BCS-BEC crossover in mix-dimensional Fermi gases

Yang, X. M.; Huang, Beibing; Wan, Shaolong

doi:10.1140/epjb/e2011-20354-0

Cited by 9 publications

(19 citation statements)

References 33 publications

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“…In this paper we observed that the nontrivial topology of NC U (1) instantons faithfully appears in the emergent gravity description. For example, NC U (1) instantons give rise to the ALE-type four-manifolds [45,66] whose nontrivial topology is encoded in bolts (noncontractible two-cycles) while NC U (1) monopoles may be realized as the ALF-type four-manifolds whose nontrivial topology is encoded in nuts (isolated points). The nice formula (111) for the Euler characteristic clearly illuminates this aspect of four-manifolds emergent from symplectic (or NC) U (1) instantons or monopoles.…”

Section: Discussionmentioning

confidence: 99%

Test of emergent gravity

2013

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In this paper we examine a small but detailed test of the emergent gravity picture with explicit solutions in gravity and gauge theory. We first derive symplectic U (1) gauge fields starting from the Eguchi-Hanson metric in four-dimensional Euclidean gravity. The result precisely reproduces the U (1) gauge fields of the Nekrasov-Schwarz instanton previously derived from the top-down approach. In order to clarify the role of noncommutative spacetime, we take the Braden-Nekrasov U (1) instanton defined in ordinary commutative spacetime and derive a corresponding gravitational metric. We show that the Kähler manifold determined by the Braden-Nekrasov instanton exhibits a spacetime singularity while the Nekrasov-Schwarz instanton gives rise to a regular geometrythe Eguchi-Hanson space. This result implies that the noncommutativity of spacetime plays an important role for the resolution of spacetime singularities in general relativity. We also discuss how the topological invariants associated with noncommutative U (1) instantons are related to those of emergent four-dimensional Riemannian manifolds according to the emergent gravity picture.

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Section: Discussionmentioning

confidence: 99%

Test of emergent gravity

2013

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“…From the gauge theory point of view, the symplectomorphisms can be identified with U (1) gauge transformations. 14,15,16 In other words, the gauge symmetry acting on U (1) gauge fields as A → A + dφ is generated by a Hamiltonian vector field X φ , i.e., satisfying ι X φ B + dφ = 0.…”

Section: Symplectization Of Spacetime Geometrymentioning

confidence: 99%

“…Hence, the final touch for the gauge/gravity duality is to find an explicit map between electromagnetism and gravity. 14,15,16 First, note that the U (1) gauge field (21) deforming an underlying symplectic structure is completely encoded into a local trivialization of the symplectic structure up to symplectomorphisms via the Darboux theorem or the Moser lemma. 17,18 Let us denote the local coordinate transformation φ : y µ → x µ (y) as…”

Section: Symplectization Of Spacetime Geometrymentioning

confidence: 99%

Emergent Geometry and Quantum Gravity

Yang

2010

Mod. Phys. Lett. A

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We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L 2 P whose physical dimension is of (length) 2 in natural unit introduces a symplectic structure of spacetime which causes a noncommutative spacetime at the Planck scale L P . The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, ω) and Riemannian geometry (M, g) where the deformations of symplectic structure ω in terms of electromagnetic fields F = dA are transformed into those of Riemannian metric g. This approach for quantum gravity allows a background independent formulation where spacetime as well as matter fields is equally emergent from a universal vacuum of quantum gravity which is thus dubbed as the quantum equivalence principle.

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“…Note that, even for purely bosonic gases, the spatial overlap between bosons has been experimentally shown to be strongly suppressed by the strong correlations emerging in 1D [41]. In addition, mixed-dimensional systems allow to study interesting few-body [42] and manybody [22,43] phenomena. We should stress that the results reported here are relevant to several experimental realizations.…”

Section: Introductionmentioning

confidence: 99%

Phase equilibrium of binary mixtures in mixed dimensions

2013

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We study the stability of a Bose-Fermi system loaded into an array of coupled one-dimensional (1D) "tubes", where bosons and fermions experience different dimensions: Bosons are heavy and strongly localized in the 1D tubes, whereas fermions are light and can hop between the tubes. Using the 174 Yb-6 Li system as a reference, we obtain the equilibrium phase diagram. We find that, for both attractive and repulsive interspecies interaction, the exact treatment of 1D bosons via the Bethe ansatz implies that the transitions between pure fermion and any phase with a finite density of bosons can only be first order and never continuous, resulting in phase separation in density space. In contrast, the order of the transition between the pure boson and the mixed phase can either be second or first order depending on whether fermions are allowed to hop between the tubes or they also are strictly confined in 1D. We discuss the implications of our findings for current experiments on 174 Yb-6 Li mixtures as well as Fermi-Fermi mixtures of light and heavy atoms in a mixed dimensional optical lattice system.

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BCS-BEC crossover in mix-dimensional Fermi gases

Cited by 9 publications

References 33 publications

Test of emergent gravity

Test of emergent gravity

Emergent Geometry and Quantum Gravity

Phase equilibrium of binary mixtures in mixed dimensions

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