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.

The Notch-Delta signaling pathway enables communication between neighboring cells during development1. It plays a critical role in the formation of ‘fine-grained’ patterns, generating distinct cell fates among groups of initially equivalent neighboring cells, and in sharply delineating neighboring regions in developing tissues 2,3,4,5. The Delta ligand has been shown to have two activities: it trans-activates Notch in neighboring cells, and cis-inhibits Notch in its own cell. However, it remains unclear how Notch integrates these two activities and how the resulting system facilitates pattern formation. To address these questions, we developed a quantitative time-lapse microscopy platform for analyzing Notch-Delta signaling dynamics in individual mammalian cells. By controlling both cis- and trans-Delta levels, and monitoring the dynamics of a Notch reporter, we measured the combined cis-trans input-output relationship for the Notch-Delta system. The data revealed a striking difference between the response of Notch to trans- and cis-Delta: While the response to trans-Delta is graded, the response to cis-Delta exhibits a sharp, switch-like response at a fixed threshold, independent of trans-Delta. We developed a simple mathematical model that shows how these behaviors emerge from the mutual inactivation of Notch and Delta proteins. This interaction generates an ultrasensitive switch between mutually exclusive sending (high Delta / low Notch) and receiving (high Notch / low Delta) signaling states. At the multicellular level, this switch can amplify small differences between neighboring cells even without transcription-mediated feedback. This Notch-Delta signaling switch facilitates the formation of sharp boundaries and lateral inhibition patterns in models of development, and provides insight into previously unexplained mutant behaviors.

The Notch signaling pathway relies on a proteolytic cascade to release its transcriptionally active intracellular domain, on force to unfold a protective domain and permit proteolysis, on extracellular domain glycosylation to tune the forces exerted by endocytosed ligands, and on a motley crew of nuclear proteins, chromatin modifiers, ubiquitin ligases, and a few kinases to regulate activity and half-life. Herein we provide a review of recent molecular insights into how Notch signals are triggered and how cell shape affects these events, and use the new insights to illuminate a few perplexing observations.

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.