Remote entanglement between a single atom and a Bose-Einstein condensate

Experimental quantum key distribution certified by Bell's theorem

Cryptographic key exchange protocols traditionally rely on computational conjectures such as the hardness of prime factorization¹ to provide security against eavesdropping attacks. Remarkably, quantum key distribution protocols such as the Bennett-Brassard scheme² provide information-theoretic security against such attacks, a much stronger form of security unreachable by classical means. However, quantum protocols realized so far are subject to a new class of attacks exploiting a mismatch between the quantum states or measurements implemented and their theoretical modelling, as demonstrated in numerous experiments^3-6. Here we present the experimental realization of a complete quantum key distribution protocol immune to these vulnerabilities, following Ekert's pioneering proposal⁷ to use entanglement to bound an adversary's information from Bell's theorem⁸. By combining theoretical developments with an improved optical fibre link generating entanglement between two trapped-ion qubits, we obtain 95,628 key bits with device-independent security^9-12 from 1.5 million Bell pairs created during eight hours of run time. We take steps to ensure that information on the measurement results is inaccessible to an eavesdropper. These measurements are performed without space-like separation. Our result shows that provably secure cryptography under general assumptions is possible with real-world devices, and paves the way for further quantum information applications based on the device-independence principle.

One decade of quantum optimal control in the chopped random basis

The chopped random basis (CRAB) ansatz for quantum optimal control has been proven to be a versatile tool to enable quantum technology applications such as quantum computing, quantum simulation, quantum sensing, and quantum communication. Its capability to encompass experimental constraints-while maintaining an access to the usually trap-free control landscape-and to switch from open-loop to closed-loop optimization (including with remote access-or RedCRAB) is contributing to the development of quantum technology on many different physical platforms. In this review article we present the development, the theoretical basis and the toolbox for this optimization algorithm, as well as an overview of the broad range of different theoretical and experimental applications that exploit this powerful technique.

Controlled Transport of Stored Light

Controlled manipulation, storage, and retrieval of quantum information is essential for quantum communication and computing. Quantum memories for light, realized with cold atomic samples as the storage medium, are prominent for their high storage efficiencies and lifetime. We demonstrate the controlled transport of stored light over 1.2 mm in such a storage system and show that the transport process and its dynamics only have a minor effect on the coherence of the storage. Extending the presented concept to longer transport distances and augmenting the number of storage sections will allow for the development of novel quantum devices such as optical racetrack memories or optical quantum registers.

High-Rate, High-Fidelity Entanglement of Qubits Across an Elementary Quantum Network

We demonstrate remote entanglement of trapped-ion qubits via a quantum-optical fiber link with fidelity and rate approaching those of local operations. Two ^{88}Sr^{+} qubits are entangled via the polarization degree of freedom of two spontaneously emitted 422 nm photons which are coupled by high-numerical-aperture lenses into single-mode optical fibers and interfere on a beam splitter. A novel geometry allows high-efficiency photon collection while maintaining unit fidelity for ion-photon entanglement. We generate heralded Bell pairs with fidelity 94% at an average rate 182 s^{-1} (success probability 2.18×10^{-4}).

Quantum Interference between Photons from an Atomic Ensemble and a Remote Atomic Ion

Many remote-entanglement protocols rely on the generation and interference of photons produced by nodes within a quantum network. Quantum networks based on heterogeneous nodes provide a versatile platform by utilizing the complementary strengths of the differing systems. Implementation of such networks is challenging, due to the disparate spectral and temporal characteristics of the photons generated by the different quantum systems. Here, we report on the observation of quantum interference between photons generated from a single ion and an atomic ensemble. The photons are produced on demand by each source located in separate buildings, in a manner suitable for quantum networking. Given these results, we analyze the feasibility of hybrid ion-ensemble remote entanglement generation.

Demonstration of slow light in rubidium vapor using single photons from a trapped ion

Practical implementation of quantum networks is likely to interface different types of quantum systems. Photonically linked hybrid systems, combining unique properties of each constituent system, have typically required sources with the same photon emission wavelength. Trapped ions and neutral atoms both have compelling properties as nodes and memories in a quantum network but have never been photonically linked because of vastly different operating wavelengths. Here, we demonstrate the first interaction between neutral atoms and photons emitted from a single trapped ion. We use slow light in ⁸⁷Rb vapor to delay photons originating from a trapped ¹³⁸Ba⁺ ion by up to 13.5 ± 0.5 ns, using quantum frequency conversion to overcome the frequency difference between the ion and neutral atoms. The delay is tunable and preserves the temporal profile of the photons. This result showcases a hybrid photonic interface usable as a synchronization tool-a critical component in any future large-scale quantum network.

