High-Fidelity Control and Entanglement of Rydberg-Atom Qubits

Individual neutral atoms excited to Rydberg states are a promising platform for quantum simulation and quantum information processing. However, experimental progress to date has been limited by short coherence times and relatively low gate fidelities associated with such Rydberg excitations. We report progress towards high-fidelity quantum control of Rydberg-atom qubits. Enabled by a reduction in laser phase noise, our approach yields a significant improvement in coherence properties of individual qubits. We further show that this high-fidelity control extends to the multi-particle case by preparing a two-atom entangled state with a fidelity exceeding 0.97(3), and extending its lifetime with a two-atom dynamical decoupling protocol. These advances open up new prospects for scalable quantum simulation and quantum computation with neutral atoms.

Figure 1

Experimental setup and single-atom Rabi oscillations. (a) The ground state $|g⟩=|5S_{1/2},F=2,m_F=-2⟩$ is coupled to $|r⟩=|70S,J=1/2,m_J=-1/2⟩$ via the intermediate state $|e⟩=|6P_{3/2},F=3,m_F=-3⟩$. (b) The lasers are locked to a reference cavity whose narrow transmission window (shaded region in inset) suppresses high-frequency phase noise. This transmitted light is used to injection lock a Fabry-Perot (FP) laser diode. The laser diode output is focused onto the array of atoms trapped in optical tweezers, with a small pickoff onto a reference CCD camera used for alignment. (c) Resonant two-photon coupling induces Rabi oscillations between $|g⟩$ and $|r⟩$. The upper plot is a typical measurement from the previous setup used in [17]. The lower plot shows typical results with the new setup, with a fitted coherence time of $27(4)\mu \mathrm{s}$. Each data point is calculated from 50–100 repeated measurements of two identically coupled atoms separated by $23\mu \mathrm{m}$ such that they are effectively noninteracting. In all figures, error bars mark 68% confidence intervals, solid lines are fits to experimental data, and dotted lines indicate the expected contrast from the numerical model.

Figure 2

Characterization of single-atom coherence and phase control. (a) The lifetime of $|r⟩$ is measured by exciting from $|g⟩$ to $|r⟩$ with a $\pi$ pulse, and then deexciting after a variable delay. The probability to end in $|g⟩$ (denoted $P_g$) decays with an extracted lifetime of $T_1=51(6)\mu \mathrm{s}$ (fitted to an exponential decay model with no offset). (b) A Ramsey experiment (blue) shows Gaussian decay with a $1/e$ lifetime of $T_2^{*}=4.5(1)\mu \mathrm{s}$, limited by thermal Doppler shifts. Inserting an additional $\pi$ pulse (orange) between the $\pi /2$ pulses cancels the effect of the Doppler shifts and results in a substantially longer coherence lifetime of $T_2=32(6)\mu \mathrm{s}$ (fitted to an exponential decay model with an offset of 0.5). (c) A single-atom phase gate is implemented by applying an independent 809 nm laser which induces a light shift $\delta =2\pi \times 5\mathrm{MHz}$ on the ground state for time $t$, resulting in an accumulated dynamical phase $\varphi =\delta t$. The gate is embedded in a spin-echo sequence to cancel Doppler shifts. In each measurement shown here, the 1013 nm laser remains on for the entire pulse sequence, while the 420 nm laser is pulsed according to the sequence shown above each plot. Each data point is calculated from 200–500 repeated measurements with a single atom per realization.

Figure 3

Coherent control and entanglement generation with two atoms. (a) The level structure for two nearby atoms features a doubly excited state $|rr⟩$, which is shifted by the interaction energy $U\gg \hslash \mathrm{\Omega }$. In this Rydberg blockade regime, the laser field only couples $|gg⟩$ to $|W⟩$. The symmetric and antisymmetric states $|W⟩$, $|D⟩=(1/\sqrt{2})(|gr⟩\pm |rg⟩)$ can be coupled by a local phase gate on one atom (pink arrow). (b) After driving both atoms on resonance for variable time, we measure the probability of the resulting two-atom states. Population oscillates from $|gg⟩$ to $|W⟩$ at the enhanced Rabi frequency $\sqrt{2}\mathrm{\Omega }$. (c) We measure the entanglement fidelity of the two atoms after a resonant $\pi$ pulse in the blockade regime. A local phase gate $Z_{\varphi }^{(1)}$ rotates $|W⟩$ into $|D⟩$, which is detected by a subsequent $\pi$ pulse. The fitted contrast 0.88(2) measures the off diagonal density matrix elements. The phase gate is implemented by an off resonant laser focused onto one atom, with a crosstalk of $<2\%$ [27]. The measurement is embedded in a spin-echo sequence to cancel dephasing from thermal Doppler shifts. (d) The four components of the density matrix correspond to an entangled state with fidelity $\mathcal{F}=0.97(3)$ (corrected for detection error). Each data point in (b) and (c) is calculated from $\sim 50$ and $\sim 250$ repeated measurements, respectively, with a single atom pair per realization. Dotted lines in (c) mark the limits of detection fidelity.

Figure 4

Extension of entangled-state lifetime via dynamical decoupling. We measure the lifetime of $|W⟩$ by exciting $|gg⟩$ to $|W⟩$ and then deexciting after a variable time (blue). The lifetime is limited by dephasing from random Doppler shifts. Inserting an additional $2\pi$ pulse (orange) in the blockade regime swaps the populations of $|gr⟩$ and $|rg⟩$ to refocus the random phase accumulation, extending the lifetime to $\sim 36\mu \mathrm{s}$ (fitted to an exponential decay with no offset, shown as the solid orange line). The initial offset in each curve is set by the ground state detection fidelity associated with the given trap-off time. All data points are calculated from 30–100 repeated measurements, averaged over nine independent, identically coupled atom pairs per realization.