Phys. Rev. Lett. 98, 070401 (2007) We examine interferometric measurements of the topological charge of
(non-Abelian) anyons. The target's topological charge is measured from its
effect on the ...interference of probe particles sent through the interferometer.
We find that superpositions of distinct anyonic charges a and a' in the target
decohere (exponentially in the number of probes particles used) when the probes
have nontrivial monodromy with the charges that may be fused with a to give a'.
Phys. Rev. Lett. 97, 016401 (2006) We examine interferometric experiments in systems that exhibit non-Abelian
braiding statistics, expressing outcomes in terms of the modular S-matrix. In
particular, ...this result applies to FQH interferometry, and we give a detailed
treatment of the Read-Rezayi states, providing explicit predictions for the
recently observed nu=12/5 plateau.
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit ...of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here we establish a similar correspondence between the Z_3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that---unlike Ising anyons---allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a two-fold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types yet depending on non-universal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.
We consider the tunneling current through a double point-contact Fabry-Perot interferometer such as used in recent experimental studies of the fractional quantum Hall plateau at filling fraction ...nu=5/2. We compare the predictions of several different models of the state of the electrons at this plateau: the Moore-Read, anti-Pfaffian, SU(2)_2 NAF, K=8 strong pairing, and (3,3,1) states. All of these predict the existence of charge e/4 quasiparticles, but the first three are non-Abelian while the last two are Abelian. We give explicit formulas for the scaling of charge e/2 and charge e/4 quasiparticle contributions to the current as a function of temperature, gate voltage and distance between the two point contacts for all three models. Based on these, we analyze several possible explanations of two phenomena reported for recent experiments by Willett et al., namely halving of the period of the observed resistance oscillations with rising temperature and alternation between the same two observed periods at low temperatures as the area of the interference loop is varied with a side gate. We conclude that the most likely explanation is that the observed alternation is due to switching between even and odd numbers of charge e/4 quasiparticles enclosed within the loop as a function of side gate voltage, which is a clear signature of the presence of non-Abelian anyons. However, there are important features of the data which do not have a simple explanation within this picture. We suggest further experiments which could help rule out some possible scenarios. We make the corresponding predictions for future tunneling and interference experiments at the other observed second Landau level fractional quantum Hall states.
We examine interferometric measurements of the topological charge of (non-Abelian) anyons. The target's topological charge is measured from its effect on the interference of probe particles sent ...through the interferometer. We find that superpositions of distinct anyonic charges a and a' in the target decohere (exponentially in the number of probes particles used) when the probes have nontrivial monodromy with the charges that may be fused with a to give a'.
We develop the general quantum measurement theory of non-Abelian anyons through interference experiments. The paper starts with a terse introduction to the theory of anyon models, focusing on the ...basic formalism necessary to apply standard quantum measurement theory to such systems. This is then applied to give a detailed analysis of anyonic charge measurements using a Mach-Zehnder interferometer for arbitrary anyon models. We find that, as anyonic probes are sent through the legs of the interferometer, superpositions of the total anyonic charge located in the target region collapse when they are distinguishable via monodromy with the probe anyons, which also determines the rate of collapse. We give estimates on the number of probes needed to obtain a desired confidence level for the measurement outcome distinguishing between charges, and explicitly work out a number of examples for some significant anyon models. We apply the same techniques to describe interferometry measurements in a double point-contact interferometer realized in fractional quantum Hall systems. To lowest order in tunneling, these results essentially match those from the Mach-Zehnder interferometer, but we also provide the corrections due to processes involving multiple tunnelings. Finally, we give explicit predictions describing state measurements for experiments in the Abelian hierarchy states, the non-Abelian Moore-Read state at \(\nu=5/2\) and Read-Rezayi state at \(\nu = 12/5\).
We examine interferometric experiments in systems that exhibit non-Abelian braiding statistics, expressing outcomes in terms of the modular S-matrix. In particular, this result applies to FQH ...interferometry, and we give a detailed treatment of the Read-Rezayi states, providing explicit predictions for the recently observed nu=12/5 plateau.
Microscopic simulation of optical gain in multi-quantum well lasers Hybertsen, M.S.; Alam, M.A.; Baraff, G.A. ...
1999 IEEE LEOS Annual Meeting Conference Proceedings. LEOS'99. 12th Annual Meeting. IEEE Lasers and Electro-Optics Society 1999 Annual Meeting (Cat. No.99CH37009),
1999, Letnik:
2
Conference Proceeding
Detailed microscopic simulations are required to explain the observed optical gain in MQW laser diodes. The accuracy of the simulation is encouraging evidence that the physical models are correct and ...supports future optimization through simulation.
