Quasi-particles are elementary excitations of condensed matter quantum phases. Demonstrating that they keep quantum coherence while propagating is a fundamental issue for their manipulation for quantum information tasks. Here, we consider anyons, the fractionally charged quasi-particles 20 of the Fractional Quantum Hall Effect occurring in two-dimensional electronic conductors in high magnetic fields. They obey anyonic statistics, intermediate between fermionic and bosonic. Surprisingly, anyons show large quantum coherence when transmitted through the localized states of electronic Fabry-Pérot interferometers, but almost no quantum interference when transmitted via the propagating states of Mach-Zehnder interferometers. Here, using a novel interferometric 25 approach, we demonstrate that anyons do keep quantum coherence while propagating. Performing two-particle time-domain interference measurements sensitive to the two-particle Hanbury Brown Twiss phase, we find 53% and 60% visibilities for anyons with charges e/5 and e/3. Our results give a positive message for the challenge of performing controlled quantum coherent braiding of anyons.
We discuss the implementation of a beam splitter for electron waves in a quantum Hall bilayer. Our architecture exploits inter-layer tunneling to mix edge states belonging to different layers. We discuss the basic working principle of the proposed coherent edge mixer, possible interferometric implementations based on existing semiconductor-heterojunction technologies, and advantages with respect to canonical quantum Hall interferometers based on quantum point contacts.
We present an interferometric scheme producing orbital entanglement in a quantum Hall system upon electron-hole pair emission via tunneling. The proposed setup is an electronic version of the optical interferometer proposed by Cabello et al. [Phys. Rev. Lett. 102, 040401 (2009)], and is feasible with present technology. It requires single-channel propagation and a single primary source. We discuss the creation of entanglement and its detection by the violation of a Bell inequality.
We study the time-dependent dynamical phase of fractional quasiparticles in quantum Hall states using Ramsey interferometry. A Ramsey two-pulse voltage modulation generates an interference term in the current noise of a quantum point contact oscillating with the dynamical phase. We show that the interference pattern probes the Green's function of the fractional quasi-particles in the time domain and reveals the fractional charge. We address both the case of a point-like tunnel junction and the case of momentum-resolved tunneling which also provides information on the speed of those quasipartic…
We combine the ideas of intensity interferometry, polarization optics and Bell's measurement into an experimental proposal which is hosted in a $ν\,$=$\,2$ quantum Hall (QH) edge state. Our interferometer comprises of a single gate, that separates the spin resolved edge states of $ν$\,=\,$2$ state. An analog of waveplate (from polarization optics) is realized by exposing the individual edges to nano-magnets over a finite length which facilitates coherent manipulation of the electron spin on the edge. We show that the in-plane rotation of magnetization direction of the nano-magnets results in o…
Electron interferometry with quantum Hall edge channels holds promise for probing and harnessing exotic exchange statistics of non-Abelian anyons. In semiconductor heterostructures, however, quantum Hall interferometry has proven challenging and often obscured by charging effects. Here we show that high-mobility monolayer graphene equipped with a series of gate-tunable quantum point contacts that act as electron beam-splitters provides a model system to perform Fabry-Pérot quantum Hall interferometry. We observe high-visibility Aharonov-Bohm interference free of charging effects and widely tun…
Since pioneering works of Hanbury-Brown and Twiss, intensity-intensity correlations have been widely used in astronomical systems, for example to detect binary stars. They reveal statistics effects and two-particle interference, and offer a decoherence-free probe of the coherence properties of light sources. In the quantum Hall edge channels, the concept of quantum optics can transposed to electrons, and an analogous two-particle interferometry can be developed, in order to characterize single-electron states. We review in this article the recent experimental and theoretical progress on this t…
We discuss devices for detection of the topological insulator phase based on the two-path electron interference. For that purpose we consider buckled silicene for which a local energy gap can be opened by vertical electric field to close one of the paths and for which the quantum spin Hall insulator conditions are controlled by the Fermi energy. In quantum spin Hall phase the interference is absent due to the separation of the spin currents and the conductance of the devices include sharp features related to localized resonances. In the normal transport conditions the two-path interference pro…
Resistance oscillations in electronic Fabry-Perot interferometers near fractional quantum Hall (FQH) filling factors 1/3, 2/3, 4/3 and 5/3 in the constrictions are compared to corresponding oscillations near integer quantum Hall (IQH) filling factors in the constrictions, appearing in the same devices and at the same gate voltages. Two-dimensional plots of resistance versus gate voltage and magnetic field indicate that all oscillations are Coulomb dominated. Applying a Coulomb charging model yields an effective tunneling charge e* \approx e/3 for all FQH constrictions and e* \approx e for IQH …
