Our network node consists of a 40Ca+ ion in a radio-frequency linear Paul trap with an optical cavity that enhances photon collection on the 854 nm electronic dipole transition (Fig. 1). A Raman laser pulse at 393 nm triggers emission, by the ion, of a photon into the cavity via a bichromatic cavity-mediated Raman transition (CMRT).23 Two indistinguishable processes are driven in the CMRT, each leading to the generation of a cavity photon and resulting in entanglement between photon polarisation and the electronic qubit state of the ion of the form \(1/\sqrt 2 (D_{J = 5/2,m_j = - 5/2},V + D_{J = 5/2,m_j = - 3/2},H)\), with horizontal (H) and vertical (V) photon polarisation and two metastable Zeeman states of the ion \((D_{J, m_j})\), see Supplementary Fig. 3. The total measured probability of obtaining an on-demand free-space photon out of the ion vacuum chamber (entangled with the ion) is P out = 0.5 ± 0.1 (Secction II, Supplementary material of this paper), enabled by the novel low-loss cavity in our setup.

Fig. 1 Simplified experiment schematic. From left to right: a single atomic ion (red sphere) in the centre of a radio-frequency linear Paul trap (gold electrodes) and a vacuum anti-node of an optical cavity. A Raman laser pulse triggers emission of an 854 nm photon into the cavity, which exits to the right. The photon, polarisation-entangled with two electronic qubit states of the ion (two Zeeman states of the D J = 5/2 manifold, not shown), is then wavelength-converted to 1550 nm using difference frequency generation involving ridge-waveguide-integrated periodically-poled lithium niobate (PPLN) chips and a strong (~1 W) pump laser at 1902 nm.26 The photon then passes through a 50 km single-mode fibre spool, is filtered with a 250 MHz bandwidth etalon (SF) to reduce noise from the conversion stage,26 and is polarisation-analysed using waveplates, a polarising beam splitter (PBS) and a solid-state single photon counting module (SPCM, InGaAs ID230 from IDQuantique). The electronic state of the ion is measured (not shown), conditional on the detection of a photon. Additional photon conversion filters are not shown.26 For further details see, Supplementary material of this paper section I Full size image

The CMRT yields an entangled state with a frequency-degenerate photon qubit (the two polarisation components have the same frequency to within the cavity linewidth23), providing a significant benefit for long distance networking: the phase of the light-matter entangled state does not depend on the time at which the photon detection event occurs at a given distance from the ion. Photon detection time fluctuates due to the intrinsic finite temporal extent of the photon wavepacket and in the case of optical path length changes, which could be significant over tens of kilometres of deployed optical fibre. Our photons are generated over several tens of microseconds, with a corresponding bandwidth of tens of kilohertz. This unusually narrow bandwidth allows for strong frequency filtering, which we exploit in the photon conversion process and could have further benefits in future deployed networks, e.g to enable co-propagating classical and quantum light. Furthermore, the corresponding photon coherence-length is potentially thousands of metres, allowing for essentially path-length-insensitive entanglement swapping between remote ions via Hong-Ou-Mandel interference.4,24,25

Single-mode fibre-coupled photons from the ion are injected into a polarisation-preserving photon conversion system (previously characterised using classical light26). In summary, a χ(2) optical nonlinearity is used to realise difference frequency generation, whereby the energy of the 854 nm photon is reduced by that of a pump-laser photon at 1902 nm, yielding 1550 nm. Two commercially available free-space and crossed PPLN ridge waveguide crystals are used, one to convert each polarisation, in a self-stable polarisation interferometer. The total fibre-coupled device conversion efficiency here is 25 ± 0.02%, for an added white noise of 40 photons per second, within the filtering bandwidth of 250 MHz centred at 1550 nm. As discussed in,26 the 854 nm line in 40Ca+ is almost unique amongst trapped-ion transitions in its potential for low-noise, highly-efficient single-step frequency conversion to the telecom C band.

Following conversion, the telecom photon is injected into a 50.47 km ‘SMF28’ single-mode fibre spool with 0.181 dB per km loss (10.4 ± 0.5% measured total transmission probability). The spool is not actively stabilised. Polarisation dynamics in an unspooled fibre could be actively controlled using methods developed in the field of quantum cryptography (e.g.,27). Finally, free-space projective polarisation analysis is performed and the photon is detected using a telecom solid-state photon detector with an efficiency of 0.10 ± 0.01 and free-running dark count rate of 2 counts per second (cps). Measurement of the ion-qubit state is performed conditional on the detection of a 50 km photon within a 30 μs time window: the Zeeman ion qubit is mapped into the established 40Ca+ optical quadrupole clock qubit28 via laser pulses at 729 nm, followed by standard fluorescence state detection (see Methods).

Quantum state tomography is performed to reconstruct the two-qubit (ion qubit and photon polarisation qubit) state, Supplementary material of this paper section III. The 247 μs photon travel time through the fibre limits the maximum attempt rate for generating a photon from the ion to 4 kHz (2 kHz if the fibre was stretched out away from our ion to force an additional delay for the classical signal ‘photon click’ to return). Here, until photon detection occurs, photon generation is (Raman laser pulses are) performed every 453 μs, yielding an attempt rate of 2.2 kHz. For the complete experimental sequence see Methods. All error bars on quantities derived from the tomographically-reconstructed states (density matrices) are based on simulated uncertainties due to finite measurement statistics (see Supplementary Material section III).

