Single Strontium Rydberg Ion Confined in a Paul Trap

Trapped Rydberg ions are a promising new system for quantum information processing. They have the potential to join the precise quantum operations of trapped ions and the strong, long-range interactions between Rydberg atoms. Combining the two systems is not at all straightforward. Rydberg atoms are severely affected by electric fields which may cause Stark shifts and field ionization, while electric fields are used to trap ions. Thus, a thorough understanding of the physical properties of Rydberg ions due to the trapping electric fields is essential for future applications. Here, we report the observation of two fundamental trap effects. First, we investigate the interaction of the Rydberg electron with the trapping electric quadrupole fields which leads to Floquet sidebands in the excitation spectra. Second, we report on the modified trapping potential in the Rydberg state compared to the ground state that results from the strong polarizability of the Rydberg ion. By controlling both effects we observe resonance lines close to their natural linewidth demonstrating an unprecedented level of control of this novel quantum platform.

Popular Summary

There are many ways to store and manipulate information in a quantum computer. One leading approach uses ions trapped in an electromagnetic field; another relies on Rydberg atoms, which are atoms with one or more electrons that are highly energized. Both methods have their advantages. The quantum states of trapped ions can be precisely controlled, whereas Rydberg atoms offer tunable long-range interactions for processing quantum logic gates. Trapped Rydberg ions are a new contender. The method combines the advantages of both systems to offer a viable route toward creating a scalable quantum computer. But combining these systems is not easy. Rydberg atoms are highly sensitive to the strong electric fields used to trap ions; thus, it seems far-fetched to excite a trapped ion to a Rydberg state. We show that Rydberg ions can be well controlled in an ion trap.

We confined a single strontium ion in a type of electromagnetic “cage” known as a Paul trap and excited the ion to a Rydberg state with a laser. This allowed us to study how the ion interacts with the trap and how the potential of the trap itself is modified by the Rydberg state. Both effects suggest techniques that could be used for implementing quantum operations and logic gates. Ions in Rydberg $S$ states, for example, are unaffected by the trap, while $D$ states display a significant coupling between electronic and vibrational states.

This experiment demonstrates an unparalleled level of control over trapped Rydberg ions and reveals fundamental physical properties of this novel quantum platform. In particular, it shows that the system can, in principle, be controlled to the precision required for future applications.

Figure 1

Experimental setup. (a) An ion is trapped in a linear Paul trap and manipulated by laser beams for Doppler cooling and fluorescence detection (422 nm), repumping (1092 and 1033 nm), electron shelving (674 nm), and Rydberg excitation (243 and 309 nm). A magnetic field with $B=(0.3564\pm 0.0008)\mathrm{mT}$ defines the quantization axis and is oriented parallel to the trap axis and the Rydberg-excitation lasers. (b) Energy level scheme of ${{}^{88}\mathrm{Sr}}^{+}$ and detection sequence of successful Rydberg excitation. Before Rydberg excitation the Doppler-cooled ion is initialized in the metastable $4D_{3/2}$ state via optical pumping. (i) The Rydberg-excitation lasers couple the initial $4D_{3/2}$ state to a Rydberg $S_{1/2}$ or $D_{3/2}$ state, which then quickly decays in multiple steps to the $5S_{1/2}$ ground state with 95% probability in $<\sim 20\mu \mathrm{s}$. (ii) Rydberg-excited population which subsequently decayed to the ground state is transferred to the metastable $4D_{5/2}$ state, allowing fluorescence detection to distinguish between successful Rydberg excitations (population in $4D_{5/2}\to \text{no fluorescence}$) and cases with no Rydberg excitations (population in $4D_{3/2}\to \text{fluorescence}$) in the final step (iii). This sequence is typically repeated 100 times for each data point.

Figure 2

Rydberg electron-quadrupole field interaction. Quadrupolar energy shifts and rf coupling due to the Rydberg electron-quadrupole field interaction $H_{eQ}$ for a Rydberg $D_{3/2}$ state.

Figure 3

Zeeman splitting in Rydberg $S_{1/2}$ states. (a) Two-photon excitation spectra to state $25S_{1/2}$. The frequency of the second Rydberg excitation laser at 309 nm is scanned while the frequency of the first Rydberg excitation laser at 243 nm is kept $2\pi \times 160\mathrm{MHz}$ blue detuned from the intermediate state resonance. The two-photon detuning is defined as the sum of the two UV-photon frequencies minus the frequency difference of the $25S_{1/2}$ and $4D_{3/2}$ states in the absence of a magnetic field ${\omega }_{243}+{\omega }_{309}-(1/\hslash )(E_{25S_{1/2}}-E_{4D_{3/2}})$. Successful Rydberg excitation is signaled by a high probability for shelving the ion to state $4D_{5/2}$. The excitation spectrum shows four resonance peaks for both lasers in an equal superposition of ${\sigma }^{+}$ and ${\sigma }^{-}$ polarization [denoted as $(\pm /\pm )$], two peaks when the second step 309-nm laser is changed to ${\sigma }^{-}$ $(\pm /-)$, and a single peak when both lasers are ${\sigma }^{+}$ $(+/+)$. Black dots are the measured data points with error bars due to quantum projection noise, blue lines are the simulated Rydberg-excitation spectra (Rabi frequencies ${\mathrm{\Omega }}_{243}=2\pi \times 0.47\mathrm{MHz}$, ${\mathrm{\Omega }}_{309}=2\pi \times 49\mathrm{MHz}$, dephasing of the Rydberg state $\delta {\omega }_{25S}=2\pi \times 2.2\mathrm{MHz}$). Off-resonant scattering from the intermediate state and spontaneous decay from the initial $4D_{3/2}$ state each contribute to the background signal. (b) Allowed transitions for Rydberg excitation to $25S_{1/2}$. The Rydberg-excitation beams are aligned with the direction of the applied magnetic field at the position of the ion; thus, electric dipole transitions which preserve the magnetic quantum number ($\pi$ transitions) are not excited. With this constraint, only four nondegenerate transitions between the $4D_{3/2}$ and $25S_{1/2}$ Zeeman sublevels remain. As the frequency of the 309-nm laser is scanned, each of the four transitions comes into resonance at a different frequency.

