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arXiv:cond-mat/9809195 · Physical Review A

Binary Bose-Einstein condensate mixtures in weakly and strongly segregated phases

Ping Ao, S. T. Chui

Published Dec 1, 1998• 329 citations
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Abstract

We perform a mean-field study of the binary Bose-Einstein condensate mixtures as a function of the mutual repulsive interaction strength. In the phase segregated regime, we find that there are two distinct phases: the weakly segregated phase characterized by a ``penetration depth'' and the strongly segregated phase characterized by a healing length. In the weakly segregated phase the symmetry of the shape of each condensate will not take that of the trap because of the finite surface tension, but its total density profile still does. In the strongly segregated phase even the total density profile takes a different symmetry from that of the trap because of the mutual exclusion of the condensates. The lower critical condensate-atom number to observe the complete phase segregation is discussed. A comparison to recent experimental data suggests that the weakly segregated phase has been observed.

DOI
10.1103/physreva.58.4836

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We perform a mean-field study of the binary Bose-Einstein condensate mixtures as a function of the mutual repulsive interaction strength. In the phase segregated regime, we find that there are two distinct phases: the weakly segregated phase characterized by a ``penetration depth'' and the strongly segregated phase characterized by a healing length. In the weakly segregated phase the symmetry of the shape of each condensate will not take that of the trap because of the finite surface tension, but its total density profile still does. In the strongly segregated phase even the total density profile takes a different symmetry from that of the trap because of the mutual exclusion of the condensates. The lower critical condensate-atom number to observe the complete phase segregation is discussed. A comparison to recent experimental data suggests that the weakly segregated phase has been observed.
We provide Monte Carlo simulation and analytic interface arguments for the absence of cylindrical symmetry in the density difference of a binary mixture of Bose-Einstein condensates in traps in the phase segregated regime. For different spin states of 87Rb,{}^{87}\mathrm{Rb},87Rb, the total density remains very symmetric however. There is a metastable symmetric phase in a substantial part of this phase segregated regime. The boundary between the symmetric and the nonsymmetric phase is a function of the relative concentration. The effect of different confining potentials is investigated.
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We theoretically study the static and dynamic behavior of a BEC immersed in a large Fermi sea of ultracold atoms under conditions of tunable interspecies interaction. The degenerate Bose-Fermi mixture is kept in an elongated trap, typical for a single-beam optical dipole trap. We focus on the case of repulsive Bose-Fermi interaction and develop mean-field models to simulate the system over a wide range of repulsion strength. We further get analytical solutions in the regimes of phase separation and weak interaction. We obtain static density profiles and the frequency of the radial breathing mode, which is an elementary dynamic phenomenon of the mixture. Our results unveil the structure of the Bose-Fermi interface and describe the origin of the frequency shift of the breathing mode when the components become phase-separated at strong repulsion. We show that the mediated interaction between bosons induced by the Fermi sea can be understood as an adiabatic second-order mean-field effect, which is valid also beyond the weak-interaction regime for relevant experimental conditions. These results are consistent with our recent observations [Lous et al., Phys. Rev. Lett. 120, 243403 (2018); Huang et al., Phys. Rev. A 99, 041602(R) (2019)] in a mixture of 41K^{41}\mathrm{K}41K and 6Li^{6}\mathrm{Li}6Li.
The interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths ${\ensuremath{\xi}}_{1}$ and ${\ensuremath{\xi}}_{2}$ and by the interspecies repulsive interaction KKK. An exact solution to the Gross-Pitaevskii (GP) equations is obtained for the special case ${\ensuremath{\xi}}_{2}/{\ensuremath{\xi}}_{1}=1/2$ and K=3/2K=3/2K=3/2. Furthermore, applying a double-parabola approximation (DPA) to the energy density featured in GP theory allows us to define a DPA model, which is much simpler to handle than GP theory but nevertheless still captures the main physics. In particular, a compact analytic expression for the interfacial tension is derived that is useful for all ${\ensuremath{\xi}}_{1},\phantom{\rule{0.28em}{0ex}}{\ensuremath{\xi}}_{2}$, and KKK. An application to wetting phenomena is presented for condensates adsorbed at an optical wall. The wetting phase boundary obtained within the DPA model nearly coincides with the exact one in GP theory.
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{g}_{ab}gab​ is a coupling constant between the components aaa and bbb). 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{g}_{ab}gab​, depending on the gas parameter $\ensuremath{\gamma}$ and temperature.
Abstract Our investigation focuses on the condensate density, excited and condensed fractions of bosons in a mixture of two-component segregated weakly interacting Bose–Einstein condensates (BECs) at zero temperature based on the Gross–Pitaevskii (GP) and Cornwall-Jackiw-Tomboulis (CJT) theories. We find that the repulsive interaction among interspecies of bosons is the origin of the local behavior and the decline of quantum fluctuation. These features are disparate to the single BEC or miscible BECs. The numerical evaluation of the condensed fraction is provided to support the experimental observation.