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Register a new userHall of Mirrors Scattering from an Impurity in a Quantum Wire
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This paper develops a scattering theory to examine how point impurities affect transport through quantum wires. While some of our new results apply specifically to hard-walled wires, others--for example, an effective optical theorem for two-dimensional waveguides--are more general. We apply the method of images to the hard-walled guide, explicitly showing how scattering from an impurity affects the wires conductance. We express the effective cross section of a confined scatterer entirely in terms of the empty waveguides Greens function, suggesting a way in which to use semiclassical methods to understand transport properties of smooth wires. In addition to predicting some new phenomena, our approach provides a simple physical picture for previously observed effects such as conductance dips and confinement-induced resonances.
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Topological quantum phases underpin many concepts of modern physics. While the existence of disorder-immune topological edge states of electrons usually requires magnetic fields, direct effects of magnetic field on light are very weak. As a result, demonstrations of topological states of photons employ synthetic fields engineered in special complex structures or external time-dependent modulations. Here, we reveal that the quantum Hall phase with topological edge states, spectral Landau levels and Hofstadter butterfly can emerge in a simple quantum system, where topological order arises solely from interactions without any fine-tuning. Such systems, arrays of two-level atoms (qubits) coupled to light being described by the classical Dicke model, have recently been realized in experiments with cold atoms and superconducting qubits. We believe that our finding will open new horizons in several disciplines including quantum physics, many-body physics, and nonlinear topological photonics, and it will set an important reference point for experiments on qubit arrays and quantum simulators.
We propose and investigate a simple one-dimensional model for a single-channel quantum wire hosting electrons that interact repulsively and are subject to a significant spin-orbit interaction. We show that an external Zeeman magnetic field, applied at the right angle to the Rashba spin-orbit axis, drives the wire into a correlated spin-density wave state with gapped spin and gapless charge excitations. By computing the ground-state degeneracies of the model with either (anti-)periodic or open boundary conditions, we conclude that the correlated spin-density state realizes a gapless symmetry-protected topological phase, as the ground state is unique in the ring geometry while it is two-fold degenerate in the wire with open boundaries. Microscopically the two-fold degeneracy is found to be protected by the conservation of the magnetization parity. Open boundaries induce localized zero-energy (midgap) states which are described, at the special Luther-Emery point of the model, by Majorana fermions. We find that spin densities at the open ends of the wire exhibit unusual long-ranged correlations despite the fact that all correlations in the bulk of the wire decay in a power-law or exponential fashion. Our study exposes the crucial importance of the long-ranged string operator needed to implement the correct commutation relations between spin densities at different points in the wire. Along the way we rederive the low-energy theory of Galilean-invariant electron systems in terms of current operators.
We study the renormalization of a non-magnetic impuritys scattering potential due to the presence of a massless collective spin mode at a ferromagnetic quantum critical point. To this end, we compute the lowest order vertex corrections in two- and three-dimensional systems, for arbitrary scattering angle and frequency of the scattered fermions, as well as band curvature. We show that only for backward scattering in D=2 does the lowest order vertex correction diverge logarithmically in the zero frequency limit. In all other cases, the vertex corrections approach a finite (albeit possibly large) value in the zero frequency limit. We demonstrate that vertex corrections are strongly suppressed with increasing curvature of the fermionic bands. Moreover, we show how the frequency dependence of vertex corrections varies with the scattering angle. We also discuss the form of higher order ladder vertex corrections and show that they can be classified according to the zero-frequency limit of the lowest order vertex correction. We show that even in those cases where the latter is finite, summing up an infinite series of ladder vertex diagrams can lead to a strong enhancement (or divergence) of the impuritys scattering potential. Finally, we suggest that the combined frequency and angular dependence of vertex corrections might be experimentally observable via a combination of frequency dependent and local measurements, such as scanning tunneling spectroscopy on ordered impurity structures, or measurements of the frequency dependent optical conductivity.
The two-dimensional electron system in an InAs quantum well has emerged as a prime candidate for hosting exotic quasi-particles with non-Abelian statistics such as Majorana fermions and parafermions. To attain its full promise, however, the electron system has to be clean enough to exhibit electron-electron interaction phenomena. Here we report the observation of fractional quantum Hall effect in a very low disorder InAs quantum well with a well-width of 24 nm, containing a two-dimensional electron system with a density $n=7.8 times 10^{11}$ cm$^{-2}$ and low-temperature mobility $1.8 times 10^6$ cm$^2$/Vs. At a temperature of $simeq35$ mK and $Bsimeq24$ T, we observe a deep minimum in the longitudinal resistance, accompanied by a nearly quantized Hall plateau at Landau level filling factor $ u=4/3$.
The desire to produce high-quality single photons for applications in quantum information science has lead to renewed interest in exploring solid-state emitters in the weak excitation regime. Under these conditions it is expected that photons are coherently scattered, and so benefit from a substantial suppression of detrimental interactions between the source and its surrounding environment. Nevertheless, we demonstrate here that this reasoning is incomplete, as phonon interactions continue to play a crucial role in determining solid-state emission characteristics even for very weak excitation. We find that the sideband resulting from non-Markovian relaxation of the phonon environment is excitation strength independent. It thus leads to an intrinsic limit to the fraction of coherently scattered light and to the visibility of two-photon coalescence at weak driving, both of which are absent for atomic systems or within simpler Markovian treatments.
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