The one-dimensional interacting Bose-Fermi mixtures, exhibiting quantum phase transitions at zero temperature, are particularly valuable for the study of quantum critical phenomena. In the present paper, we analytically study quantum phase diagram, equation of state and quantum criticality of the Bose-Fermi mixture using the thermodynamic Bethe ansatz equations. We show that thermodynamical properties display universal scaling behaviour at quantum criticality. Furthermore, quantum criticality of the Bose-Fermi mixture in an harmonic trap is also studied within the local density approximation. We thus demonstrate that the phase diagram and critical properties of the bulk system provide insights into understanding universal features of many-body critical phenomena.
We study the attractive Bose-Hubbard model with a tunable, on-site three-body constraint. It is shown that the critical behavior of the system undergoing a phase transition from pair-superfluid to superfluid at unit filling depends on the value of the three-body repulsion. In particular, we calculate critical exponents and the central charge governing the quantum phase transition.
A general approach is proposed to solve the coupled Gross-Pitaevskii equations (CGP) for K-species Bose-Einstein condensates (BEC). Analytical solutions have been obtained under the Thomas-Fermi approximation. We aim at finding out the common features of the K-species BEC. In particular, two types of phase-transitions, full-state-transition and partial-state transition, are found. In the former all species are involved in the transition, while in the latter only a few specified species are essentially involved. This leads to the criticality and the hidden criticality (previously found in multi…
The emergence of quasiparticles in strongly interacting matter represents one of the cornerstones of modern physics. However, when different phases of matter compete near a quantum critical point, the very existence of quasiparticles comes under question. Here we create Bose polarons near quantum criticality by immersing atomic impurities in a Bose-Einstein condensate (BEC) with near-resonant interactions. Using locally-resolved radiofrequency spectroscopy, we probe the energy, spectral width, and short-range correlations of the impurities as a function of temperature. Far below the superfluid…
Using the exact Bose-Fermi mapping, we study universal properties of ground-state density distributions and finite-temperature quantum critical behavior of one-dimensional hard-core bosons in trapped incommensurate optical lattices. Through the analysis of universal scaling relations in the quantum critical regime, we demonstrate that the superfluid to Bose glass transition and the general phase diagram of disordered hard-core bosons can be uniquely determined from finite-temperature density distributions of the trapped disordered system.
We investigate the finite temperature charge density wave (CDW) transition of lattice Bose gases within optical cavities in the deep Mott-insulator limit. We find a new critical regime emerges at a temperature around one-half of the on-site interaction energy, where the first order CDW transition at low temperatures terminates at a critical point and changes to a second order one. By directly calculating the critical exponents and constructing the effective theory in the corresponding critical regime, we find the emergent criticality belongs to the five-dimensional Ising universality class. Di…
We consider the problem when there are two kinds of Bosons with an attraction between them. We find the system to consist of two Bose condensates with an additional pairing order between the Bosons. The properties of this state are discussed.
We investigate a Bose-Bose mixture across the miscible-immiscible phase transition governed by quantum fluctuations in one dimension. We find the recently predicted so-called mixed bubbles as ground states close to the mean-field miscible-immiscible threshold. These bubbles form a pocket of miscibility, separated by one of the components. The collective excitations reflect the symmetry breaking resulting from the bubble formation. The partial miscibility of the system allows for persistent currents in an annular confinement. Intriguingly, the mixed bubble acts like an intrinsic weak link, conn…
We theoretically investigate estimation of the control parameter in a ferromagnetic Bose-Einstein condensate near second order quantum phase transitions. We quantify sensitivity by quantum and classical Fisher information and using the error-propagation formula. For these different metrics, we find the same, beyond-standard-quantum-limit (SQL) scaling with atom number near critical points, and SQL scaling away from critical points. We find that both depletion of the $m_f=0$ Zeeman sub-level and transverse magnetization provide signals of sufficient quality to saturate the sensitivity scaling. …
We derive the equation of state of a two-dimensional Bose gas in an optical lattice in the framework of the Bose-Hubbard model. We focus on the vicinity of the multicritical points where the quantum phase transition between the Mott insulator and the superfluid phase occurs at fixed density and belongs to the three-dimensional XY model universality class. Using a nonperturbative renormalization-group approach, we compute the pressure $P(μ,T)$ as a function of chemical potential and temperature. Our results compare favorably with a calculation based on the quantum O(2) model -- we find the same…
