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arXiv:2609.39231

Mixed bubbles in a binary mixture of spin-1 Bose-Einstein condensates

Uyen Ngoc Le, Ha Phuong Uyen Mai, Hieu Binh Le, Hiroki Saito

Published Sep 30, 2026• 0 citations
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Abstract

In mean-field theory, the ground state of a two-component Bose-Einstein condensate (BEC) in a uniform system is either uniformly mixed or totally separated. Beyond-mean-field effects introduce an additional phase, the mixed-bubble state, in which the two components remain mixed within one of the separated domains. Here we show that a mixed-bubble state can emerge in a binary mixture of spin-1 ${}^{7}{\rm{Li}}$ and ${}^{23}{\rm{Na}}$ BECs even within the mean-field framework. We further demonstrate the existence of a metastable uniformly-mixed state, which undergoes a transition to the mixed-bubble state triggered by a local perturbation.

DOI
10.48550/arxiv.2609.39231

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We investigate the ground state and dynamics of a mixture of spin-1 and spin-2 Bose-Einstein condensates of 87Rb^{87}\mathrm{Rb}87Rb atoms. For the experimentally measured interaction coefficients, the ground state exhibits phase separation between the spin-1 ferromagnetic state and the spin-2 nematic state. At the interface between them, a partially polarized spin state emerges. The uniformly mixed state of the spin-1 polar state and spin-2 biaxial nematic state is metastable, and the phase separation via nucleation can be triggered by a local disturbance.
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 that 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 explore the time evolution of two-component Bose-Einstein condensates (BECs), quasi one dimensional with respect to their spinor dynamics, following a quench from one component BECs with a U(1)\mathrm{U}(1)U(1) order parameter into two-component condensates with a $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ order parameter. In our case, these two spin components have a propensity to phase separate, i.e., they are immiscible. Remarkably, these spin degrees of freedom can equivalently be described as a single-component attractive BEC. A spatially uniform mixture of these spins is dynamically unstable, rapidly amplifying any quantum or pre-existing classical spin fluctuations. This coherent growth process drives the formation of numerous spin-polarized domains, which are far from the system's ground state. At much longer times these domains grow in size, coarsening, as the system approaches equilibrium. The experimentally observed time evolution is consistent with our fully three-dimensional stochastic-projected Gross--Pitaevskii calculation.
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, connecting the rotational behavior of the mixed bubble state to current efforts in atomtronic applications.
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.