Measurement-Based Entanglement of Noninteracting Bosonic Atoms

We demonstrate the ability to extract a spin-entangled state of two neutral atoms via postselection based on a measurement of their spatial configuration. Typically, entangled states of neutral atoms are engineered via atom-atom interactions. In contrast, in our Letter, we use Hong-Ou-Mandel interference to postselect a spin-singlet state after overlapping two atoms in distinct spin states on an effective beam splitter. We verify the presence of entanglement and determine a bound on the postselected fidelity of a spin-singlet state of (0.62±0.03). The experiment has direct analogy to creating polarization entanglement with single photons and hence demonstrates the potential to use protocols developed for photons to create complex quantum states with noninteracting atoms.

Photonic quantum state transfer between a cold atomic gas and a crystal

Interfacing fundamentally different quantum systems is key to building future hybrid quantum networks. Such heterogeneous networks offer capabilities superior to those of their homogeneous counterparts, as they merge the individual advantages of disparate quantum nodes in a single network architecture. However, few investigations of optical hybrid interconnections have been carried out, owing to fundamental and technological challenges such as wavelength and bandwidth matching of the interfacing photons. Here we report optical quantum interconnection of two disparate matter quantum systems with photon storage capabilities. We show that a quantum state can be transferred faithfully between a cold atomic ensemble and a rare-earth-doped crystal by means of a single photon at 1,552  nanometre telecommunication wavelength, using cascaded quantum frequency conversion. We demonstrate that quantum correlations between a photon and a single collective spin excitation in the cold atomic ensemble can be transferred to the solid-state system. We also show that single-photon time-bin qubits generated in the cold atomic ensemble can be converted, stored and retrieved from the crystal with a conditional qubit fidelity of more than 85 per cent. Our results open up the prospect of optically connecting quantum nodes with different capabilities and represent an important step towards the realization of large-scale hybrid quantum networks.

Highly-efficient quantum memory for polarization qubits in a spatially-multiplexed cold atomic ensemble

Quantum memory for flying optical qubits is a key enabler for a wide range of applications in quantum information. A critical figure of merit is the overall storage and retrieval efficiency. So far, despite the recent achievements of efficient memories for light pulses, the storage of qubits has suffered from limited efficiency. Here we report on a quantum memory for polarization qubits that combines an average conditional fidelity above 99% and efficiency around 68%, thereby demonstrating a reversible qubit mapping where more information is retrieved than lost. The qubits are encoded with weak coherent states at the single-photon level and the memory is based on electromagnetically-induced transparency in an elongated laser-cooled ensemble of cesium atoms, spatially multiplexed for dual-rail storage. This implementation preserves high optical depth on both rails, without compromise between multiplexing and storage efficiency. Our work provides an efficient node for future tests of quantum network functionalities and advanced photonic circuits.

Future quantum networks will require quantum memories with effective storage-and-retrieval capabilities. Here, the authors use electromagnetically-induced transparency in a high optical-depth, spatially-multiplexed cold atom ensemble to store and retrieve polarization qubits with high efficiency.

Optical quantum memory based on electromagnetically induced transparency

Electromagnetically induced transparency (EIT) is a promising approach to implement quantum memory in quantum communication and quantum computing applications. In this paper, following a brief overview of the main approaches to quantum memory, we provide details of the physical principle and theory of quantum memory based specifically on EIT. We discuss the key technologies for implementing quantum memory based on EIT and review important milestones, from the first experimental demonstration to current applications in quantum information systems.

Storing single photons emitted by a quantum memory on a highly excited Rydberg state

Strong interaction between two single photons is a long standing and important goal in quantum photonics. This would enable a new regime of nonlinear optics and unlock several applications in quantum information science, including photonic quantum gates and deterministic Bell-state measurements. In the context of quantum networks, it would be important to achieve interactions between single photons from independent photon pairs storable in quantum memories. So far, most experiments showing nonlinearities at the single-photon level have used weak classical input light. Here we demonstrate the storage and retrieval of a paired single photon emitted by an ensemble quantum memory in a strongly nonlinear medium based on highly excited Rydberg atoms. We show that nonclassical correlations between the two photons persist after retrieval from the Rydberg ensemble. Our result is an important step towards deterministic photon-photon interactions, and may enable deterministic Bell-state measurements with multimode quantum memories.