Figure 4

Rydberg electron-quadrupole field interaction for Rydberg $D_{3/2}$ states. (a) Excitation spectra and simulation results for $24D_{3/2}$. The frequency of the second Rydberg excitation laser at 309 nm is scanned while the frequency of the first Rydberg excitation laser at 243 nm is kept $2\pi \times 160\mathrm{MHz}$ blue detuned from the intermediate state resonance. The two-photon detuning is defined as the sum of the two UV-photon frequencies minus the frequency difference of the $24D_{3/2}$ and $4D_{3/2}$ states in the absence of a magnetic field, trap effects, and ac-Stark effects ${\omega }_{243}+{\omega }_{309}-(1/\hslash )(E_{25S_{1/2}}-E_{4D_{3/2}})$. The trapping parameters are $\{{\omega }_{\text{axial}},{\omega }_{\mathrm{radial}1},{\omega }_{\mathrm{radial}2}\}=2\pi \{(254\pm 3),(600\pm 10),(760\pm 10)\}\mathrm{kHz}$, radio frequency drive $\mathrm{\Omega }=2\pi \times 18.153\mathrm{MHz}$. The experimental data (error bars due to quantum projection noise) largely match the simulation results (dark blue line) when the Rydberg electron-quadrupole field interaction is taken into account (simulation parameters: Rabi frequencies ${\mathrm{\Omega }}_{243}=2\pi \times 0.09\mathrm{MHz}$, ${\mathrm{\Omega }}_{309}=2\pi \times 135\mathrm{MHz}$, dephasing of the Rydberg state $\delta {\omega }_{24D}=2\pi \times 4.1\mathrm{MHz}$). (b) Energy level scheme explaining the rf sidebands in the excitation spectra. Sidebands appear at $\pm$ the rf trapping frequency $\mathrm{\Omega }$ with respect to a neighboring Zeeman state $\mathrm{\Delta }{m}_J=\pm 2$. The resonances are additionally shifted due to the ac-Stark effect by the Rydberg excitation laser at 309 nm.

Figure 5

Modified Rydberg trapping potential. (a) Observation of a single Rydberg resonance starting from the state $4D_{5/2}{m}_J=-\frac{5}{2}$ to the Rydberg state $42S_{1/2}{m}_J=-\frac{1}{2}$. The frequency of the second Rydberg excitation laser at 307 nm is scanned while the frequency of the first Rydberg excitation laser at 243 nm is kept $2\pi \times 20\mathrm{MHz}$ red detuned from the intermediate state resonance. The two-photon detuning is defined as the sum of the two UV-photon frequencies minus the frequency difference of the $42S_{1/2}{m}_J=-\frac{1}{2}$ and $4D_{5/2}{m}_J=-\frac{5}{2}$ states, ${\omega }_{243}+{\omega }_{307}-\frac{1}{\hslash }[E(42S_{1/2}{m}_J=-\frac{1}{2})-E(4D_{5/2}{m}_J=-\frac{5}{2})]$. With sideband cooling, we observe a single resonance with linewidth $2\pi (300\pm 50)\mathrm{kHz}$, mainly limited by the laser linewidths. With only Doppler cooling, the resonance is shifted lower in energy and has smaller amplitude and asymmetric shape with $\approx 2\pi (1.4\pm 0.1)\mathrm{MHz}$ linewidth. The model curves represent a single resonance with $2\pi (300\pm 50)\mathrm{kHz}$ linewidth for the sideband-cooled case, and a thermally broadened line with $\mathrm{\Delta }\omega =-2\pi \times 20\mathrm{kHz}$ (red) [$\mathrm{\Delta }\omega =-2\pi \times 42\mathrm{kHz}$ (blue)] for the Doppler-cooled case. No fit parameters are used in the model curve of the Doppler-cooled ion resonance. The trapping parameters are $\{{\omega }_{\text{axial}},{\omega }_{\mathrm{radial}1},{\omega }_{\mathrm{radial}2}\}=2\pi \{(872\pm 5),(1660\pm 30),(1720\pm 30)\}\mathrm{kHz}$, radio frequency drive $\mathrm{\Omega }=2\pi \times 18.153\mathrm{MHz}$. (b) Energy scheme of the motional state during Rydberg excitation. Because of the different trapping potential in the Rydberg state compared to the ground state, the laser excitation is shifted out of resonance for higher motional quantum numbers.