Study Of Coherent Manipulation Of Multiple Quantum Pathways In Photon-induced Transitions

Coherence is an important feature of quantum systems that can be utilized in quan-tum control.Quantum coherent control has been applied widely and achieved fruitful results in the quantum information,quantum computing,quantum chemistry,laser cool-ing and nanotechnology and other fields.Fine control of quantum systems is always an important goal of quantum control.Quantum pathways describe the intermediate pro-cess in the evolution of quantum systems,and it is important and meaningful in scientific and appliation aspects to steer the quantum dynamics towards a specified pathway.The main research contents are as follows:(1)The dynamics of two two-photon transition(TPT)pathways in a four-level quantum system driven by a laser pulse is investigated.A global optimal solution for pulse shaping is proposed by analytically maximizing the constructive interference be-tween the two pathways,and the accurate spectral boundaries for phase modulation are obtained.The TPT rate can be enhanced by a factor of 70 with the optimal pulse instead of the transform limited pulse.Simple control strategies modulating both amplitudes and phases are also designed to increase the TPT amplitude along one pathway while decreasing that along the other simultaneously.In all strategies,the TPT amplitudes of the desired and undesired pathways in the four strategies can differ by two orders of magnitude,which indicates that the pathway dynamics can be manipulated effectively.(2)We have successfully extended the pulse shaping strategy of maximizing the total TPT amplitude to the quantum system with multiple quantum pathways.We sys-tematically analyzed the mathematical idea of the block shaping strategy.Cases with infinitesimal and finite spectral resolution are both investigated.A special example with all first transition frequencies being larger than half of the TPT frequencies is em-ployed to demonstrate our scheme.The strategy is then applied to a system containing three two-photon transition pathways,and the numerical simulation results show that two-photon transition amplitude increase by nearly two orders of magnitude,compared with the transform limited pulse.(3)Based on the model with the counter-propagating ultrashort pulse pairs,we discuss the spatial coherent control of the TPT pathways.For the simple three-level quantum system,we propose a new square wave phase shaping scheme,in addition to the common V-shaped pulse shaping scheme.We discuss the modulation of the three key control parameters in detail.We find that a clearer spatial excitation pattern can be obtained by eliminating the high-frequency one-side signals with a low-pass filter.Based on this,we design three kinds of schemes to distinct the two pathways in a four-level quantum system,namely the square-wave phase-shaping scheme,linear phase-shaping scheme and hybridize phase-shaping distinction scheme.These schemes have been implemented in the experiment,and transition pathway resolving spectroscopy of atomic rubidium is obtained.