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arXiv:2301.03031 · Physical Review Research

Spin conductivity spectrum and spin superfluidity in a binary Bose mixture

Yuta Sekino, Hiroyuki Tajima, Shun Uchino

Published Apr 26, 2023• 5 citations
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Abstract

We investigate the spectrum of spin conductivity for a miscible two-component Bose-Einstein condensate (BEC) that exhibits spin superfluidity. By using the Bogoliubov theory, the regular part being the spin conductivity at finite ac frequency and the spin Drude weight characterizing the $\ensuremath{\delta}$-function peak at zero frequency are analytically computed. We demonstrate that the spectrum exhibits a power-law behavior at low frequency, reflecting gapless density and spin modes specific to the binary BEC. At the phase transition points into immiscible and quantum-droplet states, the change in quasiparticle dispersion relations modifies the power law. In addition, the spin Drude weight becomes finite, indicating zero spin resistivity due to spin superfluidity. Our results also suggest that the Andreev-Bashkin drag density is accessible by measuring the spin conductivity spectrum.

DOI
10.1103/physrevresearch.5.023058

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•Jan 1, 2018•0 citations
We investigate the spectrum of spin conductivity for a miscible two-component Bose-Einstein condensate (BEC) that exhibits spin superfluidity. By using the Bogoliubov theory, the regular part being the spin conductivity at finite ac frequency and the spin Drude weight characterizing the \ensuremathδ\ensuremath{\delta}\ensuremathδ-function peak at zero frequency are analytically computed. We demonstrate that the spectrum exhibits a power-law behavior at low frequency, reflecting gapless density and spin modes specific to the binary BEC. At the phase transition points into immiscible and quantum-droplet states, the change in quasiparticle dispersion relations modifies the power law. In addition, the spin Drude weight becomes finite, indicating zero spin resistivity due to spin superfluidity. Our results also suggest that the Andreev-Bashkin drag density is accessible by measuring the spin conductivity spectrum.
Two-component systems consisting of mutually interacting particles can demonstrate both intracomponent transport effects and intercomponent entrainment (or drag) effects. In the presence of superfluidity, the intracomponent transport is characterized by dissipative conductivity and superfluid weight in the framework of two-fluid model, and intercomponent entrainment gives rise to normal and nondissipative drag effects. We present unified treatment of all these effects for spatially homogeneous two-component atomic Bose-Einstein condensates based on the Bogoliubov theory, focusing specifically on the drag effects. Calculating finite-frequency intra- and intercomponent conductivities with taking into account quasiparticle damping, we derive and numerically check analytical Drude-like approximations applicable at low frequencies and Lorentz-like approximations applicable at higher frequencies in the vicinity of the resonant energy of spin-to-density Bogoliubov quasiparticle conversion. As possible physical realizations of two-component atomic systems, we consider three-dimensional Bose-Bose mixtures and closely spaced two-layered systems of magnetic dipolar atoms.
We report on the measurement of the spin-dipole (SD) polarizability and of the frequency of the SD oscillation of a two-component Bose-Einstein condensate of sodium atoms occupying the $|3{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2},F=1,{m}_{F}=\ifmmode\pm\else\textpm\fi{}1\ensuremath{\rangle}$ hyperfine states. This binary spin mixture presents the important properties of being, at the same time, fully miscible and rid of the limit set by buoyancy. It is also characterized by a huge enhancement of the SD polarizability and by the consequent softening of the frequency of the SD oscillation, due to the vicinity to the transition to the immiscible phase. The experimental data are successfully compared with the predictions of theory.
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 $\ensuremath{\omega}\ensuremath{\propto}{p}^{2}$ 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.
We show that the optical spin conductivity, which is a small ac response of a bulk spin current and elusive in condensed matter systems, can be measured in ultracold atoms. We demonstrate that this conductivity contains rich information on quantum states by analyzing experimentally achievable systems such as a spin-12\frac{1}{2}21​ superfluid Fermi gas, a spin-1 Bose-Einstein condensate, and a Tomonaga-Luttinger liquid. The obtained conductivity spectra, which are absent in the Drude conductivity, reflect quasiparticle excitations and non-Fermi-liquid properties. Accessible physical quantities include the superfluid gap and the contact for the superfluid Fermi gas, gapped and gapless spin excitations as well as quantum depletion for the Bose-Einstein condensate, and the spin part of the Tomonaga-Luttinger liquid parameter elusive in cold-atom experiments. Unlike its mass transport counterpart, the spin conductivity serves as a probe applicable to clean atomic gases without disorder or lattice potentials. Our formalism can be generalized to various systems such as spin-orbit-coupled and nonequilibrium systems.
The miscibility condition for a binary mixture of two interacting Bose-Einstein condensates is shown to be deeply affected by interaction driven thermal fluctuations. These give rise to a first order phase transition to a demixed phase with full spatial separation of the two condensates, even if the mixture is miscible at zero temperature. Explicit predictions for the isothermal compressibility, the spin susceptibility, and the phase transition temperature T_{M} are obtained in the framework of Popov theory, which properly includes beyond mean-field quantum and thermal fluctuations in both the spin and density channels. For a mixture of two sodium condensates occupying the hyperfine states |F=1⟩,|m_{F}=1⟩ and |F=1,m_{F}=-1⟩, respectively, T_{M} is predicted to occur at about 0.7 times the usual BEC critical temperature.
Motivated by previous work on drag effects in superfluid Bose-Einstein condensates, the Bose-Hubbard model on the square lattice is considered using mean-field theory, and a method for computing the superfluid drag density that does not rely on Galilean invariance is employed to re-derive the drag in the weakly interacting two-component Bose-Einstein condensate. The same method is then used on the Bose-Hubbard model generalized to three-components. An exact analytic expression is not possible because of the complexity of the resulting diagonalization problem. However, Rayleigh-Schrödinger perturbation theory is used to fourth order, which yields an analytic perturbative expression for the zero temperature drag, in addition to exact numerical diagonalization to find the exact behaviour at zero and finite temperatures within mean-field theory. It is found that the presence of a third component can alter the drag in a non-trivial manner: The drag between the two initial boson components can be completely mediated by the third, and it can be both enhanced and diminished depending on the inter-component interaction strengths and signs. An attempt is also made at finding the drag in a weakly interacting two-component Bose-Einstein condensate with spin-orbit coupling, but complications arise, which are discussed. Finally, a phase diagram for the two-component condensate with interactions and spin-orbit coupling is constructed, describing the spin-imbalance, degeneracy, and distribution of spin at zero temperature. A qualitative discussion of the finite temperature behaviour suggests that the inhomogeneous weakly interacting and spin-orbit coupled superfluid Bose-Einstein condensate may in some regions in parameter space favor spin-imbalance as the temperature is increased.