Shortcut to adiabatic population transfer in quantum three-level systems: Effective two-level problems and feasible counterdiabatic driving

Shortcuts to adiabaticity in various quantum systems have attracted much attention with their wide applications in quantum information processing and quantum control. In this paper, we concentrate on a stimulated Raman shortcut-to-adiabatic passage in quantum three-level systems. To implement counterdiabatic driving but without additional coupling, we first reduce the quantum three-level systems to effective two-level problems at large intermediate-level detuning, or on resonance, apply counterdiabatic driving along with the unitary transformation and eventually modify the pump and Stokes pulses for achieving fast and high-fidelity population transfer. The required laser intensity and stability against parameter variation are further discussed, to demonstrate the advantage of shortcuts to adiabaticity.

Figure 1

$\mathrm{\Lambda }$-type three-level system for STIRAP, where the Rabi frequencies ${\mathrm{\Omega }}_{p,s}$ present the pump and Stokes pulses, $\mathrm{\Delta }$ and ${\mathrm{\Delta }}_s$ are the detunings.

Figure 2

Different Rabi frequencies for STIRAP (a) and STIRSAP (b), where Stokes (solid red) and pump (dashed blue) pulses are shown. The state evolutions of STIRAP (c) and STIRSAP (d) are also compared, where population of levels $|1\rangle$ (dashed blue), $|2\rangle$ (dotted black), and $|3\rangle$ (solid red) is presented. Parameters: ${\mathrm{\Omega }}_0=2\pi \times 5$ MHz, $\mathrm{\Delta }=2\pi \times 2.5$ GHz, $t_f=400\mu \mathrm{s}, \tau =t_f/10$, and $\sigma =t_f/6$.

Figure 3

Operation time $t_f$ versus the peak value of Rabi frequency ${\mathrm{\Omega }}_{\max }$ for STIRSAP (solid red) and STIRAP (dashed blue) when the fidelity is above $99\%$. Parameters are the same as those in Fig. 2.

Figure 4

Different Rabi frequencies for STIRAP (a) and STIRSAP (b), where Stokes (solid red) and pump (dashed blue) pulses are shown. The state evolutions of STIRAP (c) and STIRSAP (d) are also compared, where population of levels $|1\rangle$ (dashed blue), $|2\rangle$ (dotted black), and $|3\rangle$ (solid red) is presented. Parameters: ${\mathrm{\Omega }}_0=2\pi \times 5$ MHz, $t_f=1\mu \mathrm{s}, \tau =t_f/8$, and $\sigma =t_f/6$.

Figure 5

Fidelity (solid blue) versus the variation of separation time $(1+\delta )\tau$. Inset: Dependence of phase $\varphi$ (solid red) versus $\delta$ for further explanation. Parameters are the same of those in Fig. 4.

Figure 6

(a) Population of level $|3\rangle$ at final time, $P_3\left(t_f\right)$, versus the variation of laser intensity, where STIRSAP at large detuning: $t_f=1000\mu \mathrm{s}$ (solid purple) and $t_f=400\mu \mathrm{s}$ (dot-dashed blue); STIRSAP on one-photon resonance: $t_f=1\mu \mathrm{s}$ (dashed red); resonant $\pi$ pulse: $t_f=1\mu \mathrm{s}$ (dotted black). (b) $P_3\left(t_f\right)$ versus the variation of detuning, where STIRSAP at large detuning: $t_f=400\mu \mathrm{s}$ (solid blue); STIRSAP on one-photon resonance: $t_f=1\mu \mathrm{s}$ (dashed red); resonant $\pi$ pulse: $t_f=1\mu \mathrm{s}$ (dotted black). Other parameters are the same as those in Figs. 2 and 4.