A strongly entangled ion–photon state is observed (Fig. 2) over 50 km, quantified by a concurrence29 C = 0.75 ± 0.05 and state fidelity Fm = 0.86 ± 0.03 with a maximally entangled state (C = 1). Simulating a CHSH Bell inequality test30 on our tomographic data yields a value of 2.304 ± 0.125, thereby exceeding the classical bound (of 2) by 2.4 standard deviations. Using a shorter detection window (first 2/3 of the full photon wavepacket) increases the signal to noise ratio and yields Fm = 0.90 ± 0.03 and CHSH Bell inequality violation by 4.8 standard deviations at the expense of an efficiency decrease of only 10%. The quality of our light-matter entangled state therefore surpasses this stringent threshold for its subsequent application.

Fig. 2 Observation of ion-photon entanglement over 50 km of optical fibre. (i) 2D red bar chart: histogram of photon detection times (photon wavepacket in dashed box), following the generation of an 854 nm photon with a 30 μs Raman laser pulse (R) ≈ 250 μs earlier, repeated at 2.2 kHz. Ion–photon state tomography is performed for photon detection events recorded in the dashed box (total contained probability P = 5.3 × 10−4). (ii) 3D bar chart: absolute value of experimentally-reconstructed density matrix of the telecom photonic polarisation qubit (H and V are Horizontal and Vertical, respectively) and ion-qubit state (\(0 = D_{J = 5/2,m_j = - 3/2}\), \(1 = D_{J = 5/2,m_j = - 5/2}\)) Full size image

For a detailed analysis of the sources of infidelity in the entangled state see, Supplementary material of this paper section IV; here now is a short summary. In a second experiment, the telecom entangled state is reconstructed right after the conversion stage (without the 50 km spool), yielding Fm = 0.92 ± 0.02. The drop in fidelity when adding the 50 km spool can, to within statistical uncertainty, be entirely explained by our telecom photon detector dark counts (2 cps). In a third experiment, the 854 nm entangled state is reconstructed right out of the vacuum chamber (without conversion), yielding Fm = 0.967 ± 0.006. The observed drop in fidelity through the conversion stage alone is dominated by a drop in photon signal to noise signal. Here the noise consists of comparable rates of telecom detector dark counts and conversion noise (caused by Anti-Stokes Raman scattering of the pump laser26) and the signal is reduced by the finite conversion setup efficiency and the lower telecom detector’s efficiency compared to the 854 nm one. The infidelity in the 854 nm photon-ion entangled state is consistent with that achieved in.23

The total probability that a Raman pulse led to the detection of a photon after 50 km was P = 5.3 × 10−4, which given an attempt rate of 2.2 kHz yielded a click rate of ≈1 cps. Photon loss mechanisms in our experiment are discussed in, Supplementary material of this paper section II. In summary, the 50 km fibre transmission (0.1) and our current telecom detector efficiency (0.1) limit the maximum click probability to P = 0.01. The majority of other losses are in passive optical elements, and could largely be eliminated by e.g. more careful attention to coupling into optical fibres and photon conversion waveguides. In combination with state-of-the-art telecom detectors (e.g. Scontel recently supplied us superconducting nanowire detectors providing 0.8 cps dark count rate and 77% efficiency according to the company’s calibration), a total 50 km efficiency of P ≈ 0.01 would be expected and a corresponding click rate of ≈20 cps.

One of the functions played by matter in a quantum network is as a memory to store established entanglement, while entanglement is being made or processed in other parts of the network. Decoherence processes in the matter qubit will limit the distance over which it is possible to distribute quantum entanglement (the distance a photon could possibly travel in the ‘coherence time’ of the matter qubit). In our 50 km experiment, the ion qubit is already stored for the 250 μs photon travel time through the 50 km fibre, with no statistically significant reduction in the ion–photon entanglement quality (this was achieved by installing a mu-metal shield around the ion-trap vacuum chamber to attenuate ambient magnetic field fluctuations).

Additional tomographic measurements are performed to see for how long ion–photon entanglement could be stored in our ion-trap network node before decoherence in the ion-qubit would destroy it. Specifically, state tomography is performed for increasing delays introduced between measurements of the telecom photon polarisation state (0 km fibre travel distance) and measurements of the state of the ion-qubit. This is equivalent to introducing an additional storage time for the ion-qubit. The results show that strong entanglement is still present after 20 ms wait time (Fm = 0.77 ± 0.04, C = 0.57 ± 0.08), the longest wait time employed. This already opens up the possibility of distributing entanglement over several thousands of kilometers and the time to perform hundreds of single and multi-qubit ion quantum logic gates.31

A dominant source of decoherence of our ion-qubit are uncontrolled fluctuating energy-level shifts due to intensity fluctuations of the 806 nm laser field used to lock the cavity around the ion. Further attention to minimising the absolute size of these fluctuations should lead to entanglement storage times of more than ≈100 ms and therefore the possibility to distribute entanglement to the other side of the earth. Beyond this, the ion-qubit could be transferred to hyperfine clock transitions within different co-trapped ion species that offer coherence times of many seconds and longer.32