Efficient shortcuts to adiabatic passage for three-dimensional entanglement generation via transitionless quantum driving

We propose an effective scheme of shortcuts to adiabaticity for generating a three-dimensional entanglement of two atoms trapped in a cavity using the transitionless quantum driving (TQD) approach. The key point of this approach is to construct an effective Hamiltonian that drives the dynamics of a system along instantaneous eigenstates of a reference Hamiltonian to reproduce the same final state as that of an adiabatic process within a much shorter time. In this paper, the shortcuts to adiabatic passage are constructed by introducing two auxiliary excited levels in each atom and applying extra cavity modes and classical fields to drive the relevant transitions. Thereby, the three-dimensional entanglement is obtained with a faster rate than that in the adiabatic passage. Moreover, the influences of atomic spontaneous emission and photon loss on the fidelity are discussed by numerical simulation. The results show that the speed of entanglement implementation is greatly improved by the use of adiabatic shortcuts and that this entanglement implementation is robust against decoherence. This will be beneficial to the preparation of high-dimensional entanglement in experiment and provides the necessary conditions for the application of high-dimensional entangled states in quantum information processing.

Wavelength-tunable sources of entangled photons interfaced with atomic vapours

The prospect of using the quantum nature of light for secure communication keeps spurring the search and investigation of suitable sources of entangled photons. A single semiconductor quantum dot is one of the most attractive, as it can generate indistinguishable entangled photons deterministically and is compatible with current photonic-integration technologies. However, the lack of control over the energy of the entangled photons is hampering the exploitation of dissimilar quantum dots in protocols requiring the teleportation of quantum entanglement over remote locations. Here we introduce quantum dot-based sources of polarization-entangled photons whose energy can be tuned via three-directional strain engineering without degrading the degree of entanglement of the photon pairs. As a test-bench for quantum communication, we interface quantum dots with clouds of atomic vapours, and we demonstrate slow-entangled photons from a single quantum emitter. These results pave the way towards the implementation of hybrid quantum networks where entanglement is distributed among distant parties using optoelectronic devices.

Zero-Area Single-Photon Pulses

Broadband single photons are usually considered not to couple efficiently to atomic gases because of the large mismatch in bandwidth. Contrary to this intuitive picture, here we demonstrate that the interaction of ultrashort single photons with a dense resonant atomic sample deeply modifies the temporal shape of their wave packet mode without degrading their nonclassical character, and effectively generates zero-area single-photon pulses. This is a clear signature of strong transient coupling between single broadband (THz-level) light quanta and atoms, with intriguing fundamental implications and possible new applications to the storage of quantum information.

Adiabatic passage for three-dimensional entanglement generation through quantum Zeno dynamics

We propose an adiabatic passage approach to generate two atoms three-dimensional entanglement with the help of quantum Zeno dynamics in a time-dependent interacting field. The atoms are trapped in two spatially separated cavities connected by a fiber, so that the individual addressing is needless. Because the scheme is based on the resonant interaction, the time required to generate entanglement is greatly shortened. Since the fields remain in vacuum state and all the atoms are in the ground states, the losses due to the excitation of photons and the spontaneous transition of atoms are suppressed efficiently compared with the dispersive protocols. Numerical simulation results show that the scheme is robust against the decoherences caused by the cavity decay and atomic spontaneous emission. Additionally, the scheme can be generalized to generate N-atom three-dimensional entanglement and high-dimensional entanglement for two spatially separated atoms.

Proposal for the creation and optical detection of spin cat states in Bose-Einstein condensates

We propose a method to create "spin cat states," i.e., macroscopic superpositions of coherent spin states, in Bose-Einstein condensates using the Kerr nonlinearity due to atomic collisions. Based on a detailed study of atom loss, we conclude that cat sizes of hundreds of atoms should be realistic. The existence of the spin cat states can be demonstrated by optical readout. Our analysis also includes the effects of higher-order nonlinearities, atom number fluctuations, and limited readout efficiency.

