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arXiv:1110.3364 · Physical Review Letters

Time-Reversal Symmetry Breaking of p -Orbital Bosons in a One-Dimensional Optical Lattice

Xiaopeng Li, Zixu Zhang, W. Vincent Liu

Published Apr 25, 2012• 42 citations
arXivHTMLPDF

Abstract

We study bosons loaded in a one-dimensional optical lattice of twofold p-orbital degeneracy at each site. Our numerical simulations find an anti-ferro-orbital p(x)+ip(y), a homogeneous p(x) Mott-insulator phase, and two kinds of superfluid phases distinguished by the orbital order (anti-ferro-orbital and paraorbital). The anti-ferro-orbital order breaks time-reversal symmetry. Experimentally observable evidence is predicted for the phase transition between the two different superfluid phases. We also discover that the quantum noise measurement is able to provide a concrete evidence of time-reversal symmetry breaking in the first Mott phase.

DOI
10.1103/physrevlett.108.175302

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We study bosons loaded in a one-dimensional optical lattice of twofold p-orbital degeneracy at each site. Our numerical simulations find an anti-ferro-orbital p(x)+ip(y), a homogeneous p(x) Mott-insulator phase, and two kinds of superfluid phases distinguished by the orbital order (anti-ferro-orbital and paraorbital). The anti-ferro-orbital order breaks time-reversal symmetry. Experimentally observable evidence is predicted for the phase transition between the two different superfluid phases. We also discover that the quantum noise measurement is able to provide a concrete evidence of time-reversal symmetry breaking in the first Mott phase.
We present a detailed study of the Bose-Hubbard model in a ppp-band triangular lattice by focusing on the evolution of orbital order across the superfluid-Mott insulator transition. Two distinct phases are found in the superfluid regime. One of these phases adiabatically connects the weak interacting limit. This phase is characterized by the intertwining of axial ${p}_{\ifmmode\pm\else\textpm\fi{}}={p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y}$ and in-plane ${p}_{\ensuremath{\theta}}=cos\ensuremath{\theta}{p}_{x}+sin\ensuremath{\theta}{p}_{y}$ orbital orders, which break the time-reversal symmetry and lattice symmetries simultaneously. In addition, the calculated Bogoliubov excitation spectrum gaps the original Dirac points in the single-particle spectrum but exhibits emergent Dirac points. The other superfluid phase in close proximity to the Mott insulator with unit boson filling shows a detwined in-plane ferro-orbital order. Finally, an orbital exchange model is constructed for the Mott insulator phase. Its classical ground state has an emergent SO(2)\mathrm{S}\mathrm{O}(2)SO(2) rotational symmetry in the in-plane orbital space and therefore enjoys an infinite degeneracy, which is ultimately lifted by the orbital fluctuation via the order by disorder mechanism. Our systematic analysis suggests that the in-plane ferro-orbital order in the Mott insulator phase agrees with and likely evolves from the latter superfluid phase.
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Orbital degree of freedom plays an important role for understanding quantum many-body phenomena. In this paper, we study an experimentally related setup with ultracold bosons loaded into hybridized bands of two-dimensional hexagonal optical lattices. We find that the system supports various quantum many-body phases at zero temperature, including chiral superfluid and chiral Mott insulating phases by breaking time-reversal symmetry, and the time-reversal-even insulating phase, based on dynamical mean-field theory. In the deep insulating regime, the time-reversal-even phase arises from the interplay of effective Dzyaloshinskii-Moriya and Heisenberg exchange interactions. To relate to experimental situations, we make band-structure calculations to obtain the Hubbard parameters, and show that these orbital ordering phases persist also in the presence of next-nearest-neighbor hopping.
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