Realization of a crosstalk-avoided quantum network node
using dual-type qubits of the same ion species

Our experimental setup is shown schematically in Fig. 1. Two ${}^{171}\mathrm{Yb}^{+}$ ions are trapped with a separation of $12\,\mu$m and can be individually addressed by focused laser beams with a beam waist radius of about $4\,\mu$m. The communication qubit is first pumped to $|{}^{2}P_{1/2},F=0,m_{F}=0\rangle$, and then decays to one of the ${}^{2}S_{1/2},F=1$ states through the spontaneous emission of a polarization-entangled photon:

where we denote the ionic state as $|F,m_{F}\rangle$ in the ${}^{2}S_{1/2}$ levels for simplicity, and $|\sigma^{\pm}\rangle$ and $|\pi\rangle$ represent the polarization of the photon with respect to a magnetic field $B\approx 5.6\,$G which sets the quantization axis.

We collect the photon in a direction perpendicular to the magnetic field. From the radiation pattern of the dipole transition, we obtain photon states $|\pi\rangle\to c|V\rangle$ and $|\sigma^{\pm}\rangle\to c|H\rangle/\sqrt{2}$ where $|H\rangle$ and $|V\rangle$ represent horizontal and vertical polarizations, and $c$ is a small probability amplitude of detecting a photon. After applying a two-tone microwave pulse to turn $(|1,-1\rangle+|1,1\rangle)/\sqrt{2}$ into $|\downarrow\rangle\equiv|0,0\rangle$, we end up with the desired ion-photon entangled state

where $|\uparrow\rangle\equiv|1,0\rangle$.

The memory qubit can be encoded as an $S$-qubit spanned by $|0\rangle\equiv|0,0\rangle$ and $|1\rangle\equiv|1,0\rangle$. Here we use different notations for the same states to distinguish from those of the communication qubit. In the dual-type qubit scheme, we can also encode as an $F$-qubit spanned by $|0^{\prime}\rangle\equiv|{}^{2}F_{7/2},F=3,m_{F}=0\rangle$ and $|1^{\prime}\rangle\equiv|{}^{2}F_{7/2},F=4,m_{F}=0\rangle$. The two qubit types can be coherently converted into each other by focused $411\,$nm laser and global $3432\,$nm laser via the intermediate $D_{5/2}$ levels ¹⁶ as shown in Fig. 1e. We use bichromatic laser to transfer both qubit levels simultaneously so that the qubit state is insensitive to the laser dephasing. Owing to the large frequency detuning, an $F$-type memory qubit is well protected from the random scattering of $370\,$nm photons from the communication qubit.

As shown in Fig. 1b and c, we initialize the communication qubit in $|\downarrow\rangle$ by $40\,\mu$s Doppler cooling and $8\,\mu$s optical pumping, and then convert it to $|\uparrow\rangle$ by a $12\,\mu$s microwave $\pi$ pulse (MW1). Then we excite the ion to $|{}^{2}P_{1/2},F=0,m_{F}=0\rangle$ by a focused $\pi$-polarized $370\,$nm laser pulse in $2\,$ps ¹⁸ (see Methods). The ion decays to the ${}^{2}S_{1/2},F=1$ levels in a typical timescale of $1/{\mit\Gamma}\approx 8\,$ns to produce the entangled state in Eq. (1). We repeat this ion-photon entanglement generation cycle (the dashed box in Fig. 1c) until a photon is detected in a time window of $60\,$ns (although it takes about $1\,\mu$s to transfer the data).

