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arXiv:2103.00918 · Physical Review A

Spin drag and fast response in a quantum mixture of atomic gases

Federico Carlini, S. Stringari

Published Aug 2, 2021• 12 citations
arXivHTMLPDF

Abstract

By applying a sudden perturbation to one of the components of a mixture of two quantum fluids, we explore the effect on the motion of the second component on a short timescale. By implementing perturbation theory, we prove that for short times the response of the second component is fixed by the energy weighted moment of the crossed dynamic structure factor (crossed $f$-sum rule). We also show that by properly monitoring the time duration of the perturbation it is possible to identify peculiar fast spin drag regimes, which are sensitive to the interaction effects in the Hamiltonian. Special focus is given to the case of coherently coupled Bose-Einstein condensates, interacting Bose mixtures exhibiting the Andreev-Bashkin effect, normal Fermi liquids, and the polaron problem. The relevant excitations of the system contributing to the spin drag effect are identified and the contribution of the low-frequency gapless excitations to the $f$-sum rule in the density and spin channels is explicitly calculated employing the proper macroscopic dynamic theories. Both spatially periodic and Galilean boost perturbations are considered.

DOI
10.1103/physreva.104.023301

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By applying a sudden perturbation to one of the components of a mixture of two quantum fluids, we explore the effect on the motion of the second component on a short timescale. By implementing perturbation theory, we prove that for short times the response of the second component is fixed by the energy weighted moment of the crossed dynamic structure factor (crossed fff-sum rule). We also show that by properly monitoring the time duration of the perturbation it is possible to identify peculiar fast spin drag regimes, which are sensitive to the interaction effects in the Hamiltonian. Special focus is given to the case of coherently coupled Bose-Einstein condensates, interacting Bose mixtures exhibiting the Andreev-Bashkin effect, normal Fermi liquids, and the polaron problem. The relevant excitations of the system contributing to the spin drag effect are identified and the contribution of the low-frequency gapless excitations to the fff-sum rule in the density and spin channels is explicitly calculated employing the proper macroscopic dynamic theories. Both spatially periodic and Galilean boost perturbations are considered.
We investigate the propagation of spin waves in two-component mixtures of one-dimensional Bose gases interacting through repulsive contact potentials. By using quantum Monte Carlo methods we calculate static ground-state properties, such as the spin susceptibility and the spin structure factor, as a function of the coupling strengths and we determine the critical parameters for phase separation. In homogeneous mixtures, results of the velocity of spin waves and of its softening close to the critical point of phase separation are obtained by means of hydrodynamic theory and a sum-rule approach. We quantify the nondissipative drag effect, resulting from the Andreev-Bashkin current-current interaction between the two components of the gas, and we show that in the regime of strong coupling it causes a significant suppression of the spin-wave velocity.
We study a mixture of two superfluids with density–density and current–current (Andreev–Bashkin) interspecies interactions. The Andreev–Bashkin coupling gives rise to a dissipationless drag (or entrainment) between the two superfluids. Within the quantum hydrodynamics approximation, we study the relations between speeds of sound, susceptibilities and static structure factors, in a generic model in which the density and spin dynamics decouple. Due to translational invariance, the density channel does not feel the drag. The spin channel, instead, does not satisfy the usual Bijl–Feynman relation, since the f-sum rule is not exhausted by the spin phonons. The very same effect on one dimensional Bose mixtures and their Luttinger liquid description is analysed within perturbation theory. Using diffusion quantum Monte Carlo simulations of a system of dipolar gases in a double layer configuration, we confirm the general results. Given the recent advances in measuring the counterflow instability, we also study the effect of the entrainment on the dynamical stability of a superfluid mixture with non-zero relative velocity.
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.
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.
Sum rules for the dynamic structure factors are powerful tools to explore the collective behaviors in many-body systems at zero temperature as well as at finite temperatures. The recent remarkable realization of synthetic spin-orbit (SO) coupling in quantum gases is opening up new perspective to study the intriguing SO effects with ultracold atoms. So far, a specific type of SO coupling, which is generated by a pair of Raman laser beams, has been experimentally achieved in Bose-Einstein condensates of 87Rb and degenerate Fermi gases of 40K and 6Li. In the presence of SO coupling, the dynamic structure factors for the density fluctuation and spin fluctuation satisfy different sum rules. In particular, in the two-component quantum gases with inter-species Raman coupling, the f-sum rule for the spin fluctuation has an additional term proportional to the transverse spin polarization. Due to the coupling between the momentum and spin, the first moment of the dynamic structure factor does not necessarily possess the inversion symmetry, which is in strong contrast to the conventional system without SO coupling. Such an asymmetric behavior could be observed in both Fermi gases and Bose gases with Raman coupling. As a demonstration, we focus on the uniform case at zero temperature in this work. For the non-interacting Fermi gases, the asymmetric first moment appears only when the Raman detuning is finite. The asymmetric amplitude is quite limited, and it vanishes at both zero detuning and infinite detuning. For the weakly interacting Bose gases, the first moment is asymmetric in momentum space even at zero detuning, when the ground state spontaneously breaks the Z2 symmetry in the plane-wave condensation phase. Using the Bogoliubov method, the dynamic structure factor and its first moment are explicitly calculated for various interaction parameters. We find that the asymmetric behavior in the spin channel could be much more significant than in the density channel, and the asymmetric amplitude is enhanced as the interaction strength increases. Experimentally, the dynamic structure factors can be directly measured through the two photon Bragg scattering. Numeric simulations show that to observe the deviation of inversion symmetry in the first moment, the resolution of the Bragg spectroscopy should reach a required value. For the typical parameters of the rubidium atomic gas, the required resolution is about 10-2Er with Er being the recoil energy. Our predictions can be tested in the future experiment.
In this thesis we investigate the properties of mixtures of Bose gases in one dimensions at zero temperature using quantum Monte-Carlo methods. First we investigate the limiting case of an impurity interacting with an atomic bath. We characterize the impurity, by calculating its effective mass, binding energy as well as the contact parameter between the impurity and the bath. In particular, we find that the effective mass rapidly increases to very large values when the impurity gets strongly coupled to an otherwise weakly repulsive bath. Then we describe uniform balanced mixtures with repulsive interactions. We investigate the miscibility phase diagram of the two components and find that correlations do not alter the phase diagram predicted by mean-field theories. We investigate the Andreev-Bashkin effect , a non-dissipative drag between the the two components of the gas and find that the drag becomes very large in the strongly interacting regime. In non-homogeneous systems we also investigate the frequency of the spin-dipole mode. Finally we describe mixtures with attractive inter-species interactions, where one can obtain a liquid ground state because of the competition between the inter-species attraction and intra-species repulsion. We characterize the the liquid and we find that the liquid state can be formed if the ratio of coupling strengths between inter-species attractive and intra-species repulsive interactions exceeds a critical value.