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arXiv:2403.14601 · Physical Review A

Miscibility-immiscibility transition of strongly interacting bosonic mixtures in optical lattices

Rukmani Bai, Soumik Bandyopadhyay

Published Jul 25, 2025• 0 citations

Abstract

Interaction plays a key role in the mixing properties of a multicomponent system. The miscibility-immiscibility transition (MIT) in a weakly interacting mixture of Bose gases is predominantly determined by the strengths of the intra- and intercomponent two-body contact interactions. However, in the strongly interacting regime interaction-induced processes become relevant. Despite previous studies on bosonic mixtures in optical lattices, the effects of the interaction-induced processes on the MIT remains unexplored. In this work, we investigate the MIT in the strongly interacting phases of two-component bosonic mixture trapped in a homogeneous two-dimensional square optical lattice. Particularly we examine the MIT condition when both the components are in superfluid, one-body staggered superfluid, or supersolid phases. Our study uncovers that MIT condition is significantly shaped by the interplay of competing nonlocal intra- and intercomponent density-induced tunneling effects, as well as off-site interactions. Notably, we demonstrate that the MIT condition for the staggered superfluid phase exhibits an inequality that is inverted compared to the conventional MIT condition associated with superfluid or supersolid phases driven by local contact interactions. In addition, we present the phase diagram of the Bose-Hubbard model incorporating nonlocal processes, derived using a site-decoupling mean-field approach with the Gutzwiller ansatz. Our study contributes to the better understanding of miscibility properties of multicomponent systems in the strongly interacting regime.

DOI: 10.1103/r52b-bsrd

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Interaction plays a key role in the mixing properties of a multicomponent system. The miscibility-immiscibility transition (MIT) in a weakly interacting mixture of Bose gases is predominantly determined by the strengths of the intra- and intercomponent two-body contact interactions. However, in the strongly interacting regime interaction-induced processes become relevant. Despite previous studies on bosonic mixtures in optical lattices, the effects of the interaction-induced processes on the MIT remains unexplored. In this work, we investigate the MIT in the strongly interacting phases of two-component bosonic mixture trapped in a homogeneous two-dimensional square optical lattice. Particularly we examine the MIT condition when both the components are in superfluid, one-body staggered superfluid, or supersolid phases. Our study uncovers that MIT condition is significantly shaped by the interplay of competing nonlocal intra- and intercomponent density-induced tunneling effects, as well as off-site interactions. Notably, we demonstrate that the MIT condition for the staggered superfluid phase exhibits an inequality that is inverted compared to the conventional MIT condition associated with superfluid or supersolid phases driven by local contact interactions. In addition, we present the phase diagram of the Bose-Hubbard model incorporating nonlocal processes, derived using a site-decoupling mean-field approach with the Gutzwiller ansatz. Our study contributes to the better understanding of miscibility properties of multicomponent systems in the strongly interacting regime.

We investigate properties of an ultracold, two-component bosonic gas in a square optical lattice at unit filling. In addition to density-density interactions, the atoms are subject to coherent light-matter interactions that couple different internal states. We examine the influence of this coherent coupling on the system and its quantum phases by using Gutzwiller mean-field theory as well as bosonic dynamical mean-field theory. We find that the interplay of strong interspecies repulsion and coherent coupling affects the Mott insulator to superfluid transition and shifts the tip of the Mott lobe toward higher values of the tunneling amplitude. In the strongly interacting Mott regime, the resulting Bose-Hubbard model can be mapped onto an effective spin Hamiltonian that offers additional insights into the observed phenomena.

We study the miscible-immiscible quantum phase transition in a linearly coupled binary Bose-Hubbard model in one dimension that can describe the low-energy properties of a two-component Bose-Einstein condensate in optical lattices. With the quantum many-body ground state obtained from the density matrix renormalization group algorithm, we calculate the characteristic physical quantities of the phase transition controlled by the linear coupling between the two components. Furthermore we calculate the Binder cumulant to determine the critical point and construct the phase diagram. The strong-coupling expansion shows that in the Mott insulator regime the model Hamiltonian can be mapped to a spin-

1/2

\mathit{XXZ}

model with a transverse magnetic field.

