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 at zero temperature, as already anticipated in a previous work [M. Ota et al., Phys. Rev. Lett. 123, 075301 (2019)]. We further investigate the miscibility condition for binary mixtures in the presence of asymmetry in the intraspecies interactions, as well as in the masses of the two components. Furthermore, we discuss the superfluid behavior of the mixture and the temperature dependence of the Andreev-Bashkin effect.
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 at zero temperature, as already anticipated in a previous work [M. Ota et al., Phys. Rev. Lett. 123, 075301 (2019)]. We further investigate the miscibility condition for binary mixtures in the presence of asymmetry in the intraspecies interactions, as well as in the masses of the two components. Furthermore, we discuss the superfluid behavior of the mixture and the temperature dependence of the Andreev-Bashkin effect.
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.
We study the properties of a homogeneous dilute Bose-Bose gas in a weak-disorder potential at zero temperature. By using the perturbation theory, we calculate the disorder corrections to the condensate density, the equation of state, the compressibility, and the superfluid density as a function of density, strength of disorder, and miscibility parameter. It is found that the disorder potential may lead to modifying the miscibility-immiscibility condition and a full miscible phase turns out to be impossible in the presence of the disorder. We show that the intriguing interplay of the disorder and intra- and interspecies interactions may strongly influence the localization of each component, the quantum fluctuations, and the compressibility, as well as the superfluidity of the system.
The miscibility of quantum liquids is an interesting topic in many-body physics, which has been intensively investigated in 3He-4He superfluids and the mixtures of ultracold atoms. In the context of dual species Bose-Einstein condensates, the mean-field description has been well established, according to which, the miscibility condition is density independent and determined only by the ratio of inter- and intra-species interaction strength. Recently, Nadion and Petrov proposed that [ Phys. Rev. Lett. 126 115301 ], in the vicinity of the mixing-demixing threshold, quantum fluctuations play an important role to affect the equilibrium stability, and as a result, the partially miscible state emerges. This new phase of quantum matter opens up new perspectives to explore the beyond mean-field effect in ultracold atomic gases. In this work, according to the equation of state taking the Lee-Huang-Yang correction into consideration, we investigate the ground state phase diagram of repulsive binary Bose mixtures in the interacting regime suffering a weak mean-field instability. Under the thermodynamic balance conditions, the phase boundaries between the immiscible state, partially miscible state and the homogenous state are determined. For the equal-mass case, these phase transitions only take place on condition that intra-species interactions are in an asymmetric form. In terms of interaction parameters, we explicitly derive analytical expressions of the phase boundaries, which are appropriate to describe the transitions in sufficiently dilute atomic gases. At the quantum critical point, where the partially miscible state terminates, the susceptibility tensor of the density response exhibits a divergent behavior. For the unequal-mass case, the beyond-mean-field equation of state cannot be written in a compact form, thus the determination of the phase boundaries is more involved. By expanding the Lee-Huang-Yang energy expression to the terms linear in the concentration of the minority species, we analytically obtain the threshold density for the partially miscible transition. We also propose a discriminant function, from which the configuration of the partially miscible state can be identified for the given mass ratio and interaction strength. Applications of these theoretical results to experimental systems, such as sodium, potassium, and rubidium gases, are presented.
We examine the role of thermal fluctuations in binary condensate mixtures of dilute atomic gases. In particular, we use the Hartree-Fock-Bogoliubov theory with the Popov approximation to probe the impact of noncondensate atoms to the phenomenon of phase separation in two-component Bose-Einstein condensates. We demonstrate that, in comparison to T=0, there is a suppression in the phase separation of the binary condensates at $T\ensuremath{\ne}0$. This arises from the interaction of the condensate atoms with the thermal cloud. We also show that, when $T\ensuremath{\ne}0$, it is possible to distinguish the phase-separated case from the miscible from the trends in the correlation function. However, this is not the case at T=0.
In this thesis we present a detailed investigation of the role played by quantum and thermal fluctuations in ultracold Bose gases. We begin with a review of several important concepts and analytical tools within a functional integration formalism. We first focus on the so-called zero-range approximation for the interaction potential, by recovering the Bogoliubov results and the Landau two-fluid model from a field-theory perspective. In deriving the beyond-mean-field equation of state, we are going to show that a crucial point concerns the proper regularization of the divergent zero-point energy. Among the alternative approaches to investigate finite-temperatures Bose gases, we apply the kinetic theory to explain some recent results on the sound propagation in two-dimensional Bose gases. We then move to consider the eventual corrections to the thermodynamics of Bose gases due to the finite-range character of the interaction potential. The coupling constants of the finite-range model are related to measurable scattering parameters through an effective-field-theory approach. The role of finite-range corrections is considered not only in three spatial dimensions but also in systems with lower dimensionalities. Our analytical predictions are in good agreement with available Monte Carlo simulations and consistent with other theoretical frames, as the Lieb-Lininger theory for one-dimensional systems. In the third chapter, the relevance of fluctuations is investigated from an alternative point of view. Indeed, for a single-component Bose gas we have actually considered their effect as deviations of thermodynamic quantities from the mean-field and zero-range picture. In the case of collapsing Bose mixtures, we are going to show that zero-temperature fluctuations play a crucial stabilizing role against the collapse instability. Because of this peculiar mechanism, ultracold mixtures can display finite-density configurations also in free space. Inspired by recent experiments, we characterize this novel self-bound state by comparison with bright solitons, following a variational scheme. We also consider the case of binary mixtures where a coherent internal coupling is turned on. In the last chapter, we move to deal with dipolar condensates. In particular, we are interested in beyond-mean-field effects leading to the formation of inhomogeneous ground states. In order to provide a reliable answer to the open issue of superfluid properties of these structures, we present our recent numerical investigation on the phase diagram of dipolar bosons.
Multicomponent quantum gases are ideal platforms to study fundamental phenomena arising from the mutual interaction between different constituents. Particularly, due to the repulsive interactions between two species, the system may exhibit a phase separation. We develop a mean-field-based theory for a two-component Bose mixture, which is equivalent to the Hartree-Fock-Bogoliubov approximation, and derive analytical expressions for the phase boundary and miscibility. The majority of existing theories, which are valid only for weakly interacting Bose gases, predict that the phase boundary is determined by the criterion ${g}_{ab}\ensuremath{\leqslant}\sqrt{{g}_{aa}{g}_{bb}}$ (where gab is a coupling constant between the components a and b). We show that in the Bose-Einstein condensation phase ($T\ensuremath{\leqslant}{T}_{c}$) the system may remain in a stable and miscible phase also for larger values of gab, depending on the gas parameter $\ensuremath{\gamma}$ and temperature.