Hartman effect from layered PT-symmetric system

Abstract

The time taken by a wave packet to cross through a finite-layered PT-symmetric system is calculated by stationary phase method. We consider the PT-symmetric system of fix spatial length L consisting of N units of the potential system ‘$${+}\,iV$$’ and ‘$${-}\,iV$$’ of equal width ‘b’ such that $$L=2Nb$$. In the limit of large ‘b’, the tunneling time is found to be independent of L and therefore, the layered PT-symmetric system displays the Hartman effect. The interesting limit of $$N \rightarrow \infty $$ such that L remains finite is investigated analytically. In this limit, the tunneling time matches with the time taken to cross an empty space of length L. The result of this limiting case $$N \rightarrow \infty $$ also shows the consistency of phase space method of calculating the tunneling time, despite the existence of controversial Hartman effect. The reason of Hartman effect is unknown to present day; however, the other definitions of tunneling time that indicate a delay which depends upon the length of traversing region have been effectively ruled out by recent attosecond measurements.