We experimentally investigate the quantum criticality and Tomonaga-Luttinger liquid (TLL) behavior within one-dimensional (1D) ultracold atomic gases. Based on the measured density profiles at different temperatures, the universal scaling laws of thermodynamic quantities are observed. The quantum critical regime and the relevant crossover temperatures are determined through the double-peak structure of the specific heat. In the TLL regime, we obtain the Luttinger parameter by probing sound propagation. Furthermore, a characteristic power-law behavior emerges in the measured momentum distributi…
We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a hard wall trap or a harmonic oscillator trap with a tunable $δ$-function barrier at the trap center. The mixture consists of 1D Bose gas with repulsive interactions and of 1D noninteracting spin-aligned Fermi gas, both species interacting through hard-core interactions. Using a generalized Bose-Fermi mapping, we calculated the reduced single-particle density matrix and the momentum distribution of the gas as a function of barrier strength and the parity of particle number. The secondary peaks in the moment…
We present a density-functional theory for the one dimensional harmonically trapped Bose-Fermi mixture with repulsive contact interactions. The ground state density distribution of each component is obtained by solving the Kohn-Sham equations numerically based on the Local Density Approximation and the exact solution for the homogeneous system given by Bethe ansatz method. It is shown that for strong enough interaction, a considerable amount of fermions are repelled out of the central region of the trap, exhibiting partial phase separation of Bose and Fermi components. Oscillations emerge in t…
We investigate the ground state properties of Bose-Bose mixtures with Rashba-type spin-orbit (SO) coupling in a square lattice. The system displays rich physics from the deep Mott-insulator (MI) all the way to the superfluid (SF) regime. In the deep MI regime, novel spin-ordered phases arise due to the effective Dzyaloshinskii-Moriya type super-exchange interactions. By employing the non-perturbative Bosonic Dynamical Mean-Field-Theory (BDMFT), we numerically study and establish the stability of these magnetic phases against increasing hopping amplitude. We show that as hopping is increased ac…
We derive the equation of state of bosons in an optical lattice in the framework of the Bose-Hubbard model. Near the density-driven Mott transition, the expression of the pressure P(μ,T) versus chemical potential and temperature is similar to that of a dilute Bose gas but with renormalized mass m^* and scattering length a^*. m^* is the mass of the elementary excitations at the quantum critical point governing the transition from the superfluid phase to the Mott insulating phase, while a^* is related to their effective interaction at low energy. We use a nonperturbative renormalization-group ap…
Motivated by recent developments in the experimental study of Bose-Fermi mixtures, we investigate ground-state phase diagrams and excitation spectra for Bose-Fermi mixtures in a three-dimensional (3D) optical lattice. The Gutzwiller approximation is used to identify a new phase in which both superfluid bosons and metal fermions coexist. As a useful probe to identify the quantum phases, we also calculate the excitation spectra. In Mott insulator phase, two excitation features appear in the spectra that correspond to particle and hole excitations. In superfluid phase, there are Bogoliubov modes …
We consider a spin-orbit coupled configuration of spin-1/2 interacting bosons with equal Rashba and Dresselhaus couplings. The phase diagram of the system is discussed with special emphasis to the role of the interaction treated in the mean-field approximation. For a critical value of the density and of the Raman coupling we predict the occurrence of a characteristic tri-critical point separating the spin mixed, the phase separated and the single minimum states of the Bose gas. The corresponding quantum phases are investigated analyzing the momentum distribution, the longitudinal and transvers…
We systematically investigate the ground-state properties of self-bound droplets of quasi-two-dimensional binary Bose gases by using the Gaussian state theory. We find that quantum droplets consists two macroscopic squeezed phases and a macroscopic coherent phase. We map out the phase diagram and determine all phase boundaries via both numerical and nearly analytical methods. In particular, we find three easily accessible signatures for the quantum phases and the stablization mechanism of the self-bound droplets by precisely measuring their radial size. Our studies indicate that binary droplet…
We study the Mott transition of a mixed Bose-Fermi system of ultracold atoms in an optical lattice, where the number of (spinless) fermions and bosons adds up to one atom per lattice, n_F+n_B=1. For weak interactions, a Fermi surface coexists with a Bose-Einstein condensate while for strong interaction the system is incompressible but still characterized by a Fermi surface of composite fermions. At the critical point, the spectral function of the fermions, A(k,w), exhibits a pseudo-gapped behavior, rising as |w| at the Fermi momentum, while in the Mott phase it is fully gapped. Taking into acc…
We describe the dynamical preparation of magnetic states in a strongly interacting two-component Bose gas in a harmonic trap. By mapping this system to an effective spin chain model, we obtain the dynamical spin densities and the fidelities for a few-body system. We show that the spatial profiles transit between ferromagnetic and antiferromagnetic states as the intraspecies interaction parameter is slowly increased.
