Theoretical Treatments of Wavepackets

Mordechai Bixon

Hanyu Xue, Ziqian Tang, Chen Yang +3 more

Aziz and Howl argued that a classical gravitational field can generate quantum entanglement through a quantum-field-theoretic channel mediated by virtual matter propagation. However, their claimed channel is more naturally and accurately understood as semiclassical wavepacket motion in an external gravitational field, rather than as a distinctively quantum-field-theoretic entangling effect. Moreover, the result of their perturbative computation is incorrectly magnified: they selected a discontinuous wavefunction with infinite kinetic energy as the initial state and simultaneously treated it as stationary. Once a correct treatment using Gaussian wavepacket is adapted, the resulting effect will be negligibly small.

J S M Neto, Luís A. Cabral, I. G. da Paz

We present a treatment of the double-slit interference of matter-waves represented by Gaussian wavepackets. The interference pattern is modelled with Green's function propagator which emphasizes the coordinate correlations and phases. We explore the connection between phases and position–momentum correlations in the intensity, visibility and predictability of the wavepacket interference. This formulation will indicate some aspects that can be useful for theoretical and experimental treatment of particle, atom or molecule interferometry and can be discussed in introductory quantum mechanics courses.

Huyen Nguyen, John Lekner

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

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.

Yoshimasa Murayama, Mikio Namiki