Coherent Control of the Fine-Structure Qubit in a Single Alkaline-Earth Atom

We report on the first realization of a novel neutral atom qubit encoded in the spin-orbit coupled metastable states ${}^3{P}_0$ and ${}^3{P}_2$ of a single ${}^{88}\mathrm{Sr}$ atom trapped in an optical tweezer. Raman coupling of the qubit states promises rapid single-qubit rotations on par with the fast Rydberg-mediated two-body gates. We demonstrate preparation, readout, and coherent control of the qubit. In addition to driving Rabi oscillations bridging an energy gap of more than 17 THz using a pair of phase-locked clock lasers, we also carry out Ramsey spectroscopy to extract the transverse qubit coherence time $T_2$. When the tweezer is tuned into magic trapping conditions, which is achieved in our setup by tuning the tensor polarizability of the ${}^3{P}_2$ state via an external control magnetic field, we measure $T_2=1.2\mathrm{ms}$. A microscopic quantum mechanical model is used to simulate our experiments including dominant noise sources. We identify the main constraints limiting the observed coherence time and project improvements to our system in the immediate future. Our Letter opens the door for a so-far-unexplored qubit encoding concept for neutral atom-based quantum computing.

Figure 1

(a) Atomic-level scheme of ${}^{88}\mathrm{Sr}$ depicting the fine-structure qubit in the states ${}^3{P}_0$ and ${}^3{P}_2$. Arrows indicate optical transitions relevant for this Letter. Single-qubit rotations exploit Raman coupling via ${}^3{S}_1$ with single-photon detuning ${\mathrm{\Delta }}_R$ (dashed line). (b) Sketch of the experimental setup. Single ${}^{88}\mathrm{Sr}$ atoms are trapped in an optical tweezer (green). The Raman beams $R_1$ and $R_2$ (red) counterpropagate with the tweezer laser beam. The green (red) double arrow shows the linear polarization direction of the tweezer (Raman beams). An external magnetic field $\overrightarrow{B}$ in the $x\text{−}y$ plane allows us to tune the qubit magic wavelength via the azimuthal angle $\varphi$. (c) Calculated trap depth for ${}^3{P}_0$ and ${}^3{P}_2$ as a function of tweezer wavelength for two values of $\varphi$ [28, 29]. The dashed line indicates the wavelength used in the experiment. (d) Rabi oscillation of the fine-structure qubit, showing the measured population in ${}^3{P}_2$ as a function of the pulse length of the Raman lasers. The tweezer power is $P=1.45\mathrm{mW}$ and $\varphi =0°$. The gray line is a theoretical prediction including shot-to-shot fluctuations of the local Rabi frequency.

Figure 2

Ramsey interferometry of the fine-structure qubit. Ramsey fringes showing the population in ${}^3{P}_2$ as a function of the time $t_R$ between the $\pi /2$ pulses as measured in a deep (a) and shallow (b) tweezer with $P=1.45\mathrm{mW}$ and $P=46\mathrm{\mu }\mathrm{W}$, respectively. The magnetic field is set to $|\overrightarrow{B}|=3\mathrm{G}$ and $\varphi =0°$. Solid gray lines show results from a numerical simulation fit to the data, which takes into account finite temperature.

Figure 3

Magic wavelength tuning of the fine-structure qubit. Normalized Ramsey fringe contrast as a function of magnetic field angle $\varphi$ for $|\overrightarrow{B}|=3\mathrm{G}$ (triangles) and $|\overrightarrow{B}|=8\mathrm{G}$ (circles) measured at fixed $t_R=600\mathrm{\mu }\mathrm{s}$ and $t_R=700\mathrm{\mu }\mathrm{s}$, respectively. For both datasets, $P=46\mathrm{\mu }\mathrm{W}$. The solid line is a Gaussian to guide the eye. Insets show representative datasets for $\varphi =9.5°$ and $\varphi =20°$ taken at $|\overrightarrow{B}|=8\mathrm{G}$. The contrast is extracted from the amplitude of a sinusoidal fit to the Ramsey oscillations and normalized to the maximum value obtained at the magic angle.

Figure 4

Coherence time of the fine-structure qubit. (a) Ramsey signal normalized to the initial fitted fringe contrast at magic angle $\varphi =9.5°$ for $|\overrightarrow{B}|=8\mathrm{G}$ measured in the shallow tweezer ($P=46\mathrm{\mu }\mathrm{W}$). The gray lines are sinusoidal fits to the data to extract the temporal decay of the contrast. (b) Contrast extracted from fits to data as shown in (a) for $|\overrightarrow{B}|=3\mathrm{G}$, $\varphi =0°$ in the deep tweezer (squares) and for the shallow tweezer at $|\overrightarrow{B}|=3\mathrm{G}$, $\varphi =0°$ (triangles), $|\overrightarrow{B}|=3\mathrm{G}$, $\varphi =9.5°$ (crosses), and $|\overrightarrow{B}|=8\mathrm{G}$, $\varphi =9.5°$ (circles) with $T_2$ values of 36(2), 203(17), 676(70), and $1236(82)\mathrm{\mu }\mathrm{s}$, respectively. Dashed lines show fits based on a Gaussian envelope to extract the qubit coherence time $T_2$.

Figure 5

(a) Coherence time $T_2$ predicted from numerical simulations in the presence of shot-to-shot noise in the magnetic field angle $\varphi$ of magnitude $\delta \varphi$. The upper axis shows the magnitude of transverse magnetic field noise $\delta B_x$ resulting in $\delta \varphi$. The shaded region indicates $\delta B_x<10\mathrm{mG}$, and the dashed line depicts the longest $T_2$ time measured. (b) Differential light shift $\delta U$ through the tweezer focal plane caused by the polarization landscape of the high-NA beam. The dashed circle denotes the $1/e^2$ radius of the tweezer intensity. Results in (a) and (b) are calculated for the experimental parameters in Fig. 4, i.e., at magic angle and for $P=46\mathrm{\mu }\mathrm{W}$.