Since the anyonic excitations in the Kitaev toric model are perfectly localized quasiparticles, it is possible to generate dynamically the ground state and the excitations of the model Hamiltonian to simulate the anyonic interferometry. We propose a scheme in circuit QED to simulate the interferometry. The qubit-cavity interaction can be engineered to realize effective state control as well as the controlled dynamics of qubits, which are sufficient to prepare the ground states, create and remove the anyonic excitation, and simulate the anyonic interferometry. The simplicity and high fidelity o…
Quantum Hall (QH) interferometry provides an archetypal platform for the experimental realization of braiding statistics of fractional QH states. However, the complexity of observing fractional statistics requires phase coherence over the length of the interferometer, as well as suppression of Coulomb charging energy. Here, we demonstrate a new type of QH interferometer based on marginally twisted bilayer graphene (mtBLG), with a twist angle $θ$ $\approx$ $0.16$ $^{\circ}$. With the device operating in the QH regime, we observe distinct signatures of electronic Fabry-Pérot (FP) and Aharonov-Bo…
It was recently pointed out that Halperin's 113 topological order explains the transport experiments in the quantum Hall liquid at filling factor $ν=5/2$. The 113 order, however, cannot be easily distinguished from other likely topological orders at $ν=5/2$ such as the non-Abelian Pfaffian and anti-Pfaffian states and the Abelian Halperin 331 state in Fabry-Perot interferometry. We show that an electronic Mach-Zehnder interferometer provides a clear identification of these candidate $ν=5/2$ states. Specifically, the $I$-$V$ curve for the tunneling current through the interferometer is more asy…
Hanbury Brown-Twiss interferometry at the $ν=2/5$ fractional quantum Hall edge
Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Aix Marseille Univ, Université de Toulon, CNRS, CPT（艾克斯-马赛大学、土伦大学、法国国家科学研究中心、CPT）
The quantum Hall (QH) effect represents a unique playground where quantum coherence of electrons can be exploited for various applications, from metrology to quantum computation. In the fractional regime it also hosts anyons, emergent quasiparticles that are neither bosons nor fermions and possess fractional statistics. Their detection and manipulation represent key milestones in view of topologically protected quantum computation schemes. Exploiting the high degree of phase coherence, edge states in the QH regime have been investigated by designing and constructing electronic interferometers,…
We consider a Hong-Ou-Mandel interferometer for Lorentzian voltage pulses applied to Quantum Hall edge channels at filling factor $ν=2$. Due to inter-edge interactions, the injected electronic wave-packets fractionalize before partitioning at a quantum point contact. Remarkably enough, differently from what theoretically predicted and experimentally observed by using other injection techniques, we demonstrate that, when the injection occurs through time-dependent voltage pulses (arbitrarily shaped), the Hong-Ou-Mandel noise signal always vanishes for a symmetric device, and that a mismatch in …
An apparent h/fe Aharonov-Bohm flux period, where f is an integer, has been reported in coherent quantum Hall devices. Such sub-period is not expected for non-interacting electrons and thus is thought to result from interelectron Coulomb interaction. Here we report experiments in a Fabry-Perot interferometer comprised of two wide constrictions enclosing an electron island. By carefully tuning the constriction front gates, we find a regime where interference oscillations with period h/2e persist throughout the transition between the integer quantum Hall plateaus 2 and 3, including half-filling.…
It is widely believed that integer quantum Hall systems do not have fractional excitations. Here we show the converse to be true for a class of systems where integer quantum Hall effect emerges spontaneously due to the interplay of itinerant electrons and noncoplanar magnetic ordering. We show that magnetic $Z_2$ vortices in such systems, whose topological stability is guaranteed by the structure of the order parameter, indeed carry fractional charge.
Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.
We consider the electronic analog of the Hong-Ou-Mandel interferometer from quantum optics. In this realistic condensed matter device, single electrons are injected and travel along opposite chiral edge states of the integer quantum Hall effect, colliding at a quantum point contact (QPC). We monitor the fate of the colliding excitations by calculating zero-frequency current correlations at the output of the QPC. In the simpler case of filling factor $ν=1$, we recover the standard result of a dip in the current noise as a function of the time delay between electron injections. For simultaneous …
We constructed a Hall resistance formula for the fractional quantum Hall effect by analyzing the experimental data reported in [J. P. Eisenstein and H. L. Stormer, {Science} {\bf 248}, 1510 (1990)]. The formula is given as a function of magnetic induction, chemical potential and temperature. The Hall resistance function contains a single-electron energy spectrum, which has phenomenological perturbation terms with three tunable parameters. The formula yields 12 plateaus that are consistent with the experiment. The perturbations can be interpreted as precession or nutation of a Landau orbital in…
The quantum magnetotransport properties of a monolayer of molybdenum disulfide are derived using linear response theory. Especially, the effect of topological terms on longitudinal and Hall conductivity is analyzed. The Hall conductivity exhibits fractional steps in the integer quantum Hall regime. Further complete spin and valley polarization of the longitudinal conductivity is seen in presence of these topological terms. Finally, the Shubnikov-de Hass oscillations are suppressed or enhanced contingent on the sign of these topological terms.