We investigate the low energy excitations of a dilute atomic Bose gas confined in a anharmonic trap interacting with repulsive forces. The dispersion law of both surface and compression modes are derived and analyzed for large numbers of atoms in the trap, which show two branches of excitation and appear a two critical value. For a upper limit, BEC can be unstable with respect to some specific collective excitation, while for the lower limit, the frequency of collective excitation under anharmonic influence can be effectively lower than that without anharmonicity. Our work reveals the key role…
We study the low-temperature limit of the d-dimensional imperfect Bose gas. Relying on an exact analysis of the microscopic model, we establish the existence of a second-order quantum phase transition to a phase involving the Bose-Einstein condensate. The transition is triggered by varying the chemical potential and persists at non-zero temperatures T for d>2. We extract the exact phase diagram and identify the scaling regimes in the vicinity of the quantum critical point focusing on the behavior of the correlation length ξ. The length ξdevelops an essential singularity exclusively for d=2. We…
We provide a detailed presentation of the functional renormalisation group (FRG) approach for weakly-interacting Bose-Bose mixtures, including a complete discussion on the RG equations. To test this approach, we examine thermodynamic properties of balanced three-dimensional Bose-Bose gases at zero and finite temperatures and find a good agreement with related works. We also study ground-state energies of repulsive Bose polarons by examining mixtures in the limit of infinite population imbalance. Finally, we discuss future applications of the FRG to novel problems in Bose-Bose mixtures and rela…
We investigate the finite temperature spin density wave (SDW) and charge density wave (CDW) transition of two-component lattice spinor Bose gases in optical lattices in the Mott-insulator limit. At the temperature scale around half of the on-site interaction energy, we find a new critical regime emerges and features, in particular, a new bicritical line and two critical lines associated with the finite temperature SDW-CDW, homogeneous-SDW, and homogeneous-CDW transition, respectively. Direct calculation of the critical exponents for the scaling behavior and investigating on the effective theor…
The two-component mixture of Bose particles with short-range pairwise interaction at finite temperatures in three dimensions is considered. Particularly we examine, by means of the large-$N$ expansion technique, the stability of mixed state below the Bose-Einstein transition point and the temperature dependence of the condensate density for symmetric mixture of Bose gases. The presented analysis reveals the importance of finite-temperature excitations of the non-condensed particles in formation of the phase diagram of two-component Bose systems.
We examine the density profiles of the quantum degenerate Bose-Fermi mixture of $^{174}$Yb-$^{173}$Yb, experimental observed recently, in the mean field regime. In this mixture there is a possibility of tuning the Bose-Bose and Bose-Fermi interactions simultaneously using two well separated optical Feshbach resonances, and it is a good candidate to explore phase separation in Bose-Fermi mixtures. Depending on the Bose-Bose scattering length $a_\BB$, as the Bose-Fermi interaction is tuned the density of the fermions is pinched or swapping with bosons occurs.
