We identify the quantum phases in a binary mixture of dipolar bosons in two-dimensional optical lattices. Our study is motivated by the recent experimental realization of binary dipolar condensate mixtures of Er-Dy [Phys. Rev. Lett. 121, 213601 (2018)]. We model the system by using the extended two-species Bose-Hubbard model and calculate the ground-state phase diagrams by using mean-field theory. For selected cases we also obtain analytical phase boundaries by using the site-decoupled mean-field theory. For comparison we also examine the phase diagram of two-species Bose-Hubbard model. Our results show that the quantum phases with the long-range intraspecies interaction phase separate with no phase ordering. The introduction of the long-range interspecies interaction modifies the quantum phases of the system. It leads to the emergence of phase-separated quantum phases with phase ordering. The transition from the phase-separated quantum phases without phase ordering to phase ordered ones breaks the inversion symmetry.
We identify the quantum phases in a binary mixture of dipolar bosons in two-dimensional optical lattices. Our study is motivated by the recent experimental realization of binary dipolar condensate mixtures of Er-Dy [Phys. Rev. Lett. 121, 213601 (2018)]. We model the system by using the extended two-species Bose-Hubbard model and calculate the ground-state phase diagrams by using mean-field theory. For selected cases we also obtain analytical phase boundaries by using the site-decoupled mean-field theory. For comparison we also examine the phase diagram of two-species Bose-Hubbard model. Our results show that the quantum phases with the long-range intraspecies interaction phase separate with no phase ordering. The introduction of the long-range interspecies interaction modifies the quantum phases of the system. It leads to the emergence of phase-separated quantum phases with phase ordering. The transition from the phase-separated quantum phases without phase ordering to phase ordered ones breaks the inversion symmetry.
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 87Rb-41K mixtures in the combined potential of a parabolic trap and an optical lattice using the local density approximation. We fixed the number of 87Rb and varied the number of 41K, and used the parameters estimated by experiments. We show that the phase separated 87Rb-41K mixtures distribute like in a parabolic trap case. Furthermore, we find that phase separated mixtures distribute a nesting structure.
We study the quantum phase transitions in a two component Bose mixture in a one-dimensional optical lattice. The calculations have been performed in the framework of the extended Bose-Hubbard model using the finite size density matrix renormalization group method. We obtain different phase transitions for the system for integer filling. When the interspecies on-site and the nearest-neighbor interactions are larger than the intraspecies on-site and also the nearest-neighbor interaction, the system exhibits a phase separated charge-density-wave order that is characterized by the two species being spatially separated and existing in the density-wave phases.
The zero-temperature phase diagram of a binary mixture of bosonic and fermionic atoms in a one-dimensional optical lattice is studied in the framework of the Bose-Fermi-Hubbard model. By exact numerical solution of the associated eigenvalue problems, ground state observables and the response to an external phase twist are evaluated. The stiffnesses under phase variations provide measures for the boson superfluid fraction and the fermionic Drude weight. Several distinct quantum phases are identified as functions of the strength of the repulsive boson-boson and the boson-fermion interactions. In addition to the bosonic Mott-insulator phase, two other insulating phases are found, where both the bosonic superfluid fraction and the fermionic Drude weight vanish simultaneously. One of these double-insulator phases exhibits a crystalline diagonal long-range order, while the other is characterized by spatial separation of the two species.
The recent realization of a binary dipolar Bose-Einstein condensate [A. Trautmann et al., Phys. Rev. Lett. 121, 213601 (2018)] presents new exciting aspects for studying quantum droplets and supersolids in a binary mixture. Motivated by this experiment, we study the ground-state phases and dynamics of a Dy-Dy mixture. The dipolar bosonic mixture exhibits qualitatively novel and rich physics. Relying on the three-dimensional numerical simulations in the extended Gross-Pitaevskii framework, we unravel the ground-state phase diagrams and characterize their different possible phases. The emergent phases include single-droplet (SD), multiple-droplets (MD), doubly supersolid (SS), and superfluid (SF) states in both miscible and immiscible phases. Intriguing mixed ground states are observed for an imbalanced binary mixture, including a combination of SS-SF, SS-MD, and SS-SS phases. We also explore the dynamics across the phase boundaries by linear quenches of interspecies and intraspecies scattering lengths. During these dynamical processes, we observe an abrupt change in phase which initially results in some instability in the system and forms some metastable states in the intermediate timescale. However, the state produced in long-time evolution is similar to our predicted ground state. Although we demonstrate the possible results for a Dy-Dy mixture and for a specific parameter range of intraspecies and interspecies scattering lengths, our results are in general valid for other dipolar mixtures and may become an important benchmark for future experimental scenarios.
We obtain the ground-state quantum phase diagram for a two-species Bose mixture in a one-dimensional optical lattice using the finite-size density-matrix renormalization group method. We discuss our results for different combinations of inter- and intraspecies interaction strengths with commensurate and incommensurate fillings of the bosons. The phases we have obtained are a superfluid and a Mott insulator, and a phase separation where the two different species reside in spatially separate regions. The spatially separated phase is further classified into phase-separated superfluid and Mott insulator. The phase separation appears for all the fillings we have considered, whenever the interspecies interaction is slightly larger than the intraspecies interactions.
We consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional square optical lattices. The model is a variation of the extended Bose-Hubbard model and apt to study the quantum phases arising from the variation in the tilt angle $\ensuremath{\theta}$ of the dipolar bosons. At low tilt angles, ${0}^{\ensuremath{\circ}}\ensuremath{\leqslant}\ensuremath{\theta}\ensuremath{\lesssim}{25}^{\ensuremath{\circ}}$, the ground states of the system are phases with checkerboard order, which can be either checkerboard supersolids or checkerboard density waves. For high tilt angles, ${35}^{\ensuremath{\circ}}\ensuremath{\lesssim}\ensuremath{\theta}\ensuremath{\lesssim}{55}^{\ensuremath{\circ}}$, phases with striped order of the supersolid or density wave are preferred. In the intermediate domain, ${25}^{\ensuremath{\circ}}\ensuremath{\lesssim}\ensuremath{\theta}\ensuremath{\lesssim}{35}^{\ensuremath{\circ}}$, an emulsion or superfluid phase intervenes the transition between the checkerboard and the striped phases. The attractive interaction dominates at $\ensuremath{\theta}\ensuremath{\gtrsim}{55}^{\ensuremath{\circ}}$, which renders the system unstable, and there is a density collapse. For our studies we use Gutzwiller mean-field theory to obtain the quantum phases and the phase boundaries. In addition, we calculate the phase boundaries between an incompressible and a compressible phase of the system by considering second-order perturbation analysis of the mean-field theory. The analytical results, where applicable, are in excellent agreement with the numerical results. In our study, the incompressible phases have an average occupancy per site $\ensuremath{\rho}\ensuremath{\le}1$, but the compressible phases can have $\ensuremath{\rho}>1$.