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All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics
Published on: January 19, 2018
Wave tunneling and hysteresis in nonlinear junctions
Wenjie Wan1, Stefan Muenzel, Jason W Fleischer
1Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA.
Physical Review Letters
|April 7, 2010
Summary
Nonlinear tunneling through a barrier potential can be suppressed or enhanced by self-defocusing interactions, depending on initial kinetic energy. This leads to distinct hysteresis loops and the formation of dispersive shock waves.
Area of Science:
- Nonlinear optics
- Quantum mechanics
- Wave physics
Background:
- Nonlinear tunneling is crucial for understanding wave propagation in various physical systems.
- Self-defocusing media introduce complex behaviors in wave interactions.
- Barrier potentials create unique scenarios for wave transmission and reflection.
Purpose of the Study:
- To investigate the impact of nonlinearity on wave transmission through a barrier potential.
- To analyze the role of self-defocusing interactions in controlling transmission rates.
- To explore the formation of nonlinear phenomena like hysteresis and shock waves.
Main Methods:
- Theoretical analysis of a plane wave interacting with a barrier in a self-defocusing medium.
- Numerical simulations to observe spatial dynamics and transmission characteristics.
- Experimental validation using optical wave tunneling through a refractive index defect.
Main Results:
- Nonlinearity can either suppress or enhance wave transmission, contingent on initial kinetic energy relative to barrier height.
- Two distinct hysteresis loops (clockwise and counterclockwise) emerge at a specific energy threshold.
- Spatial dynamics reveal the formation of dispersive shock waves (dark soliton trains) and wave steepening.
Conclusions:
- The interplay between nonlinearity and barrier potential offers tunable control over wave transmission.
- Hysteresis phenomena and dispersive shock wave formation are key signatures of nonlinear tunneling.
- The findings are broadly applicable to any Schrödinger system with a nonlinear junction, including optical and quantum systems.
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