Confined to a two-dimensional plane, electrons in a strong magnetic field travel along the edge in one-dimensional quantum Hall channels that are protected against backscattering. These channels can be used as solid-state analogues of monochromatic beams of light, providing a unique platform for studying electron interference. Electron interferometry is regarded as one of the most promising routes for studying fractional and non-Abelian statistics and quantum entanglement via two-particle interference. However, creating an edge-channel interferometer in which electron-electron interactions pla…
We argue that dynamics of gapless Fractional Quantum Hall Edge states is essentially non-linear and that it features fractionally quantized solitons propagating along the edge. Observation of solitons would be a direct evidence of fractional charges. We show that the non-linear dynamics of the Laughlin's FQH state is governed by the quantum Benjamin-Ono equation. Non-linear dynamics of gapless edge states is determined by gapped modes in the bulk of FQH liquid. The dispersion of edge modes is traced to the double boundary layer of FQH states.
在分数量子霍尔效应下，我们测量了门控GaAs/Al $_{x}$ Ga $_{1-x}$ As异质结中二维电子系统（2DES）的对角（$ρ_{xx}$）和霍尔（$ρ_{xy}$）磁阻张量分量，以及2DES与门极之间的电容.我们在相当低的磁场下观察到了1/3和2/3分数量子霍尔效应，此时相应的量子态密度的分数极小值已经消失，表明准粒子能隙被完全抑制。
It has been shown recently that non-Abelian states and the spin-polarized and unpolarized versions of the Abelian 331 state may have identical signatures in Fabry-Pérot interferometry in the quantum Hall effect at filling factor 5/2. We calculate the Fano factor for the shot noise in a Mach-Zehnder interferometer in the 331 states and demonstrate that it differs from the Fano factor in the proposed non-Abelian states. The Fano factor depends periodically on the magnetic flux through the interferometer. Its maximal value is $2\times 1.4e$ for the 331 states with a symmetry between two flavors o…
With the recent observation of graphene-like Landau levels at the surface of topological insulators, the possibility of fractional quantum Hall effect, which is a fundamental signature of strong correlations, has become of interest. Some experiments have reported intra-Landau level structure that is suggestive of fractional quantum Hall effect. This paper discusses the feasibility of fractional quantum Hall effect from a theoretical perspective, and argues that while this effect should occur, ideally, in the $n=0$ and $|n|=1$ Landau levels, it is ruled out in higher $|n|$ Landau levels. Unlike…
We have experimentally identified fractional quasiparticle creation in a tunneling process through a local fractional quantum Hall (FQH) state. The local FQH state is prepared in a low-density region near a quantum point contact (QPC) in an integer quantum Hall (IQH) system. Shot-noise measurements reveal a clear transition from elementary-charge tunneling at low bias to fractional-charge tunneling at high bias. The fractional shot noise is proportional to T1(1 ? T1) over a wide range of T1, where T1 is the transmission probability of the IQH edge channel. This binomial distribution indicates …
We derive the effective field theory from the microscopic Hamiltonian of interacting two-dimensional (pseudo) Dirac electrons by performing a statistic gauge transformation. The quantized Hall conductance are expected to be $σ_{xy}=\frac{e^2}{h}(2k-1)$ with $k$ is arbitrary integer. There are also topological excitations which have fractional charge and obey fractional statistics.
We report a simple route to generate magnetotransport data that results in fractional quantum Hall plateaus in the conductance. Ingredients to the generating model are conducting tiles with integer quantum Hall effect and metallic linkers, further Kirchhoff rules. When connecting few identical tiles in a mosaic, fractional steps occur in the conductance values. Richer spectra representing several fractions occur when the tiles are parametrically varied. Parts of the simulation data are supported with purposefully designed graphene mosaics in high magnetic fields. The findings emphasize that th…
Intra-Landau level excitations in the fractional quantum Hall regime are not accessible via optical absorption measurements. We point out that optical probes are enabled by the periodic potentials produced by a moiré pattern. Our observation is motivated by the recent observations of fractional quantum Hall incompressible states in moiré-patterned graphene on a hexagonal boron nitride substrate, and is theoretically based on $f-$sum rule considerations supplemented by a perturbative analysis of the influence of the moiré potential on many-body states.
We report localization of fractional quantum Hall (QH) quasiparticles on graphene antidots. By studying coherent tunneling through the localized QH edge modes on the antidot, we measured the QH quasiparticle charges to be approximately $\pm e/3$ at fractional fillings of $ν= \pm 1/3$. The Dirac spectrum in graphene allows large energy scales and robust quasiparticle localization against thermal excitation. The capability of localizing fractional quasiparticles on QH antidots brings promising opportunities for realizing anyon braiding and novel quantum electronics.
The fractional quantum hall effect (FQHE) is a milestone of modern day physics, its disovery paved the way for the study of fractional charges which do not obey abelian physics. However, all FQHE require an external magnetic field in order for there to be fractionally charged electrons. This work shows a theoretical study of strongly interaction electrons in the Kagome lattice with magnetism. Under optimal conditions, a band gap opens on the surface of the material which hosts fractional Fermions. These fractional Fermions form composite quasi-electrons without the need for external magnetic f…