Conditioned on the collection of the photon perpendicular to the quantization axis in Fig. 1d, we get an entangled state $\frac{1}{\sqrt{2}}[\frac{1}{\sqrt{2}}(|1,-1\rangle+|1,1\rangle)|H\rangle+|\uparrow\rangle|V\rangle]$. However, note that the time when the spontaneous emission occurs is uncertain in the $60\,$ns time window, which means that the relative phases between these Zeeman levels cannot be determined in advance, and distribute in a range of $\Delta\omega_{\mathrm{Zeeman}}\Delta T\approx 3$. In the experimental sequence, we compensate this phase by feedforwarding the detection time of the photon into the phase of the two-tone microwave pulse (MW2 in Fig. 1c, $13\,\mu$s) so that an entangled state in Eq. (2) is obtained independent of the time of the spontaneous emission.

We then bound the entanglement fidelity by rotating the spin and the photon in different bases ¹⁹ as shown in Fig. 2. In the diagonal basis, we measure the correlation between the spin and photon as $P(\uparrow|V)=0.964\pm 0.007$, $P(\downarrow|V)=0.036\pm 0.007$, $P(\uparrow|H)=0.077\pm 0.010$ and $P(\downarrow|H)=0.923\pm 0.010$ from about 1000 trials with the error bars computed from a binomial distribution. Then we consider the off-diagonal basis where the spin and the photon are both rotated by $\pi/2$ pulses with a relative phase of $\phi$. For the spin, the rotation is achieved by the MW3 pulse in Fig. 1c, and for the photon we rotate the polarization direction by the half-wave plate in Fig. 1d. As shown in Fig. 2c, when we scan the phase of the MW3 pulse, we observe a sinusoidal oscillation in the conditional probabilities $P(\tilde{\uparrow}|\tilde{V})$ and $P(\tilde{\uparrow}|\tilde{H})$ (and thus $P(\tilde{\downarrow}|\tilde{V})$ and $P(\tilde{\downarrow}|\tilde{H})$ as well). At the optimal $\phi$ which gives largest $P(\tilde{\uparrow}|\tilde{V})-P(\tilde{\uparrow}|\tilde{H})$, we obtain $P(\tilde{\uparrow}|\tilde{V})=0.959\pm 0.008$, $P(\tilde{\downarrow}|\tilde{V})=0.041\pm 0.008$, $P(\tilde{\uparrow}|\tilde{H})=0.091\pm 0.013$, $P(\tilde{\downarrow}|\tilde{H})=0.909\pm 0.013$, as shown in Fig. 2b. From these results, we bound the ion-photon entanglement fidelity ¹⁹ as $F\geq\frac{1}{2}[P(\uparrow,V)+P(\downarrow,H)-2\sqrt{P(\downarrow,V)P(\uparrow,H)}+P(\tilde{\uparrow},\tilde{V})+P(\tilde{\downarrow},\tilde{H})-P(\tilde{\uparrow},\tilde{H})-P(\tilde{\downarrow},\tilde{V})]=(88.0\pm 1.0)\%$, which is far above the classical threshold of 0.5 and thus verifies the entanglement. We measure an entanglement generation rate $r\approx 5\,\mathrm{s}^{-1}$, which is consistent with our repetition rate of $1.6\times 10^{4}\,\mathrm{s}^{-1}$, the solid angle $\Delta{\mit\Omega}/4\pi\approx 1.3\%$ of the 0.23-NA objective, the probability $2/3$ to project to the maximally entangled state of Eq. (2), the $15\%$ fiber coupling efficiency, the $30\%$ detection efficiency of the photomultiplier tube (PMT) and the $85\%$ transmission efficiency for all the other optical elements.

As for the error budget, we estimate $2\%$ infidelity from optical pumping and state detection of the ion, $3\%$ from imperfect $\pi$ polarization of the $370\,$nm laser pulse which leads to excitation to $|{}^{2}P_{1/2},F=1,m_{F}=\pm 1\rangle$ states, $2\%$ from the misalignment of the objective to collect the photon, and $2\%$ from the dark count of the PMT. Another $6\%$ infidelity can come from the imperfect conversion from $(|1,-1\rangle+|1,1\rangle)/\sqrt{2}$ to $|0,0\rangle$, whose contributions include $4\%$ from the $2\,$ns jitter time of the control system, as well as $2\%$ from the dephasing between the two Zeeman levels during the microwave pulse. More details about the ways we calibrate the experimental system and estimate the error can be found in Supplementary Note 1.