We present a detailed study of the scattering properties of ultracold mixtures of bosonic potassium atoms. We locate 20 previously unobserved Feshbach resonances in isotopic 39K-41K mixtures. These are assigned to s-wave molecular channels by comparison to an asymptotic bound state model and coupled channels calculations. Additional Feshbach resonances are studied in spin mixtures of a single potassium isotope, both in 39K and 41K. In particular, we characterize the parameters of a selected 39K Feshbach resonance by radio-frequency association of Feshbach molecules. Our results could be exploi…
We study the localization of a cigar-shaped super-fluid Bose-Fermi mixture in a quasi-periodic bichromatic optical lattice (OL) for inter-species attraction and intra-species repulsion. The mixture is described by the Gross-Pitaevskii equation for the bosons, coupled to a hydrodynamic mean-field equation for fermions at unitarity. We confirm the existence of the symbiotic localized states in the Bose-Fermi mixture and Anderson localization of the Bose component in the interacting Bose-Fermi mixture on a bichromatic OL. The phase diagram in boson and fermion numbers showing the regions of the s…
We study a single quantized vortex in the fermionic component of a mixture of Fermi superfluid and Bose-Einstein condensate. As the density ratio between the boson and the fermion components is tuned, we identify a transition in the vortex-core structure, across which fermions in the vortex core become completely depleted even in the weak-coupling Bardeen-Cooper-Schrieffer regime. This is accompanied by changes in key properties of the vortex state, as well as by the localization of the Bose-Einstein condensate in the vortex core. The transition in the vortex-core structure can be experimental…
We study superfluid (SF) states of strongly interacting Bose-Bose mixtures with equal mass and intra-component interaction in optical lattices both in the presence and absence of a barrier potential (BP). We show that the SF order parameters obey the two-component nonlinear Schroedinger equation (NLSE) with not only cubic but also quintic nonlinearity in the vicinity of the first-order transitions to the Mott insulators with even fillings. In the case of no BP, we analyze solitary-wave (SW) solutions of the cubic-quintic NLSE. When the SF state changes from a ground state to a metastable one, …
According to the mean-field theory a condensed Bose-Bose mixture collapses when the interspecies attraction becomes stronger than the geometrical average of the intraspecies repulsions, $g_{12}^2>g_{11} g_{22}$. We show that instead of collapsing such a mixture gets into a dilute liquid-like droplet state stabilized by quantum fluctuations thus providing a direct manifestation of beyond mean-field effects. We study various properties of the droplet and find, in particular, that in a wide range of parameters its excitation spectrum lies entirely above the particle emission threshold. The drople…
Repulsive Bose-Bose mixtures are known to either mix or phase-separate into pure components. Here we predict a mixed-bubble regime in which bubbles of the mixed phase coexist with a pure phase of one of the components. This is a beyond-mean-field effect which occurs for unequal masses or unequal intraspecies coupling constants and is due to a competition between the mean-field term, quadratic in densities, and a nonquadratic beyond-mean-field correction. We find parameters of the mixed-bubble regime in all dimensions and discuss implications for current experiments.
We show that in a rotating two-component Bose mixture, the spin drag between the two different spin species shows a Hall effect. This spin drag Hall effect can be observed experimentally by studying the out-of-phase dipole mode of the mixture. We determine the damping of this mode due to spin drag as a function of temperature. We find that due to Bose stimulation there is a strong enhancement of the damping for temperatures close to the critical temperature for Bose-Einstein condensation.
The universal critical behavior of the driven-dissipative non-equilibrium Bose-Einstein condensation transition is investigated employing the field-theoretical renormalization group method. Such criticality may be realized in broad ranges of driven open systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases. The starting point is a noisy and dissipative Gross-Pitaevski equation corresponding to a complex valued Landau-Ginzburg functional, which captures the near critical non-equilibrium dynamics, and generalizes Model A for cla…
The thermodynamic and superfluid properties of the dilute two-dimensional binary Bose mixture at low temperatures are discussed. We also considered the problem of the emergence of the long-range order in these systems. All calculations are performed by means of celebrated Popov's path-integral approach for the Bose gas with a short-range interparticle potential.
We study thermal properties of a trapped Bose-Bose mixture in a dilute regime using quantum Monte Carlo methods. Our main aim is to investigate the dependence of the superfluid density and the condensate fraction on temperature, for the mixed and separated phases. To this end, we use the diffusion Monte Carlo method, in the zero-temperature limit, and the path-integral Monte Carlo method for finite temperatures. The results obtained are compared with solutions of the coupled Gross-Pitaevskii equations for the mixture at zero temperature. We notice the existence of an anisotropic superfluid den…
We study the properties of moving uniform dipolar Bose-Bose mixtures using the full Hartree-Fock-Bogoliubov theory. The analytical and numerical calculations emphasize that the competition between the relative motion of two fluids and the interspecies dipole-dipole interactions may affect the behavior of the condensed depletion, the anomalous density, the ground-state energy and second-order pair correlation. It is found that in the lower branch of the mixture, these quantities are unimportant and present an unconventional behavior.
