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Double-slit electron interferometers fabricated in high mobility two-dimensional electron gases are powerful tools for studying coherent wave-like phenomena in mesoscopic systems. However, they suffer from low visibility of the interference patterns due to the many channels present in each slit, and from poor sensitivity to small currents due to their open geometry. Moreover, these interferometers do not function in high magnetic fields--such as those required to enter the quantum Hall effect regime--as the field destroys the symmetry between left and right slits. Here we report the fabrication and operation of a single-channel, two-path electron interferometer that functions in a high magnetic field. This device is the first electronic analogue of the optical Mach-Zehnder interferometer, and opens the way to measuring interference of quasiparticles with fractional charges. On the basis of measurements of single edge state and closed geometry transport in the quantum Hall effect regime, we find that the interferometer is highly sensitive and exhibits very high visibility (62%). However, the interference pattern decays precipitously with increasing electron temperature or energy. Although the origin of this dephasing is unclear, we show, via shot-noise measurements, that it is not a decoherence process that results from inelastic scattering events.

Ever since Milliken's 1 famous experiment it is well known that the electrical charge is quantized in units of the electronic chargee. For that reason, Laughlin's 2 theoretical prediction of the existence of fractionally charged quasi particles, put forward in order to explain the Fractional Quantum Hall (FQH) effect, is very counter intuitive. The FQH effect is a phenomenon that occurs in a Two Dimensional Electron Gas (2DEG) subjected to a strong perpendicular magnetic field. This effect results from the strong interaction among the electrons and consequently current is carried by the above mentioned quasi particles. We directly observed this elusive fractional charge by utilizing a measurement of quantum shot noise. Quantum shot noise results from the discreteness of the current carrying charges and thus is proportional to their charge, Q, and to the average current I, namely, S i =2QI . Our quantum shot noise measurements unambiguously show that current in a 2DEG in the FQH regime, at a fractional filling factor ν ν=1/3, is carried by fractional charge portions e/3; in agreement with Laughlin's prediction.The energy spectrum of a Two Dimensional Electron Gas (2DEG) subjected to a strong perpendicular magnetic field, B, consists of highly degenerate Landau levels with a degeneracy per unit area p=B/φ 0 , with φ 0 =h/e the flux quantum (h being Plank's constant). Whenever the magnetic field is such that an integer number ν (the filling factor) of Landau levels are occupied, that is ν=n s /p equals an integer (n s being the 2DEG areal density), the longitudinal conductivity of the 2DEG vanishes while the Hall conductivity equals νe 2 /h with very high accuracy. This phenomenon is known as the Integer Quantum Hall (IQH) effect 3 . A similar phenomenon occurs at fractional filling factors, namely, when the filling factor equals a rational fraction with an odd denominator q and is known as the Fractional Quantum Hall effect 4 . In contrast to the IQH effect, which is well understood in terms of non interacting electrons, the FQH effect can not be explained in such terms and is believed to result from interactions among the electrons, brought about by the strong magnetic field.Laughlin 2 had argued that the FQH effect could be explained in terms quasi particles of a fractional charge -Q=e/q. Although his theory is consistent with a considerable amount of the experimental data, no experiment directly showing the existence of the fractional charge exists. The early Aharonov-Bohm measurements 5 were proved to be in principle inadequate to reveal the fractional charge 6 . A more recent experiment based on resonant tunneling by Goldman and Su 7 was reproduced and interpreted differently by Franklin et al 8 . The difficulty in such experiments is that the results provide only the average charge per state and not the charge of individual particles. Quantum shot noise, on the other hand, probes the temporal behavior of the current and thus offers a direct way to measure the charge. Indeed, as early as in 1987, Tsui 9 sugges...

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We report the observation of an unpredictable behavior of a simple, two-path, electron interferometer. Utilizing an electronic analog of the well-known optical Mach-Zehnder interferometer, with current carrying edge channels in the quantum Hall effect regime, we measured high contrast Aharonov-Bohm (AB) oscillations. Surprisingly, the amplitude of the oscillations varied with energy in a lobe fashion, namely, with distinct maxima and zeros (namely, no AB oscillations) in between. Moreover, the phase of the AB oscillations was constant throughout each lobe period but slipped abruptly by pi at each zero. The periodicity of the lobes defines a new energy scale, which may be a general characteristic of quantum coherence of interfering electrons.

Very much like the ubiquitous quantum interference of a single particle with itself, quantum interference of two independent, but indistinguishable, particles is also possible. For a single particle, the interference is between the amplitudes of the particle's wavefunctions, whereas the interference between two particles is a direct result of quantum exchange statistics. Such interference is observed only in the joint probability of finding the particles in two separated detectors, after they were injected from two spatially separated and independent sources. Experimental realizations of two-particle interferometers have been proposed; in these proposals it was shown that such correlations are a direct signature of quantum entanglement between the spatial degrees of freedom of the two particles ('orbital entanglement'), even though they do not interact with each other. In optics, experiments using indistinguishable pairs of photons encountered difficulties in generating pairs of independent photons and synchronizing their arrival times; thus they have concentrated on detecting bunching of photons (bosons) by coincidence measurements. Similar experiments with electrons are rather scarce. Cross-correlation measurements between partitioned currents, emanating from one source, yielded similar information to that obtained from auto-correlation (shot noise) measurements. The proposal of ref. 3 is an electronic analogue to the historical Hanbury Brown and Twiss experiment with classical light. It is based on the electronic Mach-Zehnder interferometer that uses edge channels in the quantum Hall effect regime. Here we implement such an interferometer. We partitioned two independent and mutually incoherent electron beams into two trajectories, so that the combined four trajectories enclosed an Aharonov-Bohm flux. Although individual currents and their fluctuations (shot noise measured by auto-correlation) were found to be independent of the Aharonov-Bohm flux, the cross-correlation between current fluctuations at two opposite points across the device exhibited strong Aharonov-Bohm oscillations, suggesting orbital entanglement between the two electron beams.