Field-Induced Phase Transitions of Repulsive Spin-1 Bosons in Optical Lattices

Abstract

We study the phase diagram of repulsively interacting spin-1 bosons in optical lattices at unit filling, showing that an externally induced quadratic Zeeman effect may lead to a rich physics characterized by various phases and phase transitions. We find that the main properties of the system may be described by an effective field model, which provides the precise location of the phase boundaries for any dimension, in excellent agreement with our numerical calculations for one-dimensional (1D) systems. Thus, our work provides a quantitative guide for the experimental analysis of various types of field-induced quantum phase transitions in spin-1 lattice bosons. These transitions, which are precluded in spin-1/2 systems, may be realized by using an externally modified quadratic Zeeman coupling, similar to recent experiments with spinor condensates in the continuum.

Bilinear-biquadratic spin-1 chain undergoing quadratic Zeeman effect

“…For this reason this phase has been dubbed "large D" phase. Recently, Rodriguez et al 16 have proposed to realize model (1) for D = 0 with spinor ultracold atoms in optical lattices. They found that by making use of Feshbach resonances in 87 Rb atoms, the interval θ ∈ (−π + arctan 1 3 ; −π/2) around the SU(3) point can be realized.…”

“…1, where for reference we mark also the region studied in 16 . Our results agree quantitatively with the description provided in 16 in this region, although we found some significant discrepancies in the boundaries of some of the phases, as we shall comment later.…”

“…Very recently, Rodriguez et al 16 have studied the phase diagram of the bilinear-biquadratic spin-1 chains undergoing quadratic Zeeman effect close to the SU (3) symmetric point. These authors have used an elegant effective field model, that allowed them to evaluate approximately the phase boundaries for the case of vanishing magnetization in any dimension.…”

“…The linear Zeeman effect is important, but not so interesting, since the magnetization is a constant of the motion, and it can effectively be "gauged out" 16 . Also, in experiments, frequently magnetic fields oscillate rapidly in time, and their effect averages to zero.…”

“…These authors have used an elegant effective field model, that allowed them to evaluate approximately the phase boundaries for the case of vanishing magnetization in any dimension. The study of reference 16 was, however, restricted to a quite limited region of parameters. The reason being that they consider only the region of the phase space achievable in alkaline ultracold gases by means of standard Feshbach resonances.…”