We systematically investigate the properties of three-dimensional dipolar binary Bose mixture at low temperatures. A set of coupled self-consistent equations of motion are derived for the two condensates. In the homogeneous case, useful analytical formulas for the condensate depletion, the anomalous density, the ground-state energy, and the equation of state are obtained. The theory is extended to the inhomogeneous case and the importance of the inhomogeneity is highlighted. Our results open up a new avenue for studying dipolar mixture droplets. Impacts of the dipole-dipole interaction on the …
We study the thermodynamic properties of binary Bose mixtures, by developing a beyond mean-field Popov theory which properly includes the effects of quantum and thermal fluctuations in both the density and spin channels. Results for key thermodynamic quantities, such as the isothermal compressibility and the magnetic susceptibility, are derived from a perturbative calculation of the grand-canonical potential. We find that thermal fluctuations can play a crucial role on the miscibility condition of a binary mixture, favoring phase separation at finite temperature even if the mixture is soluble …
We study the Landau damping in Bose-Fermi superfluid mixture at finite temperature. We find that at low temperature, the Landau damping rate will be exponentially suppressed at both the BCS side and the BEC side of Fermi superfluid. The momentum dependence of the damping rate is obtained, and it is quite different from the BCS side to the BEC side. The relations between our result and collective mode experiment in the recently realized Bose-Fermi superfluid mixture are also discussed.
We investigate the superfluidity and the coherence in dipolar binary Bose mixtures using the hydrodynamic approach. Useful analytical formulas for the excitations spectrum, the correlation function, the static structure factor, and the superfluid fraction are derived. We find that in the case of highly imbalanced mixture, the superfluidity can occur in the dilute component only at extremely low temperatures. The behavior of the first-order correlation function for both dipolar and nondipolar Bose mixtures is deeply analyzed. Then we face the two-dimensional case which encodes a non-trivial phy…
We investigate the universal thermodynamics of the two-component one-dimensional Bose gas with contact interactions in the vicinity of the quantum critical point separating the vacuum and the ferromagnetic liquid regime. We find that the quantum critical region belongs to the universality class of the spin-degenerate impenetrable particle gas which, surprisingly, is very different from the single-component case and identify its boundaries with the peaks of the specific heat. In addition, we show that the compressibility Wilson ratio, which quantifies the relative strength of thermal and quantu…
We investigate dipole modes in a trapped Bose--Fermi mixture gas in the normal phase, composed of single-species bosons and single-species fermions with $s$-wave scattering. In the extremely low temperature regime, Bose--Einstein statistics and Fermi--Dirac statistics may give rise to an interesting temperature dependence of collective modes. Applying the moment method to the linearized Boltzmann equation, we study the transition of the dipole modes between the hydrodynamic regime and the collisionless regime.
We study the collective modes of the minority component of a highly unbalanced Bose-Bose mixtures. In the miscible case the minority component feels an effective external potential and we derive an analytical expression for the mode frequencies. The latter is independent of the minority component interaction strength. In the immiscible case we find that the ground state can be a two-domain walls soliton. Although the mode frequencies are continuous at the transition, their behaviour is very different with respect to the miscible case. The dynamical behaviour of the solitonic structure and the …
We theoretically investigate finite-temperature thermodynamics and demagnetization cooling of two-component Bose-Bose mixtures in a cubic optical lattice, by using bosonic dynamical mean field theory (BDMFT). We calculate the finite-temperature phase diagram, and remarkably find that the system can be heated from the superfluid into the Mott insulator at low temperature, analogous to the Pomeranchuk effect in 3He. This provides a promising many-body cooling technique. We examine the entropy distribution in the trapped system and discuss its dependence on temperature and an applied magnetic fie…
We discuss how approximate theories for Bose-Fermi mixtures recover in the molecular limit the expected expression for Fermi-Fermi mixtures of molecules and unpaired fermions. In particular, we compare the energy of the system resulting from a T-matrix diagrammatic approach with that obtained with Variational and Fixed-Node Diffusion Quantum Monte Carlo methods.
We study the stability of the dilute Bose-Fermi and Bose-Bose mixtures with repulsive interactions in one and two dimensions in terms of the renormalization group. For the Bose-Fermi mixture, we show that the uniform mixture is stable against de-mixing in the dilute limit. For the Bose-Bose mixture, we give the stability conditions in the dilute limit. As a byproduct, we also calculate the critical temperature for the superfluid phase of the two-dimensional Bose-Fermi mixture in the extremely dilute limit.
