TY - JOUR

T1 - Effective interactions in a quantum Bose-Bose mixture

AU - Utesov, O. I.

AU - Baglay, M. I.

AU - Andreev, S. V.

PY - 2018/5/23

Y1 - 2018/5/23

N2 - 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 ω p2 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 three-dimensional weakly interacting gas the spectrum can be obtained by applying the Bogoliubov transformation to a 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 two dimensions 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.

AB - 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 ω p2 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 three-dimensional weakly interacting gas the spectrum can be obtained by applying the Bogoliubov transformation to a 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 two dimensions 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.

KW - SPIN-WAVES

KW - AMORPHOUS FERROMAGNETS

KW - MAGNETIC EXCITATIONS

KW - GAS

KW - LIQUID

KW - SYSTEM

KW - DROPLETS

KW - BOSONS

KW - STATE

UR - http://www.scopus.com/inward/record.url?scp=85047459262&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.97.053617

DO - 10.1103/PhysRevA.97.053617

M3 - Article

AN - SCOPUS:85047459262

VL - 97

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 5

M1 - 053617

ER -