Quantum adiabatic theorem is one of the most important conclusions in quantum mechanics, and is widely used in quantum theory and quantum information technology. However, since quantum adiabatic process is a very slow process, factors such as quantum environmental noise or decoherence will affect the results of quantum adiabatic calculation. Therefore, the shortcut to adiabaticity (STA) theory came into being. In this paper, we study the population inversion in a two-level quantum system within a given time, we propose a Lewis-Riesenfeld invariants technique to realize population transfer for the system without the rotating-wave approximation (RWA). According to the invariant condition, the system time-dependent invariant expression is obtained. The amplitudes of Rabi frequency and detuning in the system could be easily controlled by adjusting control parameters. For population inversion, we can get Rabi frequency and detuning by determining the parameters in the invariant. We analyze the dynamics of the system through invariant operators, therefore, no additional coupling is required. Thereby the high-fidelity population transfer can be implemented in two-level quantum system by our method, and it works even without RWA.

中文翻译：

---

没有旋转波近似的两能级量子系统中的 Lewis-Riesenfeld 不变量

量子绝热定理是量子力学中最重要的结论之一，广泛应用于量子理论和量子信息技术。但是，由于量子绝热过程是一个非常缓慢的过程，量子环境噪声或退相干等因素都会影响量子绝热计算的结果。因此，绝热（STA）理论的捷径应运而生。在本文中，我们研究了给定时间内两能级量子系统中的粒子数反转，我们提出了一种Lewis-Riesenfeld不变量技术来实现没有旋转波近似（RWA）系统的粒子数转移。根据不变条件，得到系统时间相关的不变表达式。通过调整控制参数，可以很容易地控制系统中拉比频率和失谐的幅度。对于种群反演，我们可以通过确定不变量中的参数来获得 Rabi 频率和失谐。我们通过不变算子分析系统的动力学，因此不需要额外的耦合。因此，我们的方法可以在两级量子系统中实现高保真人口转移，并且即使没有 RWA 也可以工作。