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arXiv:1211.4863 · Physical Review A

Absence of the twisted superfluid state in a mean-field model of bosons on a honeycomb lattice

Sayan Choudhury, Erich J. Mueller

Published Mar 22, 2013• 7 citations
arXivHTMLPDF

Abstract

Motivated by recent observations [Soltan-Panahi et al., Nat. Phys. 8, 71 (2012)], we study the stability of a Bose-Einstein condensate within a spin-dependent honeycomb lattice towards forming a ``twisted superfluid'' state. Our exhaustive numerical search fails to find this phase, pointing to possible non-mean-field physics.
DOI
10.1103/physreva.87.033621

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We investigate a binary mixture of bosonic atoms loaded into a state-dependent honeycomb lattice. For this system, the emergence of a so-called twisted-superfluid ground state was experimentally observed in Soltan-Panahi et al. [Nat. Phys. 8, 71 (2012)]. Theoretically, the origin of this effect is not understood. We perform numerical simulations of an extended single-band Bose-Hubbard model adapted to the experimental parameters employing the multilayer multiconfiguration time-dependent Hartree method for Bosons. Our results confirm the overall applicability of mean-field theory in the relevant parameter range, within the extended single-band Bose-Hubbard model. Beyond this, we provide a detailed analysis of correlation effects correcting the mean-field result. These have the potential to induce asymmetries in single shot time-of-flight measurements, but we find no indication of the patterns characteristic of the twisted superfluid. We comment on the restrictions of our model and possible extensions.
Cold atoms trapped in optical lattices (crystals of light) provide a pristine platform for exploring quantum many body physics. Motivated by several recent experiments, this thesis examines the equilibrium and non-equilibrium dynamics of a Bose-Einstein condensate (BEC) loaded in a low dimensional optical lattice in order to realize novel quantum phases. There are two main research directions in this thesis. The first one involves the possibility that exotic order spontaneously forms when two-component bosons are trapped in a honeycomb lattice. My studies on this theme is motivated by the observation of a “twisted superfluid” state in Prof. Klaus Sengstock’s group at Hamburg (Soltan-Panahi et al., Nat. Phys. 8, 71 (2012)). A twisted superfluid involves Bose-Einstein condensation into a state whose order parameter has a spatially varying phase. In chapter 3, I study the stability of a Bose-Einstein condensate towards forming a twisted superfluid within the framework of mean field theory. Despite a exhaustive numerical search I do not find a parameter regime with a twisted superfluid. This search involved all experimentally relevant parameter regimes and therefore mean field theory predicted that the experimentalists should not observe a twisted superfluid. I conclude that the experimental observations were either a manifestation of counter superfluidity or due to interactions during time-of-flight. Subsequent experiments showed that the observations were an artifact of the measurement process. The second research direction in this thesis is an exploration of the stability of periodically driven quantum systems (also known as Floquet systems). Floquet systems can be used to realize exotic non-equilibrium quantum phases which do not have a counterpart in static systems. However, the driving can cause these systems to heat up which presents a major obstacle to creating exotic states. To explore this issue in a concrete example, I model an experiment (Parker, Ha, and Chin, Nat. Phys. 9, 769 (2013)) where a Bose-Einstein condensate loaded in an optical lattice is subjected to periodic shaking. I investigate the stability of this Floquet BEC to interactions. This research direction consists of 3 studies. In chapter 4, I first do this analysis for a purely one-dimensional system and identify a large parameter regime where the BEC is stable. In the next two chapters, I go beyond 1D and consider the role of transverse degrees of freedom. This is because the shaken lattice experiments that I model involves a 1D array of pancakes. I find that this geometry leads to much more dissipation than a purely 1D system. This extra dissipation arises because interactions can transfer energy between different directions. In chapter 5, I consider the extreme case where there is no transverse confinement. I find that in the absence of transverse confinement, a one-dimensional Floquet BEC is generically unstable. Finally, in chapter 6, I consider harmonic transverse confinement modeling the crossover between chapters 4 and 5. I find that as the transverse confinement is made stronger, the atom loss rate initially increases, but beyond a critical transverse confinement, the atom loss disappears due to unavailability of phase space for scattering. I also predict that if the transverse confinement is tuned to the vicinity of certain magic values, the heating rate exhibits a sharp drop. I perform similar analyses for a shaken square lattice and find that generically a low-dimensional Floquet BEC can be stabilized by suitably designing the transverse confinement.
