First- and second-order superfluid–Mott-insulator phase transitions of spin-1 bosons with coupled ground states in optical lattices

Abstract

We investigate the superfluid-Mott-insulator quantum phase transition of spin-1 bosons in an optical lattice created by pairs of counterpropagating linearly polarized laser beams, driving an Fg = 1 to Fe = 1 internal atomic transition. The whole parameter space of the resulting two-component Bose-Hubbard model is studied. We find that the phase transition is not always second order as in the case of spinless bosons, but can be first order in certain regions of the parameter space. The calculations are done in the mean-field approximation by means of exact numerical diagonalization as well as within the framework of perturbaton theory. PACS numbers: 03.75.Lm,03.75.Mn,71.35.Lk The superfluid-Mott-insulator quantum phase transition (SMQPT) of spinless bosons in periodic lattices is a secondorder transion, which is characterized by a continuous variation of the order parameter ψ from ψ = 0 (superfluid phase) to ψ = 0 (Mott-insulator phase) if the amplitude of the lattice potential increases [1, 2]. In our recent paper [3], we have shown that the SMQPT in a system of spin-1 bosons can be first order as well [4]. By means of numerical calculations within the framework of the mean-field theory, it was found that in the case of 23 Na the SMQPT is second order if the number of atoms per lattice site n = 1, 3, and it is first order for n = 2. In the case of 87 Rb, the SMQPT was found to be second order for n = 1, 2, 3. In the present work, we continue the study of Ref. [3]. The main purpose is to investigate the whole parameter space of spin-1 bosons and to find the regions where the SMQPT is first and second order for arbitrary n.We consider spin-1 neutral polarizable bosons, possessing three Zeeman-degenerate internal ground and excited electronic states characterized by the magnetic quantum number m = 0, ±1 (F g = F e = 1) in a d-dimensional (d = 1, 2, 3) optical lattice. The lattice is assumed to be created by d pairs of counterpropagating linearly polarized laser waves running in d orthogonal directions and having different frequencies in different directions. The beams propagating along the 3-axis, which is chosen to be a quantization axis, are polarized along the 1or 2-axis, and the beams propagating along the 1and 2-axis are polarized along the 2and 1-axis, respectively.The running laser waves form left-and rightpolarized standing waves with Rabi frequencies Ω ν (r ν ) = Ω 0ν cos(k L r ν ), which couple internal ground and excited states by V -and Λtransitions. In order to avoid decoherence due to spontaneous emission, the detunings ∆ i must satisfy the conditions |∆ ν | ≫ γ, where γ is the spontaneous emission rate. If the laser intensities and the detunings are chosen in such a manner that Ω 2 0ν /∆ ν = Ω 2 0 /∆, ν = 1, . . . , d, the laser potential acting on the atomic ground states is given by the matrixwhich determines the isotropic lattice potential with the pe-riod π/k L and at the same time couples the atomic ground states with m = ±1. In the case of red detuning ∆ < 0, the system is described by the tw...

First-order superfluid-to-Mott-insulator phase transitions in spinor condensates

“…Metastable Mott-insulator (MMI) and meta-stable superfluid (MSF) phases emerge due to the spin barrier, and lead to first-order SF-MI phase transitions (see Figs. 1(a) and 1(c)) [14,16,17]. When 3D lattices are ramped up and down, hysteresis is expected across the phase transitions (i.e., different transition lattice depth u c ).…”

Strong-coupling expansion for the spin-1 Bose-Hubbard model

“…In addition, both the MI phases and SF-MI transitions of spin-1 bosons have been intensively studied [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The ferromagnetically interacting system is essentially similar to spinless bosons, whereas the antiferromagnetically interacting system exhibits rich physical properties.…”

“…This conjecture has been confirmed by the density matrix renormalization group (DMRG) [22] and quantum Monte Carlo simulation (QMC) [24,25] in one dimension (1D). However, mean-field (MF) studies beyond the perturbation theory [17][18][19] have shown a possible first-order SF-MI transition of the BH model for a weak antiferromagnetic interaction, such as U 2 /U 0 ≃ 0.04, which corresponds to 23 Na. This first-order transition in 1D has also been revealed by a QMC study [24].…”

Ground states of spin-1 bosons in asymmetric double wells

“…These experimental developments have stimulated extensive study of related theoretical models [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In particular, the behavior of spin-1 bosons in a double-well potential can be described by a variant of the two-site BoseHubbard Hamiltonian [25] including spin-dependent interactions [11,23] that affect physical properties of the system.…”