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.

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.

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We report the unexpected bunching of Laughlin's quasiparticles, induced by an extremely weak backscattering potential at exceptionally low electron temperatures (T<10 mK), deduced from shot noise measurements. Backscattered charges q=nue, specifically, q=e/3, q=2e/5, and q<3e/7, in the respective filling factors, were measured. For the same settings but at a slightly higher electron temperature, the measured backscattered charges were q=e/3, q=e/5, and q=e/7, as expected. Moreover, the backscattered current exhibited distinct temperature dependence that was correlated to the backscattered charge and the filling factor. This observation suggests the existence of "low" and "high" temperature backscattering states, each with its characteristic charge and energy.

ABSRACTCharged excitations in the fractional quantum Hall effect are known to carry fractional charges, as theoretically predicted and experimentally verified. Here we report on the dependence of the tunneling quasiparticle charge, as determined via highly sensitive shot noise measurements, on the measurement conditions, in the odd denominators states ν=1/3 and ν=7/3 and in the even denominator state ν=5/2. In particular, for very weak backscattering probability and sufficiently small excitation energies (temperature and applied voltage), tunneling charges across a constriction were found to be significantly higher than the theoretically predicted fundamental quasiparticle charges. 2Odd denominator fractional quantum Hall effect (FQHE) states [1,2], whose quasiparticles are expected to possess fractional statistics, have been already the focus of extensive studies [3].However, more recently, particular attention was devoted to the even denominator fractional state ν=5/2 [4], which is conjectured to be described by a Pfaffian wavefunction [5][6][7], mainly due to the expectation that its quasiparticles carry a charge e/4 and obey non-abelian statistics [5,[8][9][10]. As such, these quasiparticles may be useful for topological quantum computation [11][12][13].An important step in the experimental study of the FQHE states is the determination of the quasiparticle charge. While the fundamental quasiparticle charge in the bulk for a fractional state is expected to be unique, the charge that tunnels between two counter propagating edgeschannels might depend on the measurement conditions. Here we study the uniqueness of the tunneling charge, and search for conditions under which it is equal to the expected fundamental quasiparticle charge.Most charge measurements detect charges that tunnel either across a narrow constriction, via shot noise measurements [14][15][16][17][18], conductance measurements [19] and interference [20,21], or charges that tunnel into localized states in the bulk [22], which, in all cases, are not guaranteed to be equal to the fundamental quasiparticle charge in the bulk. Moreover, the excitation energy (applied voltage and temperature) is also expected to affect the tunneling charge. However, since charges that tunnel between edges can only be integer multiples of the fundamental charge, the smallest measured charge sets an upper bound for the fundamental charge. For example, a measurement in the ν=5/2 state of a charge e/4 rules out e/2 fundamental charges in this state.We present here measurement results of low frequency shot noise generated by partitioning. This work was motivated by our attempt to improve the accuracy of our previous measurements 3 and tighten the data points with more sensitive measurements, thus allowing us to determine the charge in a previously inaccessible low energy and very weak backscattering regimes -where shot noise is excessively small. Our new measurements revealed an interesting dependence of the conductance and the tunneling charge on the energy and the transmi...