Mean-field Bloch bands of a Bose-Einstein condensate in a honeycomb optical lattice are computed. We find that the topological structure of the Bloch bands at the Dirac point is changed completely by atomic interaction of arbitrary small strength: the Dirac point is extended into a closed curve and an intersecting tube structure arises around the original Dirac point. These tubed Bloch bands are caused by the superfluidity of the system. Furthermore, they imply the inadequacy of the tight-binding model to describe an interacting Boson system around the Dirac point and the breakdown of adiabaticity by interaction of arbitrary small strength.
Motivated by the recent experimental realization of the Haldane model by ultracold fermions in an optical lattice, we investigate phase diagrams of the hard-core Bose-Hubbard model on a honeycomb lattice. This model is closely related with a spin-1/2 antiferromagnetic (AF) quantum spin model. Nearest-neighbor (NN) hopping amplitude is positive and it prefers an AF configuration of phases of Bose-Einstein condensates. On the other hand, an amplitude of the next-NN hopping depends on an angle variable as in the Haldane model. Phase diagrams are obtained by means of an extended path-integral Monte Carlo simulation. Besides the AF state, a ${120}^{\ensuremath{\circ}}$-order state, there appear other phases including a Bose metal in which no long-range orders exist.
Abstract Observation of strong correlations and superconductivity in twisted-bilayer-graphene have stimulated tremendous interest in fundamental and applied physics. In this system, the superposition of two twisted honeycomb lattices, generating a Moire pattern, is the key to the observed flat electronic bands, slow electron velocity and large density of states. Despite these observations, a full understanding of the emerging superconductivity from the coupled layers and the appearance of a small magic angle remain a hot topic of research. Here, we demonstrate a quantum simulation platform to study superfluids in twisted bilayer lattices based on Bose-Einstein condensates loaded into spin-dependent optical lattices. The lattices are made of two sets of laser beams that independently address atoms in different spin states, which form the synthetic dimension accommodating the two layers. The twisted angle of the two lattices is controlled by the relative angle of the laser beams. We show that atoms in each spin state only feel one set of the lattice and the interlayer coupling can be controlled by microwave coupling between the spin states. Our system allows for flexible control of both the inter- and intralayer couplings. Furthermore we directly observe the spatial Moire pattern and the momentum diffraction, which confirm the presence of atomic superfluid in the bilayer lattices. Our system constitutes a powerful platform to investigate the physics underlying the superconductivity in twisted-bilayer-graphene and to explore other novel quantum phenomena difficult to realize in materials.
We demonstrate that low-lying triplon excitations in a bilayer Heisenberg antiferromagnet provide a promising avenue to realize magnetic analogs of twisted superfluid and supersolid phases that were recently reported for two-component ultracold atomic condensate in an optical lattice. Using a cluster Gutzwiller mean-field theory, we establish that Dzyaloshinskii-Moriya interactions (DMI), that are common in many quantum magnets, stabilize these phases in a magnetic system, in contrast to the pair hopping process that is necessary for ultracold atoms. The critical value of DMI for transition to the twisted superfluid and twisted supersolid phases depends on the strength of the (frustrated) interlayer interactions that can be tuned by applying external pressure on and / or shearing force between the layers. Furthermore, we show that the strength of DMI can be controllably varied by coupling to tailored circularly polarized light. Our results provide crucial guidance for the experimental search of twisted superfluid and supersolid phases of triplons in real quantum magnets.