Pairing properties of cold fermions in a honeycomb lattice

Grémaud, Benoît

doi:10.1209/0295-5075/98/47003

Cited by 3 publications

(8 citation statements)

References 40 publications

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“…The matrix h depicts the one-particle Hamiltonian, namely, hopping terms between nearest neighbors h ij σ = −t (i = j ) and chemical potential terms h jj σ = −μ jσ = −μ σ + V T (j − j c ) 2n j σ . To account properly for spatial inhomogeneities, the BCS order parameter at each site, i , is an independent variable [32][33][34], whose value is determined, for a given temperature, by a global minimization of the free energy F = − 1 β ln (Z) associated with the mean-field Hamiltonian:…”

Section: Model and Methodsmentioning

confidence: 99%

“…2 nj σ . To account properly for spatial inhomogeneities, the BCS order parameter at each site, ∆ i , is an independent variable [30,31,33], whose value is determined, for a given temperature, by a global minimization of the free energy, F = − 1 β ln (Z) associated with the mean-field Hamiltonian:…”

Section: Model and Methodsmentioning

confidence: 99%

“…From the experimental point of view, this signature of the FFLO order could be measured either directly in the density of pairs or in their velocity distribution. Of course, the present mean-field calculation does not include the thermal fluctuations which are crucial to properly describe the condensation of the pairs which, at large interaction, arises at a temperature k B T ≈ t 2 /U lower than the pair formation temperature k B T ≈ U [34,[41][42][43].…”

Section: Harmonically Confined Systemmentioning

confidence: 99%

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Pairing in a two-dimensional Fermi gas with population imbalance

et al. 2012

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Pairing in a population imbalanced Fermi system in a two-dimensional optical lattice is studied using Determinant Quantum Monte Carlo (DQMC) simulations and mean-field calculations. The approximation-free numerical results show a wide range of stability of the Fulde-Ferrell-Larkin-Ovshinnikov (FFLO) phase. Contrary to claims of fragility with increased dimensionality we find that this phase is stable across wide range of values for the polarization, temperature and interaction strength. Both homogeneous and harmonically trapped systems display pairing with finite center of mass momentum, with clear signatures either in momentum space or real space, which could be observed in cold atomic gases loaded in an optical lattice. We also use the harmonic level basis in the confined system and find that pairs can form between particles occupying different levels which can be seen as the analog of the finite center of mass momentum pairing in the translationally invariant case. Finally, we perform mean field calculations for the uniform and confined systems and show the results to be in good agreement with QMC. This leads to a simple picture of the different pairing mechanisms, depending on the filling and confining potential.Comment: 15 pages, 22 figures, submitted to PR

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Section: Model and Methodsmentioning

confidence: 99%

Section: Model and Methodsmentioning

confidence: 99%

Section: Harmonically Confined Systemmentioning

confidence: 99%

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Pairing in a two-dimensional Fermi gas with population imbalance

et al. 2012

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“…(7) for a 2D square lattice in the presence of a magnetic flux generating a π-flux per plaquette: this model exhibits Dirac points at half filling. We also consider a continuous interpolation between the πflux square lattice model and the honeycomb lattice, on which the attractive Hubbard model has been extensively studied [44][45][46][47][48].…”

Section: π-Flux Square Lattice Modelmentioning

confidence: 99%

Semimetal–superfluid quantum phase transitions in 2D and 3D lattices with Dirac points

Mazzucchi

Lepori

Trombettoni

2013

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. We study the superfluid properties of attractively interacting fermions hopping in a family of 2D and 3D lattices in the presence of synthetic gauge fields having π-flux per plaquette. The reason for such a choice is that the π-flux cubic lattice displays Dirac points and that decreasing the hopping coefficient in a spatial direction (say, t z ) these Dirac points are unaltered: it is then possible to study the 3D-2D interpolation towards the π-flux square lattice. We also consider the lattice configuration providing the continuous interpolation between the 2D π-flux square lattice and the honeycomb geometry. We investigate by a mean field analysis the effects of interaction and dimensionality on the superfluid gap, chemical potential and critical temperature, showing that these quantities continuously vary along the patterns of interpolation. In the two-dimensional cases at zero temperature and at half filling there is a quantum phase transition occurring at a critical (negative) interaction U c presenting a linear critical exponent for the gap as a function of |U − U c |. We show that in three dimensions this quantum phase transition is again retrieved, pointing out that the critical exponent for the gap changes from 1 to 1/2 for each finite value of t z .

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“…The experimental realization of loading ultracold bosons [36] and fermions [37,38] into topological lattices, here the honeycomb (graphene) lattice, in particular, has started much interest in the exotic phase diagrams of these systems [39][40][41][42]. Furthermore, it was demonstrated that initiating dynamics in topological lattices gives direct experimental access to the band structure [43] as well as topological quantities such as chern numbers [44], the Berry curvature [45] and Wilson lines [46].…”

Section: Introductionmentioning

confidence: 99%

Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices

2016

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We determine the exact dynamics of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultra-cold atoms in a deep hexagonal optical lattice. The dynamical evolution is triggered by a quench of the lattice potential, such that the interaction strength U f is much larger than the hopping amplitude J f . The quench initiates collective oscillations with frequency |U f |/(2π) in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the BCS order parameter ∆. The oscillation frequency of ∆ is not reproduced by treating the time evolution in mean-field theory. In our theory, the momentum noise (i.e. density-density) correlation functions oscillate at frequency |U f |/2π as well as at its second harmonic. For a very deep lattice, with zero tunneling energy, the oscillations of momentum occupation numbers are undamped. Non-zero tunneling after the quench leads to dephasing of the different momentum modes and a subsequent damping of the oscillations. The damping occurs even for a finite-temperature initial BCS state, but not for a non-interacting Fermi gas. Furthermore, damping is stronger for larger order parameter and may therefore be used as a signature of the BCS state. Finally, our theory shows that the noise correlation functions in a honeycomb lattice will develop strong anti-correlations near the Dirac point. 67.85.Lm

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Pairing properties of cold fermions in a honeycomb lattice

Cited by 3 publications

References 40 publications

Pairing in a two-dimensional Fermi gas with population imbalance

Pairing in a two-dimensional Fermi gas with population imbalance

Semimetal–superfluid quantum phase transitions in 2D and 3D lattices with Dirac points

Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices

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