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The fermionic Hubbard model (FHM)1 describes a wide range of physical phenomena resulting from strong electron–electron correlations, including conjectured mechanisms for unconventional superconductivity. Resolving its low-temperature physics is, however, challenging theoretically or numerically. Ultracold fermions in optical lattices2,3 provide a clean and well-controlled platform offering a path to simulate the FHM. Doping the antiferromagnetic ground state of a FHM simulator at half-filling is expected to yield various exotic phases, including stripe order4, pseudogap5, and d-wave superfluid6, offering valuable insights into high-temperature superconductivity7–9. Although the observation of antiferromagnetic correlations over short10 and extended distances11 has been obtained, the antiferromagnetic phase has yet to be realized as it requires sufficiently low temperatures in a large and uniform quantum simulator. Here we report the observation of the antiferromagnetic phase transition in a three-dimensional fermionic Hubbard system comprising lithium-6 atoms in a uniform optical lattice with approximately 800,000 sites. When the interaction strength, temperature and doping concentration are finely tuned to approach their respective critical values, a sharp increase in the spin structure factor is observed. These observations can be well described by a power-law divergence, with a critical exponent of 1.396 from the Heisenberg universality class12. At half-filling and with optimal interaction strength, the measured spin structure factor reaches 123(8), signifying the establishment of an antiferromagnetic phase. Our results provide opportunities for exploring the low-temperature phase diagram of the FHM.Antiferromagnetic phase transition is observed in a three-dimensional fermionic Hubbard system comprising lithium-6 atoms in a uniform optical lattice with approximately 800,000 sites. [ABSTRACT FROM AUTHOR]

A quantum internet that connects remote quantum processors.sup.1,2 should enable a number of revolutionary applications such as distributed quantum computing. Its realization will rely on entanglement of remote quantum memories over long distances. Despite enormous progress.sup.3-12, at present the maximal physical separation achieved between two nodes is 1.3 kilometres.sup.10, and challenges for longer distances remain. Here we demonstrate entanglement of two atomic ensembles in one laboratory via photon transmission through city-scale optical fibres. The atomic ensembles function as quantum memories that store quantum states. We use cavity enhancement to efficiently create atom-photon entanglement.sup.13-15 and we use quantum frequency conversion.sup.16 to shift the atomic wavelength to telecommunications wavelengths. We realize entanglement over 22 kilometres of field-deployed fibres via two-photon interference.sup.17,18 and entanglement over 50 kilometres of coiled fibres via single-photon interference.sup.19. Our experiment could be extended to nodes physically separated by similar distances, which would thus form a functional segment of the atomic quantum network, paving the way towards establishing atomic entanglement over many nodes and over much longer distances. The entanglement of two atomic-ensemble quantum memories via optical fibres, enabled by the use of cavity enhancement and quantum frequency conversion, is demonstrated over dozens of kilometres., Author(s): Yong Yu [sup.1] [sup.2] [sup.3] , Fei Ma [sup.1] [sup.2] [sup.3] [sup.4] , Xi-Yu Luo [sup.1] [sup.2] [sup.3] , Bo Jing [sup.1] [sup.2] [sup.3] , Peng-Fei Sun [sup.1] [sup.2] [...]

Towards realizing the future quantum internet1,2, a pivotal milestone entails the transition from two-node proof-of-principle experiments conducted in laboratories to comprehensive multi-node set-ups on large scales. Here we report the creation of memory–memory entanglement in a multi-node quantum network over a metropolitan area. We use three independent memory nodes, each of which is equipped with an atomic ensemble quantum memory3 that has telecom conversion, together with a photonic server where detection of a single photon heralds the success of entanglement generation. The memory nodes are maximally separated apart for 12.5 kilometres. We actively stabilize the phase variance owing to fibre links and control lasers. We demonstrate concurrent entanglement generation between any two memory nodes. The memory lifetime is longer than the round-trip communication time. Our work provides a metropolitan-scale testbed for the evaluation and exploration of multi-node quantum network protocols and starts a stage of quantum internet research.A metropolitan-area quantum network based on the generation of pairwise entanglement is formed by three atomic quantum memories connected to a central photonic server. [ABSTRACT FROM AUTHOR]

Author(s): Ji-Gang Ren [1, 2]; Ping Xu [1, 2]; Hai-Lin Yong [1, 2]; Liang Zhang [2, 3]; Sheng-Kai Liao [1, 2]; Juan Yin [1, 2]; Wei-Yue Liu [1, 2]; Wen-Qi [...]

