Quantum Tunneling In Atom Optics

Particles own the nature of wave in quantum mechanics.Consequently,they could transmit through a potential barrier when their kinetic energy is smaller than the barrier height.This phenomenon is called quantum tunnel effect because it is forbidden in classic mechanics and is a direct manifestation of quantum mechanics.The quantum tunnel effect is relevant to the understanding of many microscopic phenomena,such asαdecay,and now lies at the heart of designing many high precision instruments such as scanning tunneling microscopes. Though there are such successes,there are still unresolved fundamental problems in quantum tunneling research.The question formulated as "How much time does tunneling take?" was come up with shortly after the advent of the Schrhdinger equation.Hartman analyzed in1961 quantum tunneling time and predicted that the tunneling time will approach to a constant value when the thickness of the potential barrier increases.That is so-called Hartman effect.Hartman's study raises the problem whether quantum tunneling velocity is larger than the light speed and is under heavy debate.The research on quantum tunneling time is not only important,for understanding the nature of quantum mechanics,but also important for designing quantum instrumentsIn this dissertation,we investigate the running dynamics of atomic matter waves through a laser slab in details.The interaction relies on the internal energy levels of atom.Thus the tunnel of atomic wave is essentially different from conventional quantum effects in many aspects.Our main results are as follows:1.Study the dynamics of ultracold atomic matter wave of two levels transmits laser slab.A vector Schr(?)dinger equation with two components is applied to study the atom dynamics in the laser field.After diagnolizing the potential in the region of laser field,there are equivalent potential barrier and well.In contrast,in conventional work,the excited state of atom can be adiabatically eliminated when the detuning is larger than Rabi frequency,such that the vector Schr(?)dinger equation can be reduced to a scalar Schr(?)dinger equation for ground state atoms within a single optical potential barrier(blue detuning)or well(red detuning).Our work shows that adiabatically elimination can not be performed in a widely region of detuning.2.Study the phase time for atoms through a laser beam We find that the the transmission could be zero at some certain detuning,Rabi frequency and the width of laser slab.In this situation,the phase time is quite different from that predicted by the Hartman theory,and especially the phase time could be negative. This is due to the interference of both the ground state and the excited state in the tunneling processing.The same thing happens to reflection.Negative or positive peaks of phase time occurs when the reflected or transmitted coefficients tend to 0,accompanied with the jump of their phase.3.Study the ground state Goos-H(?)nchen shift of atomic matter wave.The atomic matter wave will undergo Goos-H(?)nchen shift when it obliquely impinges on a laser slab.The giant negative or positive shift are obtained because of the giant negative or positive phase time of ground stats.In addition,the incident angle or transverse momentum of atom decides the effective detuning,and finally decides the equivalent potential and well.Surely,the total Goos-H(?)nchen shift includes the affection.Even if the incident wave perpendicularly impinge the laser slab,reflected and transmitted wave have Goos-H(?)nchen shift.4.Study the tunneling of matter wave ofλtype atom.To suppress the effect of spontaneous emission rate,an atom with split magnetic multilevels is chosen to transmit through two vis-a-vis laser beams.In this Raman tunneling process,the vector Schr(?)dinger equation can be simplified to decoupled Schr(?)dinger equations in wholly space.One of the transformed component freely moves all the time. the other feels a single potential(blue detuning)or a well(red detuning),just like a particle tunneling potential in quantum mechanics.Behind the laser slab. the tunneling time can be measured via the measurement of spacial distribution of ground state.