Quantum phases in tunable state-dependent hexagonal optical lattices

Lühmann, Dirk-Sören; Jürgensen, Ole; Weinberg, Malte; Simonet, Juliette; Soltan-Panahi, Parvis; Sengstock, K.

doi:10.1103/physreva.90.013614

Cited by 31 publications

(36 citation statements)

References 46 publications

(138 reference statements)

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“…Figure 2. Parameters of the extended BH model as a function of the lattice depth, calculated according to [34] for the setup of the experiment [32].…”

Section: Setupmentioning

confidence: 99%

Beyond-mean-field study of a binary bosonic mixture in a state-dependent honeycomb lattice

et al. 2015

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Abstract. We investigate a binary mixture of bosonic atoms loaded into a statedependent honeycomb lattice. For this system, the emergence of a so-called twistedsuperfluid 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 Bose-Hubbard model adapted to the experimental parameters employing the Multi-Layer Multi-Configuration TimeDependent Hartree method for Bosons. Our results confirm the overall applicability of mean-field theory within the relevant parameter range. 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.

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“…Figure 2. Parameters of the extended BH model as a function of the lattice depth, calculated according to [34] for the setup of the experiment [32].…”

Section: Setupmentioning

confidence: 99%

Beyond-mean-field study of a binary bosonic mixture in a state-dependent honeycomb lattice

et al. 2015

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“…For the former, experimental efforts have been largely focused on the finite-temperature physics for the experimental challenge to reach the zero-temperature quantum ground states [8,9,[14][15][16][17][18][19]. For the latter, the ground state superfluid phase and the Mott-superfluid transition, have been accomplished in optical lattices of different dimensionality and geometries [6,[20][21][22][23][24][25][26][27]. It has been found that this phase transition is qualitatively captured by a Gutzwiller-type mean field theory [28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Finite temperature phase transition in a cross-dimensional triangular lattice

et al. 2019

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Atomic many-body phase transitions and quantum criticality have recently attracted much attention in non-standard optical lattices. Here we perform an experimental study of finite temperature superfluid transition of bosonic atoms confined in a three dimensional triangular lattice, whose structure can be continuously deformed to dimensional crossover regions including quasi-one and two dimensions. This non-standard lattice system provides a versatile platform to investigate manybody correlated phases. For the three dimensional case, we find that the finite temperature superfluid transition agrees quantitatively with the Gutzwiller mean field theory prediction, whereas tuning towards reduced dimensional cases, both quantum and thermal fluctuation effects are more dramatic, and the experimental measurement for the critical point becomes strongly deviated from the mean field theory. We characterize the fluctuation effects in the whole dimension crossover process. Our experimental results imply strong many-body correlations in the system beyond mean field description, paving a way to study quantum criticality near Mott-superfluid transition in finite temperature dimension-crossover lattices.

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“…Wannier functions obtained using this method, however, are not guaranteed to be real-valued and in turn depend on the choice of gauge transformation. An alternate method for constructing Wannier functions is by minimization of density-induced tunneling and density-density interactions between neighboring unit cells [27]. …”

Section: Introductionmentioning

confidence: 99%

Wannier functions using a discrete variable representation for optical lattices

Paul

Tiesinga

2016

Phys. Rev. A

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We propose a numerical method using the discrete variable representation (DVR) for constructing real-valued Wannier functions localized in a unit cell for both symmetric and asymmetric periodic potentials. We apply these results to finding Wannier functions for ultracold atoms trapped in laser-generated optical lattices. Following S. Kivelson [Phys. Rev. B 26, 4269 (1982)], for a symmetric lattice with inversion symmetry, we construct Wannier functions as eigenstates of the position operators x̂, ŷ, and ẑ restricted to single-particle Bloch functions belonging to one or more bands. To ensure that the Wannier functions are real-valued, we numerically obtain the band structure and real-valued eigenstates using a uniform Fourier grid DVR. We then show, by a comparison of tunneling energies, that the Wannier functions are accurate for both inversion-symmetric and asymmetric potentials to better than 10 significant digits when using double-precision arithmetic. The calculations are performed for an optical lattice with double-wells per unit cell with tunable asymmetry along the x axis and a single sinusoidal potential along the perpendicular directions. Localized functions at the two potential minima within each unit cell are similarly constructed, but using a superposition of single-particle solutions from the two lowest bands. We finally use these localized basis functions to determine the two-body interaction energies in the Bose-Hubbard model and show the dependence of these energies on lattice asymmetry.

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Quantum phases in tunable state-dependent hexagonal optical lattices

Cited by 31 publications

References 46 publications

Beyond-mean-field study of a binary bosonic mixture in a state-dependent honeycomb lattice

Beyond-mean-field study of a binary bosonic mixture in a state-dependent honeycomb lattice

Finite temperature phase transition in a cross-dimensional triangular lattice

Wannier functions using a discrete variable representation for optical lattices

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