Izhar Neder

Interference between two indistinguishable electrons from independent sources

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.

Controlled dephasing of electrons by non-gaussian shot noise

In a ‘controlled dephasing’ experiment1,2,3, an interferometer loses its coherence owing to entanglement of the interfering electron with a controlled quantum system, which effectively is equivalent to path detection. In previous experiments, only partial dephasing was achieved owing to weak interactions between many detector electrons and the interfering electron, leading to a gaussian-phase randomizing process4,5,6,7,8,9,10,11. Here, we report the opposite extreme, where interference is completely destroyed by a few (that is, one to three) detector electrons, each of which has a strong randomizing effect on the phase. We observe quenching of the interference pattern in a periodic, lobe-type fashion as the detector current is varied, and with a peculiar V-shaped dependence on the detector’s partitioning. We ascribe these features to the non-gaussian nature of the noise, which is also important for qubit decoherence12. In other words, the interference seems to be highly sensitive to the full counting statistics of the detector’s shot noise13,14,15,16.

Coherence oscillations in dephasing by non-Gaussian shot noise

A non-perturbative treatment is developed for the dephasing produced by the shot noise of a one-dimensional electron channel. It is applied to two systems: a charge qubit and the electronic Mach–Zehnder interferometer (MZI), both of them interacting with an adjacent partitioned electronic channel acting as a detector. We find that the visibility (interference contrast) can display oscillations as a function of detector voltage and interaction time. This is a unique consequence of the non-Gaussian properties of the shot noise, and only occurs in the strong coupling regime, when the phase contributed by a single electron exceeds π. The resulting formula reproduces the recent surprising experimental observations reported in (I Neder et al 2006 Preprint cond-mat/0610634), and indicates a general explanation for similar visibility oscillations observed earlier in the MZI at large bias voltage. We explore in detail the full pattern of oscillations as a function of coupling strength, voltage and time, which might be observable in future experiments.

Behavior of electronic interferometers in the nonlinear regime.

We investigate theoretically the behavior of the current oscillations in an electronic Mach-Zehnder interferometer (MZI) as a function of its source bias. Recently, the MZI visibility data showed an unexplained lobe pattern with a peculiar phase rigidity. Moreover, the effect did not depend on the MZI path length difference. We argue that these effects may be a new many-body manifestation of particle-wave duality in quantum mechanics. When biasing the interferometer sources so much that multiple electrons are on each arm at any instant in time, quantum shot noise (a particle phenomena) must affect the interference pattern of the electrons that create it. A solution to the interaction Hamiltonian presented here shows that the interference visibility has a lobe pattern with applied bias that has a period proportional to the average path length and independent of the path length difference, together with a phase rigidity.

Anomalous response to gate voltage application in mesoscopic LaAlO3/SrTiO3devices

We report on resistivity and Hall measurements performed on a series of narrow mesa devices fabricated from LaAlO_3/SrTiO_3 single interface heterostructure with a bridge width range of 1.5-10 microns. Upon applying back-gate voltage of the order of a few Volts, a strong increase in the sample resistance (up to factor of 35) is observed, suggesting a relatively large capacitance between the Hall-bar and the gate. The high value of this capacitance is due to the device geometry, and can be explained within an electrostatic model using the Thomas Fermi approximation. The Hall coefficient is sometimes a non-monotonic function of the gate voltage. This behavior is inconsistent with a single conduction band model. We show that a theoretical two-band model is consistent with this transport behavior, and indicates a metal to insulator transition in at least one of these bands.