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arXiv:1011.0273

Communicating with a wave packet using quantum superarrival

Dipankar Home, A. S. Majumdar, A. Matzkin

Published Nov 1, 2010• 0 citations
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Abstract

An analytical treatment of a propagating wave packet incident on a transient barrier reveals a counterintuitive quantum mechanical effect in which, for a particular time interval, the time-varying transmission probability {\it exceeds} (`superarrival') that for the free propagation of the wave packet. It is found that the speed with which the information about the barrier perturbation propagates across the wave packet can exceed the group velocity of the wave packet. An interesting implication of this effect regarding information transfer is analyzed by showing one-to-one correspondence between the strength of the barrier and the magnitude of `superarrival'.

DOI
10.48550/arxiv.1011.0273

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An analytical treatment of a propagating wave packet incident on a transient barrier reveals a counterintuitive quantum mechanical effect in which, for a particular time interval, the time-varying transmission probability {\it exceeds} (superarrival') that for the free propagation of the wave packet. It is found that the speed with which the information about the barrier perturbation propagates across the wave packet can exceed the group velocity of the wave packet. An interesting implication of this effect regarding information transfer is analyzed by showing one-to-one correspondence between the strength of the barrier and the magnitude of superarrival'.
An analytical treatment of a propagating wavepacket incident on a transient barrier reveals an effect in which, for a particular time interval, the time-varying transmission probability exceeds that for the free propagation of the wavepacket. We show that this effect can be interpreted semiclassically. This effect is quantified and it is shown that its magnitude is in one-to-one correspondence with the strength of the barrier, a feature that has the potential to be used in a scheme for key generation. It is found that the speed with which the information about the barrier perturbation propagates across the wavepacket can exceed the group velocity of the wavepacket. An application to the speed-up of entanglement generation is also considered.
A curious effect is uncovered by calculating the time evolving probability of reflection of a Gaussian wave packet from a rectangular potential barrier while it is perturbed by reducing its height. A time interval is found during which this probability of reflection is larger (superarrivals) than in the unperturbed case. This nonclassical effect can be explained by requiring a wave function to act as a ``field'' through which an action, induced by the perturbation of the boundary condition, propagates at a speed depending on the rate of reducing the barrier height.
Scattering of a Gaussian wavepacket from rectangular potential barriers with increasing widths or heights is studied numerically. It is seen that during a certain time interval the time-evolving transmission probability increases compared to the corresponding unperturbed cases. In the literature this effect is known as superarrival in transmission probability. We present a trajectory-based explanation for this effect by using the concept of quantum potential energy and computing a selection of Bohmian trajectories. Relevant parameters in superarrivals are determined for the case that the barrier width increases linearly during the dispersion of the wavepacket. Nonlinearity in time perturbation is also considered.
An interesting analytical expression is obtained for the coordinate probability distribution of a wave packet transmitted through a potential barrier. In the large-time asymptotics the distribution is given in terms of the transmission amplitude and the phase-space quasidistribution of the initial (not necessarily pure) state. The distortion of a (broad) wave packet due to the barrier penetration is determined by two timelike parameters, given by the energy derivative of the complex transmission amplitude. The resulting change of the packet shape reveals a dependence on the detector position and incorporates a possible speed-up effect and a negative dispersion.
Superarrival, a quantum effect where a wave packet arrives earlier than its free-space counterpart, is investigated in fractional nanostructured media. We model a Gaussian wave packet interacting with a uniformly decelerating potential barrier or well using the fractional Schrödinger equation and the Split-Step Finite Difference method. The impact of the Lévy stability index, wave packet width, and initial distance on superarrival is analyzed. Results show that fractional media strongly enhance superarrival, especially for wider, low-energy packets interacting with barriers. These findings underscore the role of nonlocality in quantum transport and suggest potential applications in nanoscale optoelectronic devices such as tunable delay lines, ultrafast modulators, and quantum information processors.