An Unusual Effect Of Schodinger Wave Packet With Orbital Angular Momentum Moving In Gravity

A system with angular momentum has novel phenomena,such as the polarizationdependent transverse shift of a polarized light beam's intensity center when observed from a reference frame tilted with respect to the direction of propagation.This phenomenon is named the Geometric Spin Hall Effect of Light(GSHE).The similar phenomenon for spin-polarized electrons is also reported.In this paper,we go a step further to study the novel effect of angular momentum on a quantum wave packet from two perspective.Firstly,the non-zero momentum of the wave packet is given as a result of its dynamical evolution in gravity,not as an initial condition in the normal GSHE.Secondly,we consider the orbital angular momentum of a wave packet with richer structure.Strictly speaking,we should solve the Dirac equation in a gravitational field to answer the question.But it is too difficult to calculate the wave packet with an orbital angular momentum.So as a first attempt,we find a wave packet with the transverse orbital angular momentum,then write a program to simulate its evolution in the gravity.By calculating the centers of the momentum density and energy flux,we find a similar phenomenon: the centers of its momentum density and energy flux also have a transverse shift which depends on the angular momentum.We call this phenomenon the gravity-induced Geometric Spin Hall Effect.We also find that the transverse shift of the center of the energy flux is about twice as that of the momentum density.The transverse shift of the wave packet depends on the angular momentum,so it means a violation of the universality of free fall.We can test the equivalence principle more precisely with the quantum system such as a wave packet.