The Application Of Wave Function Monte Carlo Method In Open Quantum System

Open quantum system is usually not in a pure state, whose state cannot be describedby a general sense of wave function, but a reduced density operator summing oraveraging over all the degrees of reservoir. And the evolution of a reduced densityoperator is determined by master equation. Wave Function Monte Carlo method(WFMC) is an approximate approach aimed at improving the efficiency of solving anopen quantum system problem numerally. The reduced density operator is yieldedfrom a “pure state” in WFMC, the effect of reservoir makes the effective Hamiltoniannon-Hermition. The Schr dinger equation withthis non-Hermition Hamiltoniandominates the evolution of system wave function. Thus, the square modulus of thewave function is not maintained, on which the probability of quantum jump isdepended. The validity of this WFMC treatment is that the WFMC evolves the openquantum system equivalently with the Lindlad master equation. In an N-dimensionalsystem, the number of variables decreases from N2that in master equation to N,which is more proper to large system and is already widely applied in investigation ofopen quantum system.Because of the blockade effect caused by the dipole-dipole interaction betweenRydberg atoms, atoms a Rydberg system can entangle each other, which becomes anideal object for investigation of open quantum system. In this paper, the collectivequantum jump of Rydberg system was studied by using the WFMC method. Firstly,we implemented the WFMC algorithm in C++. A delay function treatment is used inour implementation, which decreased the times of calling random generator much less.And then used it to investigate a1D Rydberg chain, considering the dipole-dipoleinteraction between atoms as a constant. We got a same outcome with other relatedstudy. Secondly, we considered the situation that the dipole-dipole interaction varieswith the angle between the dipole moment of two Rydberg atoms, because the angledistribution is affected by quantum jump and in return, have effect on the quantumjump of system. We considered the evolving procedure of a Rydberg system, in which each atom is initially in ground state and driven by a laser, and while there is aquantum jump, the dipole-dipole interaction would be redistributed randomly. Thereare two situation been studied: firstly, the magnitude of dipole-dipole interaction is aconstant, while the sign varies randomly with quantum jump, it means the extremesituation where the dipole moments of two atoms are parallel orantiparallel. And wefound that if the system was stimulated resonantly, there is a significant enhancementof the collective quantum, because the resonant condition is always maintained.Secondly, the magnitude of dipole-dipole interaction varies closely around an averagevalue, simulating the situation where angle between two dipole moments distributedin some range. We found that if the initial resonance is not hold, the probability ofsimulating atoms to Rydberg states would increase.