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arXiv:1210.0799 · Physical Review Letters

Enhancing the Thermal Stability of Majorana Fermions with Redundancy Using Dipoles in Optical Lattices

Fei Lin, V. W. Scarola

Published Nov 25, 2013• 4 citations
arXivHTMLPDF

Abstract

Pairing between spinless fermions can generate Majorana fermion excitations that exhibit intriguing properties arising from nonlocal correlations. But, simple models indicate that nonlocal correlation between Majorana fermions becomes unstable at nonzero temperatures. We address this issue by showing that anisotropic interactions between dipolar fermions in optical lattices can be used to significantly enhance thermal stability. We construct a model of oriented dipolar fermions in a square optical lattice. We find that domains established by strong interactions exhibit enhanced correlation between Majorana fermions over large distances and long times even at finite temperatures, suitable for stable redundancy encoding of quantum information. Our approach can be generalized to a variety of configurations and other systems, such as quantum wire arrays.

DOI
10.1103/physrevlett.111.220401

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Pairing between spinless fermions can generate Majorana fermion excitations that exhibit intriguing properties arising from nonlocal correlations. But, simple models indicate that nonlocal correlation between Majorana fermions becomes unstable at nonzero temperatures. We address this issue by showing that anisotropic interactions between dipolar fermions in optical lattices can be used to significantly enhance thermal stability. We construct a model of oriented dipolar fermions in a square optical lattice. We find that domains established by strong interactions exhibit enhanced correlation between Majorana fermions over large distances and long times even at finite temperatures, suitable for stable redundancy encoding of quantum information. Our approach can be generalized to a variety of configurations and other systems, such as quantum wire arrays.
Pairing between spinless fermions can generate Majorana fermion excitations that exhibit intriguing properties arising from non-local correlations. But simple models indicate that non-local correlation between Majorana fermions becomes unstable at non-zero temperatures. We address this issue by showing that anisotropic interactions between dipolar fermions in optical lattices can be used to significantly enhance thermal stability. We construct a model of oriented dipolar fermions in a square optical lattice. We find that domains established by strong interactions exhibit enhanced correlation between Majorana fermions over large distances and long times even at finite temperatures, suitable for stable redundancy encoding of quantum information. Our approach can be generalized to a variety of configurations and other systems, such as quantum wire arrays.
Ultracold dilute atomic gases are highly controllable systems whose properties are fundamentally determined by the interatomic interactions.In typical experiments on ultra cold gases particles interact dominantly via a short-range isotropic potential.However, during the last years a new generation of experiments is starting to explore systems, where an additional interaction, the long-range and anisotropic dipole-dipole interaction plays a significant or possibly dominant role.The effects induced by the anisotropy of the dipole-dipole interaction are crucially enhanced if the dipolar gas is confined in a deep optical lattice.In this thesis we study novel phenomena in such systems of dipolar gases in deep optical lattices.The nonlocal nonlinearity introduced by the dipole-dipole interaction plays a crucial role in the physics of dipolar Bose-Einstein condensates.In particular, it may distort significantly the stability of straight vortex lines.Remarkably, in the presence of a periodic potential along the vortex line, the spectrum of transverse modes shows a roton-like minimum, which eventually destabilizes the straight vortex when the BEC as a whole is still stable, opening the possibility for new scenarios for vortex line configurations in dipolar gases.We have analyzed this instability, and showed that it leads to a second-order-like phase transition from a straight vortex line into novel helical or snake-like configurations, depending on the dipole orientation.Strong 1D lattices usually lead to unconnected two-dimensional gases.The long-range character of the dipole-dipole interactions leads to a novel scenario where non-overlapping gases at different sites may interact significantly.We show that the excitations of non-overlapping condensates in 1D optical lattices acquire a band-like character, being collectively shared by different sites.In particular, the hybridization of the modes significantly enhances the rotonization of the excitations, and may induce roton-instability.We discuss the observability of this effect in on-going experiments.Fermionic polar molecules in deep 1D optical lattices may form selfassembled filaments when the electric dipoles are oriented along the lattice axis.These composites are bosons or fermions depending on the number of molecules per chain, leading to a peculiar and complex Bose-Fermi mixture, vi which we discuss in detail for the simplest case of a three-well potential.We show that the interplay between filament binding energy, transverse filament modes, and trimer Fermi energy leads to a rich variety of possible scenarios ranging from a degenerate Fermi gas of trimers to a binary mixture of two different types of bosonic dimers.We study the intriguing zero temperature and finite temperature physics of these composites for the particular case of an ideal filament gas loaded in 1D sites, and discuss possible methods to probe these chain mixtures.