Given the above entanglement generation rate, we expect a typical timescale of hundreds of milliseconds to obtain an ion-photon entanglement. Therefore, we want to extend the storage lifetime of the dual-type qubit to a similar timescale to demonstrate its compatibility with the ion-photon quantum network. Since our dual-type qubit is encoded in the hyperfine clock states, it is largely insensitive to the fluctuation in the magnetic field or the AC Stark shift of the scattered laser beams. However, since finally we will bring the $F$-qubit back to the $S$-type for detection, even a small frequency mismatch in the bichromatic laser on Hertz-level from the qubit transition frequency can accumulate into considerable phase shift during the sub-second storage. Therefore, we apply spin echoes by converting the qubit to the $S$-type, performing a microwave $\pi$ pulse, and then converting it to the $F$-type again, as shown in the experimental sequence in Fig. 3a. In this way, the phase shift on the two qubit states cancel with each other. We further choose to use two spin echoes for a balance between the imperfect qubit-type conversion and the cancellation of the phase errors.

To benchmark the storage fidelity of the memory qubit, we initialize it as an $S$-qubit in one of the six mutually unbiased bases (MUBs) ²⁰ $|0\rangle$, $|1\rangle$, $|+\rangle$, $|-\rangle$, $|L\rangle$, $|R\rangle$ with equal probability, convert it to the $F$-type, store for a total time $T=4\tau$ separated by two spin echoes, and finally move it back to the $S$-type to measure the storage fidelity. For a fair comparison with the later experiment, here we use an EMCCD to measure the memory qubit state instead of the PMT. As shown in Fig. 3b, the fidelity oscillates with the storage time, and can be well fitted by a single-frequency noise at around $(57.3\pm 0.1)\,$Hz and a dephasing time $T_{2}=(2.8\pm 0.7)\,$s ^{21; 22} (see Methods). This frequency varies slightly when we repeat the experiment and its source is still under investigation. For a typical storage time $T=200\,$ms, the storage fidelity for the 6 basis states are summarized in Fig. 3c, which gives an average fidelity of $(83.9\pm 0.4)\%$ where the error bar represents one standard error for the average of the total $9000$ trials. The infidelity contains three round-trips of the qubit-type conversion with $3\%$ error each (see Methods), $2.5\%$ from state preparation and detection using an EMCCD, and $(1-e^{-T/T_{2}})/2\approx 3\%$ from the decoherence during long-time storage.

With the ion-photon entanglement and the long-time storage of the dual-type qubit demonstrated separately, now we can combine them together to establish a crosstalk-avoided quantum network node. The experimental sequence is basically to insert the ion-photon entanglement generation on the communication qubit (Fig. 1c) into the storage time $4\tau=200\,$ms of the memory qubit (Fig. 3a), as shown in Fig. 4a. We repeat the entanglement generation attempts until a photon is collected or the storage time window is used up. For the simplicity of the control sequence, here we only attempt to generate entanglement in the middle $2\tau=100\,$ms, which corresponds to a success probability of about $40\%$ for each trial given the generation rate of $5\,\mathrm{s}^{-1}$. Note that this nonunity success rate does not affect our estimation of the crosstalk error, which is proportional to the number of generated photons, not that of the collected ones.

