Jürgen Eschner

A quantum repeater segment is a basic building block of a quantum repeater, generating buffered entanglement of quantum memories to connect quantum repeater cells. It also enables the connection between quantum computers. In the implementation we present here, photons emitted from two co-trapped free-space coupled $^{40}$Ca$^+$ ions are converted to the telecom-C band and interfered after transmission over 440$\,$m of optical fiber (220$\,$m per arm), where a photonic Bell measurement is performed to create entanglement between the memories. With this scheme we generate an entangled $\left|Ψ^+\right\rangle$ Bell state with $\ge 68(8)\,$% fidelity, highlighting trapped $^{40}$Ca$^+$ ions as a promising quantum repeater hardware platform.

We investigate the indistinguishability of Raman photons generated from two trapped $^{40}$Ca$^+$ ions using few-nanosecond excitation pulses. We elucidate how spontaneous scattering back to the initial state affects Hong-Ou-Mandel interference. We identify the mean number of back-decays as a measurable single-emitter quantity that correlates with achievable interference visibility of photons from two identical emitters.

The quantum repeater cell is a basic building block for a quantum network, as it allows to overcome the distance limitations due to unavoidable fiber loss in direct transmission. We demonstrate the implementation of a quantum repeater cell, based on two free-space coupled $^{40}$Ca$^+$ ions in the same trap that act as quantum memories. We demonstrate the asynchronous generation of atom-photon and photon-photon entanglement by controlled emission of single photons from the individually addressed ions and entanglement swapping. We discuss the fidelity as well as the scaling of the generated rate.

We analyze elementary building blocks for quantum repeaters based on fiber channels and memory stations. Implementations are considered for three different physical platforms, for which suitable components are available: quantum dots, trapped atoms and ions, and color centers in diamond. We evaluate and compare the performances of basic quantum repeater links for these platforms both for present-day, state-of-the-art experimental parameters as well as for parameters that could in principle be reached in the future. The ultimate goal is to experimentally explore regimes at intermediate distances, up to a few 100 km, in which the repeater-assisted secret key transmission rates exceed the maximal rate achievable via direct transmission. We consider two different protocols, one of which is better adapted to the higher source clock rate and lower memory coherence time of the quantum dot platform, while the other circumvents the need of writing photonic quantum states into the memories in a heralded, non-destructive fashion. The elementary building blocks and protocols can be connected in a modular form to construct a quantum repeater system that is potentially scalable to large distances.

Entanglement between a stationary quantum system and a flying qubit is an essential ingredient of a quantum-repeater network. It has been demonstrated for trapped ions, trapped atoms, color centers in diamond, or quantum dots. These systems have transition wavelengths in the blue, red or near-infrared spectral regions, whereas long-range fiber-communication requires wavelengths in the low-loss, low-dispersion telecom regime. A proven tool to interconnect flying qubits at visible/NIR wavelengths to the telecom bands is quantum frequency conversion. Here we use an efficient polarization-preserving frequency converter connecting 854$\,$nm to the telecom O-band at 1310$\,$nm to demonstrate entanglement between a trapped $^{40}$Ca$^{+}$ ion and the polarization state of a telecom photon with a high fidelity of 98.2 $\pm$ 0.2$\%$. The unique combination of 99.75 $\pm$ 0.18$\%$ process fidelity in the polarization-state conversion, 26.5$\%$ external frequency conversion efficiency and only 11.4 photons/s conversion-induced unconditional background makes the converter a powerful ion-telecom quantum interface.

We present the implementation of a programmable atom-photon quantum interface, employing a single trapped $^{40}$Ca$^+$ ion and single photons. Depending on its mode of operation, the interface serves as a bi-directional atom-photon quantum-state converter, as a source of entangled atom-photon states, or as a quantum frequency converter of single photons. The interface lends itself particularly to interfacing ions with single or entangled photons in hybrid quantum networks.

We report on a single-photon-to-single-atom interface, where a single photon generated by Spontaneous Parametric Down Conversion (SPDC) is absorbed by a single trapped ion. The photon is heralded by its time-correlated partner generated in the SPDC process, while the absorption event is heralded by a single photon emitted in its course. Coincidence detection marks doubly-heralded absorption, enabling photon-to-atom quantum state transfer [1, 2]. Background in the coincidence measurement is strongly suppressed by a new method that discriminates real absorption events from dark count-induced coincidences.

We present, characterize, and apply a photonic quantum interface between the near infrared and telecom spectral regions. A singly resonant optical parametric oscillator (OPO) operated below threshold, in combination with external filters, generates high-rate ($>2.5\cdot10^6~{\rm s}^{-1}$) narrowband photon pairs ($\sim 7$ MHz bandwidth); the signal photons are tuned to resonance with an atomic transition in Ca$^+$, while the idler photons are at telecom wavelength. Quantum interface operation is demonstrated through high-rate absorption of single photons by a single trapped ion ($\sim 670~{\rm s}^{-1}$), heralded by coincident telecom photons.

Together with photon emission, the absorption of a single photon by a single atom is a fundamental process in matter-light interaction that manifests its quantum mechanical nature. As an experimentally controlled process, it is a key tool for the realization of quantum technologies. In particular, in an atom/photon based quantum network scenario, in which localized atomic particles are used as quantum information processing nodes while photons are used as carriers of quantum information between distant nodes, controlling both emission and absorption of single photons by single atoms is required for quantum coherent state mapping between the two entities. Most experimental efforts to date have focused on establishing the control of single photon emission by single trapped atoms, and the implementation of quantum networking protocols using this interaction. In this chapter, we describe experimental efforts to control the process of single photon absorption by single trapped ions. We describe a series of experiments in which polarization entangled photon pairs, generated by a spontaneous parametric down-conversion source, are coupled to a single ion. First the source is operated to generate heralded single photons, and coincidences between the absorption event of one photon of the pair and the detection of the heralding partner photon are observed. We then show how polarization control in the process is established, leading to the manifestation of the photonic polarization entanglement in the absorption process. Finally, we introduce protocols in which this interaction scheme is harnessed to perform tasks in a quantum network, such as entanglement distribution among distant nodes of the network, and we demonstrate a specific protocol for heralded, high-fidelity photon-to-atom quantum state transfer.

We investigate quantum beats in the arrival-time distribution of single photons from a single trapped $^{40}$Ca$^+$ ion, revealing their fundamentally different physical origins in two distinct experimental situations: In a $Λ$-type level scheme the interference of two 854-nm absorption amplitudes suppresses and enhances the emission process of Raman-scattered 393-nm photons; in a V-type level scheme the interference of two 393-nm emission amplitudes causes a rotation of their dipole emission pattern resulting in a temporal modulation of the detected photons. For both cases we demonstrate coherent control over the quantum-beat phase through the phases of the atomic and photonic input states, which also allows controlled adjustment of the total photon detection efficiency.

We establish heralded interaction between two remotely trapped single 40Ca+ ions through the exchange of single photons. In the sender ion, we release single photons with controlled temporal shape on the P_3/2 to D_5/2 transition and transmit them to the distant receiver ion. Individual absorption events in the receiver ion are detected by quantum jumps. For continuously generated photons, the absorption reduces significantly the lifetime of the long-lived D_5/2 state. For triggered single-photon transmission, we observe coincidence between the emission at the sender and quantum jump events at the receiver.

We report on the efficient generation of single photons, making use of spontaneous Raman scattering in a single trapped ion. The photons are collected through in-vacuum high-NA objectives. Photon frequency, polarization and temporal shape are controlled through appropriate laser parameters, allowing for photons in a pure quantum state.