We experimentally demonstrate $PT$-symmetric optical lattices with periodical gain and loss profiles in a coherently prepared four-level $N$-type atomic system. By appropriately tuning the pertinent atomic parameters, the onset of $PT$-symmetry breaking is observed through measuring an abrupt phase-shift jump between adjacent gain and loss waveguides. The experimental realization of such a readily reconfigurable and effectively controllable $PT$-symmetric waveguide array structure sets a new stage for further exploiting and better understanding the peculiar physical properties of these non-Hermitian systems in atomic settings.

Weak cross-Kerr nonlinearities between single photons and coherent states are the basis for many applications in quantum-information processing. These nonlinearities have so far mainly been discussed in terms of highly idealized single-mode models. We develop a general theory of the interaction between continuous-mode photonic pulses and apply it to the case of a single photon interacting with a coherent state. We quantitatively study the validity of the usual single-mode approximation using the concepts of fidelity and conditional phase. We show that high fidelities, nonzero conditional phases, and high photon numbers are compatible, under conditions where the pulses fully pass through each other and where unwanted transverse-mode effects are suppressed.

We present a simple architecture for deterministic quantum circuits operating on single-photon qubits. Few resources are necessary to implement two elementary gates and can be recycled for computing with large numbers of qubits. The deterministic realization of some key multiqubit gates, such as the Fredkin and Toffoli gate, is greatly simplified in this approach.

We study the interaction of two photons in a Rydberg atomic ensemble under the condition of electromagnetically induced transparency, combining a semiclassical approach for pulse propagation and a complete quantum treatment for quantum state evolution. We find that the blockade regime is not suitable for implementing photon-photon cross-phase modulation due to pulse absorption and dispersion. However, approximately ideal cross-phase modulation can be realized based on relatively weak interactions, with counterpropagating and transversely separated pulses.

We propose a scheme for realizing quantum repeaters with Rydberg-blockade-coupled atomic ensembles, based on a recently proposed collective encoding strategy. Rydberg-blockade-mediated two-qubit gates and efficient cooperative photon emission are employed to create ensemble-photon entanglement. Thanks to deterministic entanglement swapping operations via Rydberg-based two-qubit gates, and to the suppression of multiexcitation errors by the blockade effect, the entanglement distribution rate of the present scheme is higher by orders of magnitude than the rates achieved by other ensemble-based repeaters. We also show how to realize temporal multiplexing with this system, which offers an additional speedup in entanglement distribution.

We present a quantum repeater protocol that generates the elementary segments of entangled photons through the communication of qubus in coherent states. The input photons at the repeater stations can be in arbitrary states to save the local state preparation time for the operations. The flexibility of the scheme accelerates the generation of the elementary segments (close to the exact Bell states) to a high rate for practical quantum communications. The entanglement connection to long distances is simplified and sped up, possibly realizing an entangled pair of high quality within the time in the order of that for classical communication between two far-away locations.