Majorana modes and p-wave superfluids for fermionic atoms in optical lattices

Bühler, Adam; Lang, Nicolai; Kraus, Christina V.; Möller, Gunnar; Huber, Sebastian; Büchler, Hans Peter

doi:10.1038/ncomms5504

Cited by 79 publications

(77 citation statements)

References 55 publications

(85 reference statements)

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“…After the submission of this manuscript, we became aware of a related paper 48, which puts forward an idea of generating p-wave interaction on the optical lattice.…”

Section: Discussionmentioning

confidence: 99%

Chiral superfluidity with p-wave symmetry from an interacting s-wave atomic Fermi gas

Liu¹,

Li²,

Wu³

et al. 2014

Nat Commun

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Chiral p-wave superfluids are fascinating topological quantum states of matter that have been found in the liquid 3 He-A phase and arguably in the electronic Sr 2 RuO 4 superconductor. They are fundamentally related to the fractional 5/2 quantum Hall state, which supports fractional exotic excitations. Past studies show that they require spin-triplet pairing of fermions by p-wave interaction. Here we report that a p-wave chiral superfluid state can arise from spin-singlet pairing for an s-wave interacting atomic Fermi gas in an optical lattice. This p-wave state is conceptually distinct from all previous conventional p-wave states as it is for the centre-of-mass motion, instead of the relative motion. It leads to spontaneous generation of angular momentum, finite Chern numbers and topologically protected chiral fermionic zero modes bounded to domain walls, all occuring at a higher critical temperature in relative scales. Signature quantities are predicted for the cold atom experimental condition.

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“…After the submission of this manuscript, we became aware of a related paper 48, which puts forward an idea of generating p-wave interaction on the optical lattice.…”

Section: Discussionmentioning

confidence: 99%

Chiral superfluidity with p-wave symmetry from an interacting s-wave atomic Fermi gas

Liu¹,

Li²,

Wu³

et al. 2014

Nat Commun

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“…If the density of Fisher's zeros diverges, then the slopes of cusps in Re ( ) f t ′ inside the Fisher area diverge similarly. It occurs not only in the Haldane model, but also in the so-called BHS model [87], or in the lattice version of the chiral ( ) p ip + -superconductor [88], in which = ( sin , sin , cos cos ) is the number of such gaps) and will evolve into its subspace M . If the phase ergodicity holds for all k (i.e.…”

Section: Topology and Dynamical Quantum Phase Transitionsmentioning

confidence: 99%

Dynamical quantum phase transitions (Review Article)

Zvyagin

2016

Low Temperature Physics

132

126

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During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and thermodynamics in equilibrium. Since the dynamics of a many-body quantum system typically involve many excited eigenstates, with a non-thermal distribution, the time evolution of such a system provides an unique way for investigation of non-equilibrium quantum statistical mechanics. Last decade such new subjects like quantum quenches, thermalization, pre-thermalization, equilibration, generalized Gibbs ensemble, etc. are among the most attractive topics of investigation in modern quantum physics. One of the most interesting themes in the study of dynamics of quantum many-body systems out of equilibrium is connected with the recently proposed important concept of dynamical quantum phase transitions. During the last few years a great progress has been achieved in studying of those singularities in the time dependence of characteristics of quantum mechanical systems, in particular, in understanding how the quantum critical points of equilibrium thermodynamics affect their dynamical properties. Dynamical quantum phase transitions reveal universality, scaling, connection to the topology, and many other interesting features. Here we review the recent achievements of this quickly developing part of low-temperature quantum physics. The study of dynamical quantum phase transitions is especially important in context of their connection to the problem of the modern theory of quantum information, where namely non-equilibrium dynamics of many-body quantum system plays the major role. PACS

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“…Most importantly, perhaps, emergent quasiparticles in twodimensional topological phases of matter can acquire nonAbelian statistics and may provide quantum states with highly nonlocal entanglement that form an ideal basis for quantum information processing [2]. Many unanswered questions about topological systems remain, despite recent developments in the field exploring phase transitions (notably those driven by topological Bose condensation) [3][4][5][6][7][8][9][10], stability of topological phases to perturbations [11][12][13][14][15], coupling of multiple nonAbelian subsystems [16][17][18][19][20], or creation of non-Abelian theories from coupling simpler subsystems [21][22][23][24][25]. It is in these general realms that this paper seeks to explore.…”

Section: Introductionmentioning

confidence: 99%

Josephson-coupled Moore-Read states

et al. 2014

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We study a quantum Hall bilayer system of bosons at total filling factor ν = 1, and study the phase that results from short-ranged pair tunneling combined with short-ranged interlayer interactions. We introduce two exactly solvable model Hamiltonians which both yield the coupled Moore-Read state [Phys. Rev. Lett. 108, 256809 (2012)] as a ground state, when projected onto fixed particle numbers in each layer. One of these Hamiltonians describes a gapped topological phase, while the other is gapless. However, on introduction of a pair-tunneling term, the second system becomes gapped and develops the same topological order as the gapped Hamiltonian. Supported by the exact solution of the full zero-energy quasihole spectrum and a conformal field-theory approach, we develop an intuitive picture of this system as two coupled composite fermion superconductors. In this language, pair tunneling provides a Josephson coupling of the superconducting phases of the two layers, and gaps out the Goldstone mode associated with particle transport between the layers. In particular, this implies that quasiparticles are confined between the layers. In the bulk, the resulting phase has the topological order of the Halperin 220 phase with U(1) 2 ×U(1) 2 topological order, but it is realized in the symmetric/antisymmetric basis of the layer index. Consequently, the edge spectrum at a fixed particle number reveals an unexpected U(1) 4 ×U(1) structure.

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Majorana modes and p-wave superfluids for fermionic atoms in optical lattices

Cited by 79 publications

References 55 publications

Chiral superfluidity with p-wave symmetry from an interacting s-wave atomic Fermi gas

Chiral superfluidity with p-wave symmetry from an interacting s-wave atomic Fermi gas

Dynamical quantum phase transitions (Review Article)

Josephson-coupled Moore-Read states

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