Dynamic Decoherence Control of a Solid-State Nuclear-Quadrupole Qubit

We report on the application of a dynamic decoherence control pulse sequence on a nuclear-quadrupole transition in ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$. Process tomography is used to analyze the effect of the pulse sequence. The pulse sequence was found to increase the decoherence time of the transition to over 30 seconds. Although the decoherence time was significantly increased, the population terms were found to rapidly decay on the application of the pulse sequence. The increase of this decay rate is attributed to inhomogeneity in the ensemble. Methods to circumvent this limit are discussed.

Figure 1

(a) Pulse sequences used in experiment: ${\mathrm{RF}}_1$: 2 pulse spin echo, ${\mathrm{RF}}_2$: Inversion Recovery ${\mathrm{RF}}_3$: Decoupling pulse sequence. The coherence generated by the initial pulse is rephased by a pair of $\pi$, $-\pi$ pulses separated by the cycling time ${\tau }_c$, iterated $N$ times. The laser is common to all pulse sequences. (b) All ground state hyperfine levels other than $m_I=-1/2$ interact via RF frequencies ${\omega }_1$, ${\omega }_2$, ${\omega }_3$ with laser radiation either at the read frequency ${\omega }_r$ or pump frequency ${\omega }_p$. Through spontaneous emission from the electronic excited state the group of ions interacting with both ${\omega }_r$ and ${\omega }_p$ via any common excited state will be optically pumped into the $m_I=-1/2$ state. Bold states are the critical point transition.

Figure 2

Spin echo decay at the critical point field (◇) and detuned from the critical point field by $\sim 2\mathrm{G}$ (·) and $\sim 5\mathrm{G}$ (○) in the $Z$ direction).

Figure 3

Decoupled echo decays with ${\tau }_c=7.5\mathrm{ms}$ (⋆), 10 ms (◇), 15 ms ($\nabla$), 20 ms (×) corresponding to $T_2=27.9$, 21.1, 15.2, 10.9 s. Inversion recovery measurements (○) yield $T_1=145\mathrm{s}$.

Figure 4

Dependence of decoherence time on the decoupling sequence cycling time ${\tau }_c$ both at the critical point (○) and with the magnetic field misaligned to give a coherence time of $T_2=100\mathrm{ms}$ (×). Lines do not represent a physical model.

Figure 5

Comparison of experimental to theoretical process tomography results for the decoupling pulse sequence with 1, 10, 100, and 1000 iterations. Imaginary components omitted for clarity. The states are labeled 1, 2, 3, 4 corresponding to $|0⟩⟨0|$, $|0⟩⟨1|$, $|1⟩⟨0|$, and $|1⟩⟨1|$.