Paul阱中共线两离子量子力学问题

Quantum mechanical problem for two ions in a Paul trap

运用熟知的级数截断方法,设计程序计算了线性Paul阱中两离子量子门系统Schrodinger方程的精确解,分析了质心波函数几个较低能级的态,并作出对应的几率分布图;计算相对距离的方均差△r2>h/2,相对运动的动量方均差△p2<h/2,并满足量子力学的Heiscnberg不确定度关系△r·△p>h/2,它满足压缩态的条件,即质心处于基态时,两离子相对位置的量子态是一个压缩态,并得到了两离子纠缠态的表达式。纠缠的存在对量子计算和量子信息有影响,量子测量的不确定度和纠缠是在实验中应加以考虑的问题。

By use of the well-known truncating series method, A program for calculating the Schroedinger exact solutions of quantum gate by two ions confined in a linear Paul trap is presented. The lower energy＇s state function for center of mass is analyzed. Probability distributing grawing is given. We calculate quantum state of variance in relatively position Ar^2 〉 h/2 and quantum state of variance in relatively momentum Ap^2 〈 h/2, the variance in position and momentum given by the Heisenberg uncertainty principle Ar·Ap 〉 h/2. It is a condition for squeezed states. We conclude that with center of mass in ground state, the quantum states of two ions in relatively position are squeezed states, and the quantum state of two ions is an entanglement state. Uncertainty of quantum measurement and entanglement must be consider in experiment.