两能级系统中高保真度布居数反转

High-fidelity population inversion of two-level system

两能级量子系统中布居数反转的研究是量子调控中的前沿课题之一,在原子、分子物理以及量子信息等领域有着至关重要的意义.本文运用复合绝热通道技术,研究了正余弦函数形式外场驱动的两能级量子系统在有限时间内的跃迁问题,实现了有限时间内该系统的高保真度布居数反转.讨论了外场耦合强度、失谐强度等参数对跃迁概率的影响,发现只要选择合适的控制相位,在很大的参数范围内能够抑制跃迁概率的振荡,保真度能达到1,系统误差小于10?4,从而实现高效、快速、稳定,具有很好的参数鲁棒性的布居数完全反转.接着运用经典哈密顿量分析和验证了该方法的有效性和可行性.该技术适用于任何两能级系统,也能推广到多能级系统中,在量子信息、量子光学以及冷原子系统等领域有着广泛的应用.

Population inversion from an initial quantum state to a desired quantum state represents an exciting new frontier for quantum manipulation; that frontier is endowed with a strong interdisciplinary character and connections to other scientific fields, including atomic, molecular, and optical physics, as well as in solid-state devices, for fundamental studies, nuclear magnetic resonance and other spectroscopic techniques, metrology, interferometry, optical control of chemical reactions or quantum-information applications. Two-level systems are ubiquitous in these areas, and the driving of a population inversion is an important operation. So far various schemes for population transfer to a target state from an initial state have been proposed in theory and implemented in experiment. To be useful, such methods must, of course, be reliable, fast, and robust. Most literatures on two-level models investigated population inversion, which could be modelled by infinite-time processes. In this paper, by using a composite adiabatic passage（CAP） technique—in which the single pulse driving the quantum transition is replaced by a sequence of pulses with well-defined control phases, we investigate the population inversion problem of two-level quantum system with a finite duration. We take a sinusoidally varying pulse model that continuously vanishes at the beginning and the end of the finite duration as an example. The high-fidelity population inversion of the two-level system with finite duration is achieved. We discuss the effects of both coupling strength and detuning strength on the transition probability. It is found that this protocol could suppress the oscillations in the transition probability and reduce the admissible error bellow the 410？quantum computation benchmark. The fidelity can arrive at 1, even with simple three- and five-composite pulse sequences. The protocol combines the advantages of adiabatic passage and composite pulses techniques. By choosing the composite phases appropriately, a high-fidelity, fast, stable and extremely robust complete population inversion is achieved for the finite-time two-level model. The values of the composite phases are universal for they do not depend on the pulse shapes and the chirp as long as the latter satisfy the symmetry property. Furthermore, the classical Hamiltonian is applied to describe the dynamic properties of the quantum system and further verify the effectiveness and feasibility of the proposed CAP technique. The results we present here are general and in principle apply to any two- and multi-level quantum systems. The accuracy of the CAP technique and its robustness against parameter variations make the protocol suitable for ultrahigh-fidelity quantum manipulation. We believe that the protocol can be widely used in many different areas of science, ranging from the quantum information, the quantum chemical, and the quantum optics to the ultracold atomic and molecular physics.