Fast quantum state engineering via universal SU(2) transformation

We introduce a simple yet versatile protocol to inverse engineer the time-dependent Hamiltonian in two- and three-level systems. In the protocol, by utilizing a universal SU(2) transformation, a given speedup goal can be obtained with large freedom to select the control parameters. As an illustration example, the protocol is applied to perform population transfer between nitrogen-vacancy (NV) centers in diamond. Numerical simulation shows that the speed of the present protocol is fast compared with that of the adiabatic process. Moreover, the protocol is also tolerant to decoherence and experimental parameter fluctuations. Therefore, the protocol may be useful for designing an experimental feasible Hamiltonian to engineer a quantum system.

Figure 1

(a) Dependence on $t/T$ of the pulses $g_x,g_z$ for case I. (b) Time evolution for states $|1\rangle$ $\left(P_1\right)$ and $|2\rangle$ $\left(P_2\right)$.

Figure 2

(a) Dependence on $t/T$ of the pulses $g_x,g_z$ for case II with $A_1=8\pi$. (b) Time evolution for states $|1\rangle$ $\left(P_1\right)$ and $|2\rangle$ $\left(P_2\right)$.

Figure 3

(a) Schematic setup of the fused-silica microsphere cavity, where two identical NV centers in diamond are attached around the equator of the cavity. (b) Level diagram for an NV center, with $\lambda$ $\left(\mathrm{\Omega }\right)$ the coupling strength between the NV center and the WGM (laser pulse). Quantum information is encoded in the spin states $m_s=0$ and $m_s=-1$.

Figure 4

(a) ${\tilde{\mathrm{\Omega }}}_1\left(t\right)$ and ${\overline{\mathrm{\Omega }}}_1\left(t\right)$ versus $t/T$. (b) ${\tilde{\mathrm{\Omega }}}_2\left(t\right)$ and ${\overline{\mathrm{\Omega }}}_2\left(t\right)$ versus $t/T$.

Figure 5

(a) The final fidelity $F\left(T\right)$ of state $|{\psi }_5\rangle$ versus $\lambda T$. (b) Populations of $|{\psi }_1\rangle$ $(P_1$, the solid blue line), $|{\psi }_2\rangle$ $(P_2$, the dashed-dotted yellow line), $|{\psi }_3\rangle$ $(P_3$, the solid purple line), $|{\psi }_4\rangle$ $(P_4$, the dotted green line), $|{\psi }_5\rangle$ $(P_5$, the dashed red line) versus $t/T$.

Figure 6

The fidelities of the target state $|{\psi }_5\rangle$ versus $t/T$ with different methods: solid green line, using the present method with $\lambda =30/T$; dashed-dotted red line, STIRAP with $\lambda =30/T$ and ${\mathrm{\Omega }}_0^{\prime }=12/T$; dashed blue line, STIRAP with $\lambda =60/T$ and ${\mathrm{\Omega }}_0^{\prime }=24/T$; and dotted purple line, STIRAP with $\lambda =80/T$ and ${\mathrm{\Omega }}_0^{\prime }=32/T$.

Figure 7

The final fidelity $F\left(T\right)$ versus $\kappa /\lambda$ and $\gamma /\lambda$.

Figure 8

(a) The final fidelity $F\left(T\right)$ versus $\delta T/T$ and $\delta \lambda /\lambda$. (b) The final fidelity $F\left(T\right)$ versus $\delta {\overline{\mathrm{\Omega }}}_0/{\overline{\mathrm{\Omega }}}_0$ and $\delta \lambda /\lambda$. (c) The final fidelity $F(T)$ versus $\delta T/T$ and $\delta {\overline{\mathrm{\Omega }}}_0/{\overline{\mathrm{\Omega }}}_0$.