The effects of miscibility in interacting two-component classical fluids are relevant in a broad range of daily applications. When considering quantum systems, two-component Bose–Einstein condensates provide a well-controlled platform where the miscible–immiscible phase transition can be completely characterized. In homogeneous systems, this phase transition is governed only by the competition between intra- and inter-species interactions. However, in more conventional experiments dealing with trapped gases, the pressure of the confinement increases the role of the kinetic energy and makes the system more miscible. In the most general case, the miscibility phase diagram of unbalanced mixtures of different atomic species is strongly modified by the atom number ratio and the different gravitational sags. Here, we numerically investigate the ground-state of a 23Na–39K quantum mixture for different interaction strengths and atom number ratios considering realistic experimental parameters. Defining the spatial overlap between the resulting atomic clouds, we construct the phase diagram of the miscibility transition which could be directly measured in real experiments.

We study the ground-state properties of mixtures of strongly interacting bosonic atoms in an optical lattice. Applying a mean-field approximation to the Hubbard model for Bose-Bose mixtures, we calculate the densities and superfluid order parameters for both species. Due to the repulsive interaction between the two species, the system exhibits phase separation. First, in the extreme limit of the zero-hopping case, we derive analytical expressions for the phase boundaries. In particular, we derive the conditions for phase separation in the Mott insulator phase. We find that the conditions for the phase separation depend on the on-site interactions as well as the occupation numbers. In particular, we show that the coexisting state appears by varying the on-site inter-species interaction. We also show the phase diagram of the finite hopping case. Second, we calculate the spatial density profile of

^{87}

Rb-

^{41}

K mixtures in the combined potential of a parabolic trap and an optical lattice using the local density approximation. We fixed the number of

^{87}

Rb and varied the number of

^{41}

K, and used the parameters estimated by experiments. We show that the phase separated

^{87}

Rb-

^{41}

K mixtures distribute like in a parabolic trap case. Furthermore, we find that phase separated mixtures distribute a nesting structure.

In this paper, we investigate the quantum phases of two-component bosons in a non-Hermitian optical lattice system featuring a nonreciprocal hopping phase factor. Our analysis focuses on the Bose–Hubbard model in a two-dimensional (2D) square lattice, utilizing the inhomogeneous dynamical Gutzwiller mean-field theory (DGMFT) to examine the ground state. The impact on quantum phases of the inter component interaction varies in the weak-interaction (the inter-component interactions are smaller than intra-component interactions, i.e., [Formula: see text]) and in the strong-interaction (the inter-component interactions are bigger than intra-component interactions, i.e., [Formula: see text]) regime. In the weak regime, we observe a diverse range of quantum phases, including vortex-like liquid, MI islands (the Mott insulator (MI) islands periodically distributed in the superfluid (SF) background) and SF islands (the SF islands periodically distributed in the MI background), and the inter-component counterflow superfluid (CFSF) phases. In the strong regime, we observe phase separation of the two-component bosons.

We investigate quantum phases of the Bose-Bose mixtures in a two dimensional (2D) square lattice under artificial magnetic flux. Our analysis employs the inhomogeneous Dynamical Gutzwiller Mean-Field Theory (DGMFT) to investigate ground state within the two-component Bose-Hubbard model. The results based on various inter-component interactions and magnetic flux. In the case of weak inter-component interaction (wherein the inter-component interactions remain subordinate to intra-component interactions, symbolically expressed as |Uab|≤U), we observe a multitude of captivating quantum phases within the Bose-Bose mixtures. These include the emergence of the jagged density-wave supersolid(SS) phase, the latticed-like density-wave SS phase, and counterflow superfluid (CFSF) phase. Notably, the introduction of artificial magnetic flux expands the range of existence for CFSF phase. In the case of strong inter-component interaction(wherein the inter-component interactions surpass intra-component interactions, symbolically expressed as Uab>U), we delve deeper into the classification of the spatially separated phase, aptly termed the phase separated supersolid (P-SS).