13 research outputs found
Cooper pairing near charged black holes
We show that a quartic contact interaction between charged fermions can lead
to Cooper pairing and a superconducting instability in the background of a
charged asymptotically Anti-de Sitter black hole. For a massless fermion we
obtain the zero mode analytically and compute the dependence of the critical
temperature T_c on the charge of the fermion. The instability we find occurs at
charges above a critical value, where the fermion dispersion relation near the
Fermi surface is linear. The critical temperature goes to zero as the marginal
Fermi liquid is approached, together with the density of states at the Fermi
surface. Besides the charge, the critical temperature is controlled by a four
point function of a fermionic operator in the dual strongly coupled field
theory.Comment: 1+33 pages, 4 figure
Kitaev's quantum double model from a local quantum physics point of view
A prominent example of a topologically ordered system is Kitaev's quantum
double model for finite groups (which in particular
includes , the toric code). We will look at these models from
the point of view of local quantum physics. In particular, we will review how
in the abelian case, one can do a Doplicher-Haag-Roberts analysis to study the
different superselection sectors of the model. In this way one finds that the
charges are in one-to-one correspondence with the representations of
, and that they are in fact anyons. Interchanging two of such
anyons gives a non-trivial phase, not just a possible sign change. The case of
non-abelian groups is more complicated. We outline how one could use
amplimorphisms, that is, morphisms to study the superselection
structure in that case. Finally, we give a brief overview of applications of
topologically ordered systems to the field of quantum computation.Comment: Chapter contributed to R. Brunetti, C. Dappiaggi, K. Fredenhagen, J.
Yngvason (eds), Advances in Algebraic Quantum Field Theory (Springer 2015).
Mainly revie
Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2
Recent theories suggest that the excitations of certain quantum Hall states
may have exotic braiding statistics which could be used to build topological
quantum gates. This has prompted an experimental push to study such states
using confined geometries where the statistics can be tested. We study the
transport properties of quantum point contacts (QPCs) fabricated on a
GaAs/AlGaAs two dimensional electron gas that exhibits well-developed
fractional quantum Hall effect, including at bulk filling fraction 5/2. We find
that a plateau at effective QPC filling factor 5/2 is identifiable in point
contacts with lithographic widths of 1.2 microns and 0.8 microns, but not 0.5
microns. We study the temperature and dc-current-bias dependence of the 5/2
plateau in the QPC, as well as neighboring fractional and integer plateaus in
the QPC while keeping the bulk at filling factor 3. Transport near QPC filling
factor 5/2 is consistent with a picture of chiral Luttinger liquid edge-states
with inter-edge tunneling, suggesting that an incompressible state at 5/2 forms
in this confined geometry
Topological quantum computing with Read-Rezayi states.
Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which, in principle, can be used for topological quantum computation. We present a prescription for efficiently finding braids which can be used to carry out a universal set of quantum gates on encoded qubits based on anyons of the Read-Rezayi states with k>2, k not equal 4. This work extends previous results which only applied to the case k=3 (Fibonacci) and clarifies why, in that case, gate constructions are simpler than for a generic Read-Rezayi state
Spin-orbit coupling and spirals in doped La2CuO4
Spin-orbit coupling in doped La2CuO4 can result in (1) a novel electron-phonon coupling involving soft oxygen tilting phonons, and (2) stabilization of a commensurate antiferromagnetic state over a spiral state in the presence of a sufficiently large tilt distortion. This second effect may be responsible for the unusual electronic properties of La1.88Ba0.12CuO4. © 1992 The American Physical Society.link_to_subscribed_fulltex
Quantum computing with non-Abelian quasiparticles
In topological quantum computation quantum information is stored in exotic states of matter which are intrinsically protected from decoherence, and quantum operations are carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three dimensional space-time, and the corresponding quantum operations depend only on the topology of the braids formed by these world-lines. We describe recent work showing how to find braids which can be used to perform arbitrary quantum computations using a specific kind of quasiparticle (those described by the so-called Fibonacci anyon model) which are thought to exist in the experimentally observed v = 12/5 fractional quantum Hall state. © World Scientific Publishing Company