Mean-field theory for the Mott-insulator–paired-superfluid phase transition in the two-species Bose-Hubbard model

Abstract

The standard mean-field theory for the Mott-insulator-superfluid phase transition is not sufficient to describe the Mott-insulator-paired-superfluid phase transition. Therefore, by restricting the two-species Bose-Hubbard Hamiltonian to the subspace of paired particles, and using perturbation theory, here we derive an analytic mean-field expression for the Mott-insulator-paired-superfluid transition boundary. PACS number(s): 03.75.−b, 37.10.Jk, 67.85.−d I. INTRODUCTIONFollowing the recent observation of Mott-insulatorsuperfluid phase transition with ultracold atomic Bose gases loaded into optical lattices [1-4], there has been intense theoretical activity in analyzing many Hubbard-type lattice models [5]. Among them the two-species Bose-Hubbard model, which can be studied with two-component Bose gases loaded into optical lattices, is one of the most popular. This is because, in addition to the Mott-insulator and single-speciessuperfluid phases, it has been predicted that this model has at least two additional phases: an incompressible super-counter flow and a compressible paired-superfluid phase [6][7][8][9][10][11].Our main interest here is in the latter phase, where a direct transition from the Mott-insulator phase to the pairedsuperfluid phase (superfluidity of composite bosons, i.e., Bose-Bose pairs) has been predicted, when both species have integer fillings and the interspecies interaction is sufficiently large and attractive. In this paper, we derive an analytic mean-field expression for the Mott-insulator-paired-superfluid transition boundary in the two-species Bose-Hubbard model. The remaining paper is organized as follows. After introducing the model Hamiltonian in Sec. II, first we derive the mean-field theory in Sec. II A, and then present typical phase diagrams in Sec. II B. A brief summary of our conclusions is given in Sec. III.

High-order symbolic strong-coupling expansion for the Bose-Hubbard model

“…42 We conclude that our paper works out in detail a general symbolic high-order perturbation theory, whose applicability is not limited to the Bose-Hubbard model. Instead it may also be suitable to analyze other lattice systems, which describe, for instance, the supersolidsolid transition, 8 a mixture of two bosonic species, 16,17 three-body interactions, 18 and even frustrated systems like Kagome superlattices 43 suffering from the sign problem. Furthermore it should be noted that our theoretical high-precision results could, in principle, be checked with in situ density measurements 44 and single atom detection 45 as they are possible these days, for instance, with the quantum gas microscope 46 or the scanning electron microscope.…”

“…In comparison with the mean-field approach, 2 this strong-coupling expansion method shows a higher accuracy for lower spatial dimensions, especially after an extrapolation to higher orders. Therefore, SCE has been used successfully to study the Bose-glass phase in the superlattice, 15 twospecies bosons loaded into d-dimensional hypercubic optical lattices, 16,17 and the supersolid-solid quantum phase transition. 18 In particular, the strong-coupling expansion method has turned out to be efficient for the secondorder transition from an incompressible to a compressible phase.…”