We consider impurity atoms embedded in a two-component Bose-Einstein condensate in a quasi-one dimensional regime. We study the effects of repulsive coupling between the impurities and Bose species on the equilibrium of the system for both miscible and immiscible mixtures by numerically solving the underlying coupled Gross-Pitaevskii equations. Our results reveal that the presence of impurities may lead to a miscible-immiscible phase transition due to the interaction of the impurities and the two condensates. Within the realm of the Bogoliubov-de Gennes equations we calculate the quantum fluct…
We theoretically investigate strong-coupling properties of a Bose-Fermi mixture. In the mass- and population-balanced case, two of the authors have shown that a strong hetero-pairing interaction in this mixture brings about coupling phenomena between Fermi atomic excitations and Bose atomic and composite molecular excitations, that appear as an anomalous multiple peak structure in the single-particle spectral weight (SW). [D. Kharga, {\it et. al.}, J. Phys. Soc. Jpn. {\bf 86}, 084301 (2017)]. In this paper, extending this previous work, we show that, although these many-body phenomena are sens…
We study the low-temperature thermodynamics of weakly-interacting uniform liquids in one-dimensional attractive Bose-Bose mixtures.~The Bogoliubov approach is used to simultaneously describe quantum and thermal fluctuations. First, we investigate in detail two different thermal mechanisms driving the liquid-to-gas transition, the dynamical instability and the evaporation, and we draw the phase diagram. Then, we compute the main thermodynamic quantities of the liquid, such as the chemical potential, the Tan's contact, the adiabatic sound velocity and the specific heat at constant volume. The st…
We investigate a Bose-Fermi mixture in a three-dimensional optical lattice, trapped in a harmonic potential. Using Generalized Dynamical Mean-Field theory, which treats the Bose-Bose and Bose-Fermi interaction in a fully non-perturbative way, we show that for experimentally relevant parameters a peak in the condensate fraction close to the point of vanishing Bose-Fermi interaction is reproduced within a single band framework. We identify two physical mechanisms contributing to this effect: the spatial redistribution of particles when the interspecies interaction is changed and the reduced phas…
We study a harmonically confined Bose-Bose mixture using quantum Monte Carlo methods. Our results for the density profiles are systematically compared with mean-field predictions derived through the Gross-Pitaevskii equation in the same conditions. The phase space as a function of the interaction strengths and the relation between masses is quite rich. The miscibility criterion for the homogeneous system applies rather well to the system, with some discrepancies close to the critical line for separation. We observe significant differences between the mean-field results and the Monte Carlo ones…
In this thesis, the properties of mixtures of Bose-Einstein condensates at $T = 0$ have been investigated using quantum Monte Carlo (QMC) methods and Density Functional Theory (DFT) with the aim of understanding physics beyond the mean-field theory in Bose-Bose mixtures.
In the present work we discuss inter-species entanglement in Bose-Bose mixtures trapped in optical lattices. This work is motivated by the observation that, in the presence of a second component, the Mott-insulator lobe shifts {\em{differently}} on the hole- and particle-side with respect to the Mott lobe of the single species system (Phys. Rev. A 82, 021601, Laser Phys. 21, 1443). We use perturbation theory, formulated in a Hilbert space decomposed by means of lattice symmetries, in order to show that the nonuniform shift of the Mott lobe is a consequence of an inter-species entanglement whic…
Recent experiments confirmed that fluctuations beyond the mean-field approximation can lead to self-bound liquid droplets of ultra-dilute binary Bose mixtures. We proceed beyond the beyond-mean-field approximation, and study liquid Bose mixtures using the variational hypernetted-chain Euler Lagrange method, which accounts for correlations non-perturbatively. Focusing on the case of a mixture of uniform density, as realized inside large saturated droplets, we study the conditions for stability against evaporation of one of the components (both chemical potentials need to be negative) and agains…
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 Bogoliub…
In this work, we present a theoretical study for the collective oscillation modes, i.e. quadrupole, radial and axial mode, of a mixture of Bose and Fermi superfluids in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a molecular Bose-Einstein condensate (BEC) in harmonic trapping potentials with cylindrical symmetry of experimental interest. To this end, we start from the coupled superfluid hydrodynamic equations for the dynamics of Bose-Fermi superfluid mixtures and use the scaling theory that has been developed for a coupled system. The collective oscillation modes of Bose…
