From Notch signaling to fine-grained patterning: Modeling meets experiments.

Notch signaling is the canonical signaling pathway between neighboring cells. It plays an important role in fine-grained patterning processes such as the formation of checkerboard-like differentiation patterns and sharp boundaries between developing tissues. While detailed information about many of the genes and proteins involved have been identified, we still lack a quantitative mechanistic understanding of these processes. Here we discuss several recent studies that provide novel insights into Notch-dependent patterning by combining mathematical models with quantitative experimental results. Such approaches allow identification of mechanisms and design principles controlling how patterns are generated in a reproducible and robust manner.

An electronic Mach-Zehnder interferometer.

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.

Charge distribution in a Kondo-correlated quantum dot.

We report on direct measurement of charge and its distribution in a Kondo correlated quantum dot (QD). A noninvasive potential-sensitive detector, in proximity with a QD, reveals that, although the conductance of the QD is significantly enhanced as it enters the Kondo regime, the average charge remains unaffected. This demonstrates the separation between spin and charge degrees of freedom. We find, however, under certain conditions, an abrupt redistribution of charge in the QD, taking place with an onset of Kondo correlation. This suggests a correlation between the spin and charge degrees of freedom.

Phase evolution in a Kondo-correlated system.

We measured the phase evolution of electrons as they traverse a quantum dot (QD) formed in a two-dimensional electron gas that serves as a localized spin. The traversal phase, determined by embedding the QD in a double path electron interferometer and measuring the quantum interference of the electron wave functions manifested by conductance oscillation as a function of a weak magnetic field, evolved by pi radians, a range twice as large as theoretically predicted. As the correlation weakened, a gradual transition to the familiar phase evolution of a QD was observed. The specific phase evolution observed is highly sensitive to the onset of Kondo correlation, possibly serving as an alternative fingerprint of the Kondo effect.

Controlled dephasing of electrons via a phase sensitive detector.

We demonstrate a controlled dephasing experiment via exploiting a unique entangled interferometer-detector system, realized in an electronic mesoscopic structure. We study the dephasing process both from the which path information available in the detector and, alternatively, from the direct effect of the detector on the interferometer. Detection is possible only due to an induced phase change in the detector. Even though this phase change cannot actually be measured, strong dephasing of the interferometer took place. The intricate role of detector's noise and coherency are investigated.

Correlations between ground and excited state spectra of a quantum Dot

The ground and excited state spectra of a semiconductor quantum dot with successive electron occupancy were studied with linear and nonlinear magnetoconductance measurements. A direct correlation was observed between the mth excited state of the N-electron system and the ground state of the (N + m)-electron system for m up to 4. The results are consistent with a single-particle picture in which a fixed spectrum of energy levels is successively filled, except for a notable absence of spin degeneracy. Further departures from the single-particle picture due to electron-electron interaction were also observed. Magnetoconductance fluctuations of ground states show anticrossings where wave function characteristics are exchanged between adjacent levels.