We show that it is possible to get gain without inversion at high frequency in a three-level ladder type scheme driven by a single driving laser. The transition from the ground state to first excited state is driven by a low-frequency resonant laser field. The next excited state lies far above the first one; therefore its resonant frequency can be much higher than that of the lower transition, and hence one should go beyond the most commonly used rotating wave approximation consisting of retaining only resonant terms (slowly oscillating) in the Hamiltonian. We solve the master equation, both analytically (under proper approximations) and numerically, with the full Hamiltonian keeping counter-rotating highly non-resonant terms. We show a dressed state picture explaining spectral features of gain-absorption profiles. Also we present a kind of phase diagram in the plane γ –Λ, where γ and Λ are spontaneous emission rate and incoherent pumping rate, respectively. The who...

中文翻译：

---

梯形方案中的非共振激光，无反转增益

我们表明，在由单个驱动激光器驱动的三电平梯型方案中，可以在高频下获得增益而无需反相。从基态到第一激发态的转变是由低频共振激光场驱动的。下一个激发态远高于第一个。因此，它的共振频率可能比较低跃迁的共振频率高得多，因此，它应该超越最常用的旋转波近似，即仅在哈密顿量中保留共振项（缓慢振荡）。我们用解析的（在适当的近似值下）和数值上的主方程式求解，同时完整的哈密顿量保持反向旋转的高度非谐振项。我们展示了一张修饰好的状态图，解释了增益吸收曲线的频谱特征。同样，我们在γ–Λ平面上给出了一种相图，其中γ和Λ分别是自发发射率和非相干抽运率。WHO...