Effective interactions in a quantum Bose-Bose mixture

Abstract

We generalize the Beliaev diagrammatic theory of an interacting spinless Bose-Einstein condensate to the case of a binary mixture. We derive a set of coupled Dyson equations and find analytically the Green's functions of the system. The elementary excitation spectrum consists of two branches, one of which takes the characteristic parabolic form in the limit of a spin-independent interaction. We observe renormalization of the magnon mass and the spin-wave velocity due to the Andreev-Bashkin entrainment effect. For a 3D weakly-interacting gas the spectrum can be obtained by applying the Bogoliubov transformation to the second-quantized Hamiltonian in which the microscopic two-body potentials in each channel are replaced by the corresponding off-shell scattering amplitudes. The superfluid drag density can be calculated by considering a mixture of phonons and magnons interacting via the effective potentials. We show that this problem is identical to the second-order perturbative treatment of a Bose polaron. In 2D the drag contributes to the magnon dispersion already in the first approximation. Our consideration provides a basis for systematic study of emergent phases in quantum degenerate Bose-Bose mixtures.

14 pages, 5 figures

References in corpus (10)

• 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
• Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperfine ground state
• Observation of Roton Mode Population in a Dipolar Quantum Gas
• Coherent magnon optics in a ferromagnetic spinor Bose-Einstein condensate
• Andreev-Bashkin effect in superfluid cold gases mixture
• Beyond mean-field properties of binary dipolar Bose mixtures at low temperatures
• Ground-state energy and depletions for a dilute binary Bose gas
• 2D dilute Bose mixture at low temperatures

Cited by in corpus (25)

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• Beyond Lee-Huang-Yang description of self-bound Bose mixtures
• Self-bound Bose mixtures
• Observation of Two Sound Modes in a Binary Superfluid Gas
• Phonon Stability and Sound Velocity of Quantum Droplets in a Boson Mixture
• Universality of miscible-immiscible phase separation dynamics in two-component Bose-Einstein condensates
• Manifestation of relative phase in dynamics of two interacting Bose-Bose droplets
• Intermolecular forces and correlations mediated by a phonon bath
• Beyond mean-field corrections to the quasiparticle spectrum of superfluid Fermi gases
• Functional renormalization for repulsive Bose-Bose mixtures at zero temperature
• Dipolar polaritons squeezed at unitarity
• Weakly-interacting Bose-Bose mixtures from the functional renormalisation group
• Large-$N$ expansion for condensation and stability of Bose-Bose mixtures at finite temperatures
• Spin and Density Modes in a Binary Fluid of Light
• Spin conductivity spectrum and spin superfluidity in a binary Bose mixture
• First-order, continuous, and multicritical Bose-Einstein condensation in Bose mixtures
• Spin-orbit coupled depairing of a dipolar biexciton superfluid
• Magnetoroton in a two-dimensional Bose-Bose mixture
• Self-localization of magnons and magnetoroton in a binary Bose-Einstein condensate
• Polaronic neutron in dilute alpha matter: A $p$-wave Bose polaron
• Spin-orbit coupled mean-field Bose gas at finite temperature
• Controllable fusion of electromagnetic bosons in two-dimensional semiconductors
• Phase diagram of two-component mean-field Bose mixtures
• Many-body effects in the excitations and dynamics of trapped Bose-Einstein condensates
• Finite-frequency normal and superfluid drag effects in two-component atomic Bose-Einstein condensates