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Coherent population transfer in quantum systems is of fundamental importance in many fields spanning atomic and molecular collision dynamics, information processing for qubit systems. Stimulated Raman nonadiabatic passage technique, when implemented in an externally driven three-level system, provides an efficient approach for realizing accelerated population transfer while maintaining robust quantum coherence, without the rotating wave approximation. However, previous protocols employ multiple pulses and imply that Rabi frequencies have a few oscillations during dynamical evolution. In this paper, under two-photon resonance, we utilize the gauge transformation method to inversely design a Λ-configuration three-level system that can be solved exactly. By invoking a $SU(3)$ transformation, we establish the connection between Schrödinger representation and gauge representation with which the effective Hamiltonian is an Abelian operator. Subsequently, we construct the desired Hamiltonian and further investigate its dynamic behavior. The result demonstrate that, by imposing appropriate boundary conditions on the control parameters, high-fidelity population transfer can be achieved in ideal evolution. In addition, for the practical case with pulse truncation and intermediate state decay, the fidelities of specific models can reach about $99.996\%$ and for $99.983\%$. Compared to other existing nonadiabatic quantum control schemes, we show that the present scheme has the distinctive advantages. Firstly, instead of introducing an additional microwave field, we achieve the desired quantum control by applying only a few sets of Stokes and pump pulses. Moreover this approach does not exhibit Rabi oscillations in the dynamic process, nor does it present singularities in the pulse itself.
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Keywords:
- three-level systems /
- SU(3) Lie algebra /
- without the rotating-wave approximation /
- nonadiabatic population transfer
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图 1 三能级系统中量子态$|1\rangle$(实蓝线)、$|2\rangle$(虚红线)和$|3\rangle$(虚绿线)的布居数随时间的演化. (a)和(b)分别对应于方程(26)和(28)描述的模型
Figure 1. Time evolution of populations for states $|1\rangle$ (solid blue), $|2\rangle$ (dashed red), and $|3\rangle$ (dashed green) in models (a) and (b), as described by equations (26) and (28).
图 2 在量子态$|2\rangle$衰变的情况下, 保真度F相对于无量纲量$\gamma t$的演化. 这里分别设置参数$\Gamma/\gamma=0.005$(实红线), $0.01$(虚蓝线)和$0.03$(虚绿线). (a) 由方程(26)描述的模型, 保真度最终可以分别达到$F(2\pi)=99.996\%$, $99.985\%$和$99.869\%$; (b) 由方程(28)描述的模型, 保真度最终可以分别达到$F(6\pi)=99.983\%$, $99.938\%$和$99.584\%$
Figure 2. The evolution of fidelity F as a function of the dimensionless quantity $\gamma t$, in the presence of decay. Here we have set $\Gamma/\gamma=0.005$(solid red), $0.01$(dashed blue), and $0.03$(dashed green). (a) For the model described by equation (26), the final fidelities can achieve as $F(2\pi)=99.996\%$, $99.985\%$, and $99.869\%$; (b) For the model described by equation (28), the final fidelities can achieve as $F(6\pi)=99.983\%$, $99.938\%$, and $99.584\%$.
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