Coherent all-optical control of ultracold atoms arrays in permanent magnetic traps

We propose a hybrid architecture for quantum information processing based on magnetically trapped ultracold atoms coupled via optical fields. The ultracold atoms, which can be either Bose-Einstein condensates or ensembles, are trapped in permanent magnetic traps and are placed in microcavities, connected by silica based waveguides on an atom chip structure. At each trapping center, the ultracold atoms form spin coherent states, serving as a quantum memory. An all-optical scheme is used to initialize, measure and perform a universal set of quantum gates on the single and two spin-coherent states where entanglement can be generated addressably between spatially separated trapped ultracold atoms. This allows for universal quantum operations on the spin coherent state quantum memories. We give detailed derivations of the composite cavity system mediated by a silica waveguide as well as the control scheme. Estimates for the necessary experimental conditions for a working hybrid device are given.

Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy

Long-lived and high-fidelity memory for a photonic polarization qubit (PPQ) is crucial for constructing quantum networks. We present a millisecond storage system based on electromagnetically induced transparency, in which a moderate magnetic field is applied on a cold-atom cloud to lift Zeeman degeneracy and, thus, the PPQ states are stored as two magnetic-field-insensitive spin waves. Especially, the influence of magnetic-field-sensitive spin waves on the storage performances is almost totally avoided. The measured average fidelities of the polarization states are 98.6% at 200  μs and 78.4% at 4.5 ms, respectively.

Phase measurement of fast light pulse in electromagnetically induced absorption

We report the phase measurement of a fast light pulse in electromagnetically induced absorption (EIA) of the 5S₁/₂ (F = 2)-5P₃/₂ (F' = 3) transition of ⁸⁷Rb atoms. Using a beat-note interferometer method, a stable measurement without phase dithering of the phase of the probe pulse before and after it has passed through the EIA medium was achieved. Comparing the phases of the light pulse in air and that of the fast light pulse though the EIA medium, the phase of the fast light pulse at EIA resonance was not shifted and maintained to be the same as that of the free-space light pulse. The classical fidelity of the fast light pulse according to the advancement of the group velocity by adjusting the atomic density was estimated to be more than 97%.

Generation of three-dimensional entangled state between a single atom and a Bose-Einstein condensate via adiabatic passage

Inspired by a recently experiment by M. Lettner et al. [Phys. Rev. Lett. 106, 210503 (2011)], we propose a robust scheme to prepare three-dimensional entanglement state between a single atom and a Bose-Einstein condensate (BEC) via stimulated Raman adiabatic passage (STIRAP) technique. The atomic spontaneous radiation, the cavity decay, and the fiber loss are efficiently suppressed by the engineering adiabatic passage. Our strictly numerical simulation shows our proposal is good enough to demonstrate the generation of three-dimensional entanglement with high fidelity and within the current experimental technology.

Quantum storage of heralded polarization qubits in birefringent and anisotropically absorbing materials

Storage of quantum information encoded into heralded single photons is an essential constituent of long-distance quantum communication based on quantum repeaters and of optical quantum information processing. The storage of photonic polarization qubits is, however, difficult because many materials are birefringent and have polarization-dependent absorption. Here we present a simple scheme that eliminates these polarization effects, and we demonstrate it by storing heralded polarization qubits into a solid-state quantum memory. The quantum memory is implemented with a biaxial yttrium orthosilicate (Y2SiO5) crystal doped with rare-earth ions. Heralded single photons generated from a filtered spontaneous parametric down-conversion source are stored, and quantum state tomography of the retrieved polarization state reveals an average fidelity of 97.5±0.4%, which is significantly higher than what is achievable with a measure-and-prepare strategy.

Realization of reliable solid-state quantum memory for photonic polarization qubit

Faithfully storing an unknown quantum light state is essential to advanced quantum communication and distributed quantum computation applications. The required quantum memory must have high fidelity to improve the performance of a quantum network. Here we report the reversible transfer of photonic polarization states into collective atomic excitation in a compact solid-state device. The quantum memory is based on an atomic frequency comb (AFC) in rare-earth ion-doped crystals. We obtain up to 0.999 process fidelity for the storage and retrieval process of single-photon-level coherent pulse. This reliable quantum memory is a crucial step toward quantum networks based on solid-state devices.