and self-bound droplet in Rabi-coupled Bose mixtures
- Beyond Lee-Huang-Yang description of self-bound Bose mixtures
- Comparative study of strong coupling theories of a trapped Fermi gas at unitarity
- Self-bound Bose mixtures
- Spin-orbit coupling induced quantum droplet in ultracold Bose-Fermi mixtures
- Mean field thermodynamics of a spin-polarized spherically trapped Fermi gas at unitarity
- Microscopic pairing theory of a binary Bose mixture with interspecies attractions: bosonic BEC-BCS crossover and ultradilute low-dimensional quantum droplets
- Finite-range effects in ultradilute quantum drops
- Theory for Self-Bound States of Dipolar Bose-Einstein Condensates
- Collective oscillations of a confined Bose gas at finite temperature in the random-phase approximation
Cited by in corpus (14)
- Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
- Collective excitations of a spherical ultradilute quantum droplet
- Formation and quench of homonuclear and heteronuclear quantum droplets in one dimension
- Quadratic fractional solitons
- Vortex-ring quantum droplets in a radially-periodic potential
- Thermal destabilization of self-bound ultradilute quantum droplets
- Revisiting a stability problem of two-component droplets
- Ultradilute self-bound quantum droplets in Bose-Bose mixtures at finite temperature
- The Effective Single-mode model of a Binary Boson Mixture in the Quantum Droplet Region
- Two-dimensional quantum droplets in binary quadrupolar condensates
- Functional renormalization for repulsive Bose-Bose mixtures at zero temperature
- Breakdown of the single-mode description of ultradilute quantum droplets in binary Bose mixtures: A perspective from a microscopic bosonic pairing theory
- Self-evaporation dynamics of quantum droplets in a 41K-87Rb mixture
- Rotational dynamics induced by low energy binary collisions of quantum droplets