At the end of the experimental sequence, we use an EMCCD to measure the states of the two qubits simultaneously. Again, we prepare the memory qubit in one of the six MUBs randomly. For 1800 successful trials when the communication qubit and the photon are measured in the diagonal basis (with the conditional probability shown in Fig. 4b), we get about 300 trials for each MUB and an average storage fidelity of $(83.6\pm 0.8)\%$. This is consistent with the storage fidelity $(83.9\pm 0.4)\%$ without ion-photon entanglement generation within the error bars, thus proves a negligible crosstalk error. In comparison, without the dual-type qubit encoding, the memory qubit would have experienced much larger crosstalk error which would have been detected under our experimental precision, and would have even exceeded our overall measured storage infidelity of $16\%$ with the technical errors included (see Supplementary Note 2 for details). We also repeat the measurement for the communication qubit and the photon in the off-diagonal basis in Fig. 4c. This gives us a bound for entanglement fidelity $F\geq(84.8\pm 0.9)\%$. The additional $3.2\%$ infidelity compared with the entanglement fidelity in Fig. 2 mainly comes from the state detection error when switching from the PMT to the EMCCD (see Supplementary Note 1 for details).

We use a $2\,$ps ultrafast $370\,$nm laser pulse to pump the communication qubit from $|{}^{2}S_{1/2},F=1,m_{F}=0\rangle$ to $|{}^{2}P_{1/2},F=0,m_{F}=0\rangle$. The pulsed laser comes from a mode-locked Ti:sapphire laser with $739\,$nm central wavelength, and is frequency-doubled to $369.5\,$nm by a second harmonic generator system (SHGS). Before the SHGS, an electro-optic modulator is used to pick a single pulse from the $76\,$MHz pulse train, giving an extinction ratio of about $10^{5}:1$. More details can be found in our previous work ¹⁸.

To calibrate the pulse area, we apply a microwave $\pi$ pulse to the state after spontaneous emission, so as to convert the population from $|{}^{2}S_{1/2},F=1,m_{F}=0\rangle$ to $|{}^{2}S_{1/2},F=0,m_{F}=0\rangle$, which appears dark whereas the other states in the ${}^{2}S_{1/2},F=1$ manifold appear bright in our detection scheme. Ideally, if the laser has a pulse area of $\pi$, the probability of getting a bright state in the end will be $2/3$. Otherwise, we expect a bright state probability $(2/3)\sin^{2}(\theta/2)$ where $\theta$ is the pulse area. As shown in Supplementary Figure 1 in Supplementary Note 4, we fit this curve and obtain a laser $\pi$ pulse with the excitation probability to the $|{}^{2}P_{1/2},F=0,m_{F}=0\rangle$ state reaching $P_{e}\approx 99\%$.

Consider a single-frequency noise with amplitude $A$, frequency $\omega$ and a random phase $\varphi$ on the qubit frequency ^{21; 22}, the Hamiltonian can be written as: $H=A\cos(\omega t+\varphi)\sigma_{z}/2$. We start from the superposition state $(|0\rangle+|1\rangle)/\sqrt{2}$. After the storage time of $T=4\tau$ separated by two $\pi$ pulses, we obtain a phase shift between $|0\rangle$ and $|1\rangle$ as

Thus the dephasing of the off-diagonal terms of the density matrix is given by

and we obtain a fidelity for the stored $|+\rangle$ state as $(1+\langle e^{i\Delta\phi}\rangle)/2$.

In the experiment, we fit the measured fidelity in Fig. 3b vs. the total storage time $T=4\tau$ by $F(T)=\{1+J_{0}[(8A/\omega)\sin^{2}(\omega T/8)\sin(\omega T/4)]e^{-T/T_{2}}\}/2-c$ where an exponential decay term is used to represent the pure dephasing time $T_{2}$ and a constant $c$ is subtracted to account for the state preparation and measurement (SPAM) error.

We calibrate the coherent conversion fidelity of the dual-type qubit by repeating the $S$-$F$-$S$ round-trip cycles for $N$ times, and fit the decay of the average state fidelity over an MUBs by $F=F_{0}(1-\epsilon)^{N}$. As shown in Supplementary Figure 2 in Supplementary Note 5, we extract a SPAM fidelity of $F_{0}=97.0\%$ and the round-trip conversion error of $\epsilon=3.1\%$.

Data Availability: The data that support the findings of this study are available from the authors upon request. Source data are provided with this paper.