Signatures of neutral quantum Hall modes in transport through low-density constrictions

Constrictions in fractional quantum Hall (FQH) systems not only facilitate backscattering between counter-propagating edge modes, but also may reduce the constriction filling fraction $\nu_c$ with respect to the bulk filling fraction $\nu_b$. If both $\nu_b$ and $\nu_c$ correspond to incompressible FQH states, at least part of the constriction region is surrounded by composite edges, whose low energy dynamics is characterized by a charge mode and one or several neutral modes. In the incoherent regime, decay of neutral modes describes the equilibration of composite FQH edges, while in the limit of coherent transport, the presence of neutral modes gives rise to universal conductance fluctuations. In addition, neutral modes renormalize the strength of scattering across the constriction, and thus can determine the relative strength of forward and backwards scattering.Comment: corrected description of the results of Ref. [10], Ref. [17] adde

Are Microwave Induced Zero Resistance States Necessarily Static?

We study the effect of inhomogeneities in Hall conductivity on the nature of the Zero Resistance States seen in the microwave irradiated two-dimensional electron systems in weak perpendicular magnetic fields, and we show that time-dependent domain patterns may emerge in some situations. For an annular Corbino geometry, with an equilibrium charge density that varies linearly with radius, we find a time-periodic non-equilibrium solution, which might be detected by a charge sensor, such as an SET. For a model on a torus, in addition to static domain patterns seen at high and low values of the equilibrium charge inhomogeneity, we find that, in the intermediate regime, a variety of nonstationary states can also exist. We catalog the possibilities we have seen in our simulations. Within a particular phenomenological model, we show that linearizing the nonlinear charge continuity equation about a particularly simple domain wall configuration and analyzing the eigenmodes allows us to estimate the periods of the solutions to the full nonlinear equation.Comment: Submitted to PR

Proposed experiments to probe the non-abelian \nu=5/2 quantum Hall state

We propose several experiments to test the non-abelian nature of quasi-particles in the fractional quantum Hall state of \nu=5/2. One set of experiments studies interference contribution to back-scattering of current, and is a simplified version of an experiment suggested recently. Another set looks at thermodynamic properties of a closed system. Both experiments are only weakly sensitive to disorder-induced distribution of localized quasi-particles.Comment: Additional references and an improved figure, 5 page

The theory of coherent dynamic nuclear polarization in quantum dots

We consider the dynamic nuclear spin polarization (DNP) using two electrons in a double quantum dot in presence of external magnetic field and spin-orbit interaction, in various schemes of periodically repeated sweeps through the S-T+ avoided crossing. By treating the problem semi-classically, we find that generally the DNP have two distinct contributions - a geometrical polarization and a dynamic polarization, which have different dependence on the control parameters such as the sweep rates and waiting times in each period. Both terms show non-trivial dependence on those control parameter. We find that even for small spin-orbit term, the dynamical polarization dominates the DNP in presence of a long waiting period near the S-T+ avoided crossing, of the order of the nuclear Larmor precession periods. A detailed numerical analysis of a specific control regime can explain the oscillations observed by Foletti et.~al.~in arXiv:0801.3613.Comment: 22 pages, 6 figure

Driven nonlinear dynamics of two coupled exchange-only qubits

Inspired by creation of a fast exchange-only qubit (Medford et al., Phys. Rev. Lett., 111, 050501 (2013)), we develop a theory describing the nonlinear dynamics of two such qubits that are capacitively coupled, when one of them is driven resonantly at a frequency equal to its level splitting. We include conditions of strong driving, where the Rabi frequency is a significant fraction of the level splitting, and we consider situations where the splitting for the second qubit may be the same or different than the first. We demonstrate that coupling between qubits can be detected by reading the response of the second qubit, even when the coupling between them is only of about $1\%$ of their level splittings, and calculate entanglement between qubits. Patterns of nonlinear dynamics of coupled qubits and their entanglement are strongly dependent on the geometry of the system, and the specific mechanism of inter-qubit coupling deeply influences dynamics of both qubits. In particular, we describe the development of irregular dynamics in a two-qubit system, explore approaches for inhibiting it, and demonstrate existence of an optimal range of coupling strength maintaining stability during the operational time.Comment: 11 pages, 6 figures; One additional figure with changes to the text about the results. Additional references include