Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics

Three-level quantum systems, which possess some unique characteristics beyond two-level ones, such as electromagnetically induced transparency, coherent trapping, and Raman scatting, play important roles in solid-state quantum information processing. Here, we introduce an approach to implement the physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics (MSDs). It can be used to control accurately population transfer and entanglement generation for three-level quantum systems in a nonadiabatic way. Moreover, we propose an experimentally realizable hybrid architecture, based on two nitrogen-vacancy-center ensembles coupled to a transmission line resonator, to realize our transitionless scheme which requires fewer physical resources and simple procedures, and it is more robust against environmental noises and control parameter variations than conventional adiabatic passage techniques. All these features inspire the further application of MSDs on robust quantum information processing in experiment.

Figure 1

Comparisons of robustness of the population transfer based on the STIRAP and MSDs. (a) The time-dependent effective coupling strengths ${\eta }_1$ and ${\eta }_2$ are in the Gaussian shapes as ${\eta }_j={\eta }_0{e}^{-{[(t-t_j)/T]}^2}$ ($j=1,2$) with ${\eta }_0/2\pi =1.6\mathrm{MHz}, t_1=0.75\mu \mathrm{s}, t_2=0.25\mu \mathrm{s}$, and $T=0.408\mu \mathrm{s}$. Time evolution of the population $P_k\left(t\right)$ during the population transfer from $|{\varphi }_2\rangle$ to $|{\varphi }_1\rangle$ based on (b) STIRAP and (c) MSDs, respectively. When the time delay of ${\eta }_1$ is changed to be $t_1=0.9\mu \mathrm{s}$ and other parameters remain invariant, time evolution of the effective coupling strengths and the populations based on STIRAP and MSDs are shown in (d), (e), and (f), respectively.

Figure 2

Time evolutions of the populations in the superposition state generation scheme for $|{\varphi }_1\rangle , |{\varphi }_2\rangle$, and $|{\varphi }_3\rangle$ based on (a) the STIRAP and (b) MSDs, respectively, with ${\eta }_0/2\pi =1.6\mathrm{MHz}, t_3=1.15\mu \mathrm{s}, t_4=0.25\mu \mathrm{s}$, and $T=0.408\mu \mathrm{s}$.

Figure 3

(a) Schematic diagram of the hybrid quantum system, which consists of two NVEs coupled to a high-Q TLR. (b) The $V$-type energy-level configuration for the ground state of NVE driven by the resonator and appropriate external magnetic fields.

Figure 4

(a) Fidelity of the population transfer scheme with MSDs from $|{\varphi }_2\rangle =|0eg\rangle$ to $|{\varphi }_1\rangle =|0ge\rangle$ under the influence of dissipations. In the simulation, ${\kappa }^{-1}=50\mu \mathrm{s}$ [32], ${\gamma }^{-1}=6\mathrm{ms}, {\gamma }_{\phi }^{-1}=600\mu \mathrm{s}$ [33], and other parameters are the same as those for Fig. 1. (b) Fidelity of the population transfer scheme with MSDs for different cavity decay rates ${\kappa }^{\prime }$ (in units of $\kappa$).