190 research outputs found
Braiding Interactions in Anyonic Quantum Walks
The anyonic quantum walk is a dynamical model describing a single anyon
propagating along a chain of stationary anyons and interacting via mutual
braiding statistics. We review the recent results on the effects of braiding
statistics in anyonic quantum walks in quasi-one dimensional ladder geometries.
For anyons which correspond to spin-1/2 irreps of the quantum groups ,
the non-Abelian species gives rise to entanglement between the
walker and topological degrees of freedom which is quantified by quantum link
invariants over the trajectories of the walk. The decoherence is strong enough
to reduce the walk on the infinite ladder to classical like behaviour. We also
present numerical results on mixing times of or Ising model anyon
walks on cyclic graphs. Finally, the possible experimental simulation of the
anyonic quantum walk in Fractional Quantum Hall systems is discussed.Comment: 13 pages, submitted to Proceedings of the 2nd International
Conference on Theoretical Physics (ICTP 2012
Realization of Arbitrary Gates in Holonomic Quantum Computation
Among the many proposals for the realization of a quantum computer, holonomic
quantum computation (HQC) is distinguished from the rest in that it is
geometrical in nature and thus expected to be robust against decoherence. Here
we analyze the realization of various quantum gates by solving the inverse
problem: Given a unitary matrix, we develop a formalism by which we find loops
in the parameter space generating this matrix as a holonomy. We demonstrate for
the first time that such a one-qubit gate as the Hadamard gate and such
two-qubit gates as the CNOT gate, the SWAP gate and the discrete Fourier
transformation can be obtained with a single loop.Comment: 8 pages, 6 figure
Non-Abelian Chern-Simons theory from a Hubbard-like model
Here, we provide a simple Hubbard-like model of spin-1/2 fermions that gives rise to the SU(2)-symmetric Thirring model that is equivalent, in the low-energy limit, to the Yang-Mills-Chern-Simons model. First, we identify the regime that simulates the SU(2) Yang-Mills theory. Then, we suitably extend this model so that it gives rise to the SU(2) Chern-Simons theory with level k≥2 that can support non-Abelian anyons. This is achieved by introducing multiple fermionic species and modifying the Thirring interactions, while preserving the SU(2) symmetry. Our proposal provides the means to theoretically and experimentally probe non-Abelian SU(2) level k topological phases
Transport properties of anyons in random topological environments
The quasi one-dimensional transport of Abelian and non-Abelian anyons is
studied in the presence of a random topological background. In particular, we
consider the quantum walk of an anyon that braids around islands of randomly
filled static anyons of the same type. Two distinct behaviours are identified.
We analytically demonstrate that all types of Abelian anyons localise purely
due to the statistical phases induced by their random anyonic environment. In
contrast, we numerically show that non-Abelian Ising anyons do not localise.
This is due to their entanglement with the anyonic environment that effectively
induces dephasing. Our study demonstrates that localisation properties strongly
depend on non-local topological interactions and it provides a clear
distinction in the transport properties of Abelian and non-Abelian statistics.Comment: 9 pages, 5 figure
Seeing Majorana fermions in time-of-flight images of spinless fermions coupled by s-wave pairing
The Chern number, nu, as a topological invariant that identifies the winding
of the ground state in the particle-hole space, is a definitive theoretical
signature that determines whether a given superconducting system can support
Majorana zero modes. Here we show that such a winding can be faithfully
identified for any superconducting system (p-wave or s-wave with spin-orbit
coupling) through a set of time-of-flight measurements, making it a diagnostic
tool also in actual cold atom experiments. As an application, we specialize the
measurement scheme for a chiral topological model of spinless fermions. The
proposed model only requires the experimentally accessible s-wave pairing and
staggered tunnelling that mimics spin-orbit coupling. By adiabatically
connecting this model to Kitaev's honeycomb lattice model, we show that it
gives rise to nu = \pm 1 phases, where vortices bind Majorana fermions, and
nu=\pm 2 phases that emerge as the unique collective state of such vortices.
Hence, the preparation of these phases and the detection of their Chern numbers
provide an unambiguous signature for the presence of Majorana modes. Finally,
we demonstrate that our detection procedure is resilient against most
inaccuracies in experimental control parameters as well as finite temperature.Comment: 9+4 pages, 11 figures, expanded versio
Cold atom simulation of interacting relativistic quantum field theories
We demonstrate that Dirac fermions self-interacting or coupled to dynamic
scalar fields can emerge in the low energy sector of designed bosonic and
fermionic cold atom systems. We illustrate this with two examples defined in
two spacetime dimensions. The first one is the self-interacting Thirring model.
The second one is a model of Dirac fermions coupled to a dynamic scalar field
that gives rise to the Gross-Neveu model. The proposed cold atom experiments
can be used to probe spectral or correlation properties of interacting quantum
field theories thereby presenting an alternative to lattice gauge theory
simulations.Comment: 5 pages, 3 figues, Phys. Rev. Lett. versio
Decoherence-free dynamical and geometrical entangling phase gates
It is shown that entangling two-qubit phase gates for quantum computation
with atoms inside a resonant optical cavity can be generated via common laser
addressing, essentially, within one step. The obtained dynamical or geometrical
phases are produced by an evolution that is robust against dissipation in form
of spontaneous emission from the atoms and the cavity and demonstrates
resilience against fluctuations of control parameters. This is achieved by
using the setup introduced by Pachos and Walther [Phys. Rev. Lett. 89, 187903
(2002)] and employing entangling Raman- or STIRAP-like transitions that
restrict the time evolution of the system onto stable ground states.Comment: 10 pages, 9 figures, REVTEX, Eq. (20) correcte
Topological Degeneracy and Vortex Manipulation in Kitaev's Honeycomb Model
The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the Abelian topological degeneracy. We derive a perturbative low-energy effective Hamiltonian that is valid to all orders of the expansion and for all possible toroidal configurations. Using this form we demonstrate at what order the system's topological degeneracy is lifted by finite size effects and note that in the thermodynamic limit it is robust to all orders. Further, we demonstrate that the loop symmetries themselves correspond to the creation, propagation, and annihilation of fermions. We note that these fermions, made from pairs of vortices, can be moved with no additional energy cost
Entropic manifestations of topological order in three dimensions
We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological properties is richer than the two-dimensional case. In addition to the reduction of the entropy caused by a nonzero vacuum expectation value of contractible loop operators, a topological invariant emerges that increases the entropy if the model consists of nontrivially braiding anyons. As a result the three-dimensional topological entanglement entropy provides only partial information about the two entropic topological invariants
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