Modular entanglement of atomic qubits using photons and phonons

Quantumentanglement is thecentral resourcebehindquantum information science, from quantum computation and simulation1,2 to enhanced metrology3 and secure communication1. These applications require the quantum control of large networks of qubits to realize gains and speed increases over conventional devices. However, propagating entanglement becomes di cult or impossible as the system grows in size. Here, we demonstrate the first step in a modular approach4 to scaling entanglement by using complementary quantum buses on a collection of three atomic ion qubits stored in two remote ion trap modules. Entanglement within a module is achieved with deterministic near-field interactions through phonons5, and remote entanglement between modules is achieved with a probabilistic interaction through photons6. This minimal system allows us to address generic issues in the synchronization of entanglement with multiple buses. It points the way towards a modular large-scale quantum information architecture that promises less spectral crowding and thus potentially less decoherence as the number of qubits increases4. We generate this modular entanglement faster than the observed remotely entangled qubit-decoherence rate, showing that entanglement can be scaled simply by adding more modules. Smallmodules of qubits have been entangled throughnative local interactions in many physical platforms, such as trapped atomic ions through their Coulomb interaction5, Rydberg atoms through their electric dipoles7,8, nitrogen-vacancy centres in diamond through their magnetic dipoles9, and superconducting Josephson junctions through capacitive or inductive couplings10,11. However, each of these systems is confronted with practical limits to the number of qubits that can be reliably controlled, stemming from inhomogeneities, the complexity and density of the interactions between the qubits, or quantum decoherence. Scaling beyond these limits can be achieved by invoking a second type of interaction that can extend the entanglement to other similar qubit modules. Such an architecture should therefore exploit both the local interactions within the qubit modules, and also remote interactions between modules (an example architecture is shown in Fig. 1). One promising approach is to directly move qubits between different modules12,13, but this approach is limited by the difficulty of moving qubits over large distances. Optical interfaces provide ideal buses for extending entanglement betweenmodules14,15, as optical photons can propagate over macroscopic distances with negligible loss. Several qubit systems have been entangled through remote optical buses, such as atomic ions16, neutral atoms17 and nitrogen-vacancy centres in diamond18. In the experiment reported here, we juxtapose local phonon and remote photon entanglement buses using trapped atomic ion qubits, balancing the requirements of each interface within the same qubit system. The observed entanglement rate within and between modules is faster than the observed entangled qubitdecoherence rate. This is critical in quantum modular architectures because the required resource scaling is superexponential in the ratio of decoherence rate to entanglement rate4. This ratio is observed to be 0.2 in this experiment, many orders of magnitude lower than previous experiments demonstrating remote entanglement17–19. Overcoming the resource scaling requirement makes trapped ions a leading candidate for realizing a quantum network. The qubits in this experiment are defined by the two hyperfine ‘clock’ states, |F=0,mF=0〉≡ |0〉 and |F=1,mF=0〉≡ |1〉, which are separated by ω0= 2π × 12.64282 GHz in the S1/2 manifold of trapped 171Yb+ atoms. Laser cooling, optical pumping, and readout occur via standard state-dependent fluorescence techniques20. The qubits are trapped in two independent modules separated by∼1m, as shown in Fig. 1a. (The ion traps, light collection optics and interferometer could in principle be part of a modular, scalable architecture, as shown in Fig. 1b.) To generate remote entanglement between atoms in physically separated ion trap modules, we synchronously excite each atom with a resonant fast laser pulse16. A fraction of the resulting spontaneously emitted light is collected into an optical fibre, with each photon’s polarization (σ or σ) entangled with its parent atom owing to atomic selection rules (Fig. 2a). Each photon passes through a quarter-wave plate that maps circular to linear polarization (σ→H and σ→V ), and then the two photons interfere on a 50/50 beamsplitter, where detectors monitor the output (see Fig. 1a and Methods)19. We select the two-photon Bell states of light |HV 〉 + eiφD |VH〉, where φD is 0 or π depending on which pair of detectors registers the photons21. Finally, a series of microwave pulses transfers the atoms into the {|0〉, |1〉} basis (Fig. 2b), ideally resulting in the heralded entangled state of the two remote atomic qubits |01〉+eiφAB |10〉. The intermodular phase is given by