Phase Coherent Control Of Atomic Tunneling

With the development of the science and technology, many research works have been deepen from macroscopic to microscopic levels,for example,using laser technology to cool and trap atom. With the development of the laser shaping technology, the narrowing of laser bandwidth, we can even use it to manipulate atoms.For the studies of cold atoms we mainly focused on the single or double drive double trap system, from which we obtain a lot of interesting physics experimental phenomena, such as tunneling coherent destruction, tunneling assisted by chaos,multiphoton resonance, etc. But the research about the double drive frequency is a multiple relationship between the phase when the coherence between them for particle tunneling e?ect in the double trap sound very little. So this paper focus on the study of the e?ect of relationship between the driven frequencies of double drive system on the particles’ tunneling in double trap. The content of this paper is divided into four chapters.In the ?rst chapter,we give a brief introduction of this paper,with emphasis on atoms’ cooling and trap, two-mode approximate of a period double drive system.Floquet theory and quntum Noon State.In the second chapter,we have considered a double well two particles system with coupling term and deviation term depended on time,and the frequency of coupling drive and the frequency of deviation is multiple relation and the phase in coherence between them, the interaction is weak. We have the Floquet state and quasi-energy spectrum whose population is unchanged by high frequency approximation. Analysis solution of non-Floquet state have be obtained by superposition of Floquet states. We have discussed the coupling frequency is o?set frequency of odd-even times, phase when the odd and even coherent aimed at the in?uence of the energy, when the phase relation is odd-times coherent, quasi-energy spectrum is a function of parameter of deviation driven and interaction strength, andthe collapse of zero order Bessel function happen; When is even coherent, energy spectrum of the intersection no longer occur in the Bessel function of zero, but is associated with bias coe?cient, we can adjust and bias of the two related coe?cient to adjust the size of the energy spectrum of the point of collapse. In non-Floquet state, we also discussed the coupling frequency is partial frequency of odd-even times, the phase between them when the odd and even coherent e?ects on quantum tunneling. When the frequency of the relationship between them is an odd number of times, the odd coherent phase arises, we can by adjusting the initial conditions for the preparation of di?erent single state, NOON state, at this time,the probability of particles in trap will not change over time, tunneling occurs;When the frequency of the relationship between them is even times, even coherent phase arises, in the double trap particles tunneling, the probability is a function of driving parameters and interaction intensity changes over time, these results we veri?ed from the numerical and they meet very well. According to coupling driving frequency is o?set odd-even times that of the driving frequency, the phase when the coherence between them, we design the particles to the tunneling and tunneling to di?erent NOON state of the switch, our research plan has brought quantum tunneling switch more convenient operation.In chapter three,we study a driven double-well system that the Hamitonian operator is expressed by angular momentum operator according to the relation between annihilation or creation operator and angular momentum and is divided into the perturbation and unperturbed. We got the unperturbed system Floquet energy and Floquet mode, and with Floquet mode based vector get the zero order solution in the form of superposition. For ?rst-order perturbation equation,we use the zero order solution obtained its exact solution, described by the zero order solution shows from any initial state of the transition to the described by the primary solution at the end of the two adjacent state transition probability. Here,di?erent state corresponding to di?erent particle distribution in the double trap,the transition between di?erent states is equivalent to di?erent forms of quantum tunneling.At the same time under the high frequency approximation obtained Floquet the?rst-order correction of energy, and get the Floquet spectrum diagram.In addi-tion, we discussed the coupling relationship between strength and competitive strength of the interaction and coupling drive frequency multiple relationship with frequency o?set on the impact of energy spectrum, reveals the coupling driving frequency and the phase o?set between the driven frequency, the even coherent tunneling from any initial state of the particles to two adjacent to the in?uence of the ?nal state. Found that when the ratio is even number, tunneling at a certain probability; And when the multiples for odd number, tunneling destroyed by coherent.The fourth chapter, for the work of this paper, this chapter makes a summary and conclusion, and for the development prospect of this research ?eld that is in the coherent control of quantum tunneling in laser ?eld manipulates a brief outlook.