Abstract I analyze the emergence of Majorana zero modes (MZM) in a one dimensional ultracold fermionic system confined by an optical lattice inside a high-Q cavity. This forms a quantum optical lattice due to the cavity backaction, with emergent long range interactions controlled by the light pumped into the system and thus long range pairing. I investigate the possibility of formation and emergence of edge modes using exact diagonalization with self-consistent order parameters and singular value decomposition of the Hamiltonian in the Majorana representation. I analyze the spectral properties of the system, the mass gap and amplitude of the MZM with a unified framework. The interplay of cavity induced interactions and effective p -wave short range interactions controls the emergence of the signatures of MZM. I find that under certain conditions MZM distinctively emerge leading to superradiant topological phases of matter. These MZM have potential applications for quantum information as they are topologically protected analogous to the behavior of the Kitaev chain. The techniques employed lead to a scheme based on the Majorana representation and exact diagonalization with self consistent conditions using Hartree–Fock–Bogoliubov theory in real space for finite systems that can be applied to other fermionic and analog systems termed Light-Matter-Majorana. A promising landscape for the exploration of short range and long range topological order with superradiance is found.
I analyze the emergence of Majorana zero modes (MZM) in a one dimensional ultracold fermionic system confined by an optical lattice inside a high-Q cavity. This forms a quantum optical lattice due to the cavity backaction, with emergent long range interactions controlled by the light pumped into the system and thus long range pairing. I investigate the possibility of formation and emergence of edge modes using exact diagonalization and singular value decomposition of the Hamiltonian in the Majorana representation, while computing the mass gap of the MZM and its spectral properties. The interplay of cavity induced interactions and effective ppp-wave short range interactions controls the emergence of the signatures of MZM. I find that under certain conditions MZM distinctively emerge leading to a superradiant topological phase of matter. These MZM have potential applications for quantum information as they are topologically protected analogous to the behaviour of the Kitaev chain. The techniques employed lead to a scheme based on the Majorana representation and exact diagonalization with self consistent conditions that can be applied to other fermionic and analog systems termed Light-Matter-Majorana.
There has been growing interest in investigating properties of elementary particles predicted by the standard model. Examples of such studies include exploring their low-energy analogs in a condensed-matter system, where they arise as collective states or quasiparticles. Here we show that a toolbox for systematically engineering the emergent elementary fermions, i.e., Dirac, Weyl, and Majorana fermions, can be built in a single atomic system composed of a spinless magnetic dipolar Fermi gas in a three-dimensional optical lattice. The designed direction-dependent dipole-dipole interaction leads to both the basic building block, i.e., in-plane p+ipp+ipp+ip superfluid pairing instability, and the manipulating tool, i.e., out-of-plane Peierls instability. It is shown that the Peierls instability provides a natural way of tuning the topological nature of p+ipp+ipp+ip superfluids and can transform the fermion's nature between distinct emergent particles. Our scheme should contribute to the search for elementary particles through manipulating the topology.
We study strongly correlated ground states of dipolar fermions in a honeycomb optical lattice with spatial variations in hopping amplitudes. Similar to strained graphene, such nonuniform hopping amplitudes produce valley-dependent pseudomagnetic fields for fermions near the two Dirac points, resulting in the formation of Landau levels. The dipole moments aligned perpendicular to the honeycomb plane yield a long-range repulsive interaction. By exact diagonalization in the zeroth-Landau-level basis, we show that this repulsive interaction stabilizes a variety of valley-polarized fractional quantum Hall states such as Laughlin and composite-fermion states. The present system thus offers an intriguing platform for emulating fractional quantum Hall physics in a static optical lattice. We calculate the energy gaps above these incompressible states and discuss the temperature scales required for their experimental realization.