Quantum key distribution (QKD) uses individual light quanta in quantum superposition states to guarantee unconditional communication security between distant parties. However, the distance over which QKD is achievable has been limited to a few hundred kilometres, owing to the channel loss that occurs when using optical fibres or terrestrial free space that exponentially reduces the photon transmission rate. Satellite-based QKD has the potential to help to establish a global-scale quantum network, owing to the negligible photon loss and decoherence experienced in empty space. Here we report the development and launch of a low-Earth-orbit satellite for implementing decoy-state QKDa form of QKD that uses weak coherent pulses at high channel loss and is secure because photon-number-splitting eavesdropping can be detected. We achieve a kilohertz key rate from the satellite to the ground over a distance of up to 1,200 kilometres. This key rate is around 20 orders of magnitudes greater than that expected using an optical fibre of the same length. The establishment of a reliable and efficient space-to-ground link for quantum-state transmission paves the way to global-scale quantum networks., Author(s): Sheng-Kai Liao [1, 2]; Wen-Qi Cai [1, 2]; Wei-Yue Liu [1, 2]; Liang Zhang [2, 3]; Yang Li [1, 2]; Ji-Gang Ren [1, 2]; Juan Yin [1, 2]; Qi [...]

Quantum teleportation (1) provides a 'disembodied' way to transfer quantum states from one object to another at a distant location, assisted by previously shared entangled states and a classical communication channel. As well as being of fundamental interest, teleportation has been recognized as an important element in long-distance quantum communication (2), distributed quantum networks (3) and measurement-based quantum computation (4, 5). There have been numerous demonstrations of teleportation in different physical systems such as photons (6-8), atoms (9), ions (10, 11), electrons (12) and superconducting circuits (13). All the previous experiments were limited to the teleportation of one degree of freedom only. However, a single quantum particle can naturally possess various degrees of freedom--internal and external--and with coherent coupling among them. A fundamental open challenge is to teleport multiple degrees of freedom simultaneously, which is necessary to describe a quantum particle fully and, therefore, to teleport it intact. Here we demonstrate quantum teleportation of the composite quantum states of a single photon encoded in both spin and orbital angular momentum. We use photon pairs entangled in both degrees of freedom (that is, hyper-entangled) as the quantum channel for teleportation, and develop a method to project and discriminate hyper-entangled Bell states by exploiting probabilistic quantum non-demolition measurement, which can be extended to more degrees of freedom. We verify the teleportation for both spin-orbit product states and hybrid entangled states, and achieve a teleportation fidelity ranging from 0.57 to 0.68, above the classical limit. Our work is a step towards the teleportation of more complex quantum systems, and demonstrates an increase in our technical control of scalable quantum technologies., Quantum teleportation is a linear operation applied to quantum states, and so teleporting multiple degrees of freedom (DoFs) should be possible in theory (1). Suppose Alice wishes to teleport to [...]

Transferring an unknown quantum state over arbitrary distances is essential for large-scale quantum communication and distributed quantum networks. It can be achieved with the help of long-distance quantum teleportation (1,2) [...]

Scalable quantum computing can be achieved only if quantum bits are manipulated in a fault-tolerant fashion. Topological error correction--a method that combines topological quantum computation with quantum error correction--has the highest known tolerable error rate for a local architecture. The technique makes use of cluster states with topological properties and requires only nearest-neighbour interactions. Here we report the experimental demonstration of topological error correction with an eight-photon cluster state. We show that a correlation can be protected against a single error on any quantum bit. Also, when all quantum bits are simultaneously subjected to errors with equal probability, the effective error rate can be significantly reduced. Our work demonstrates the viability of topological error correction for fault-tolerant quantum information processing., Quantum computers exploit the laws of quantum mechanics and can solve many problems exponentially more efficiently than their classical counterparts (1,3). However, in the laboratory the ubiquitous decoherence of quantum [...]

Quantum communication is a method that offers efficient and secure ways for the exchange of information in a network. Large-scale quantum communication (1,4) (of the order of 100 km) has [...]

Author(s): Zhi Zhao [1]; Yu-Ao Chen [1]; An-Ning Zhang [1]; Tao Yang [1]; Hans J. Briegel [2]; Jian-Wei Pan (corresponding author) [1, 3] Quantum-mechanical entanglement of three [1, 2] or [...]

Author(s): Philip Walther [1]; Jian-Wei Pan [1, 3]; Markus Aspelmeyer [1]; Rupert Ursin [1]; Sara Gasparoni [1]; Anton Zeilinger (corresponding author) [1, 2] Superposition is one of the most distinctive [...]

Author(s): Jian-Wei Pan (corresponding author); Sara Gasparoni; Rupert Ursin; Gregor Weihs; Anton Zeilinger (corresponding author) Distribution of entangled states between distant locations is essential for quantum communication [1, 2, 3] [...]

Author(s): Jian-Wei Pan (corresponding author); Sara Gasparoni; Markus Aspelmeyer; Thomas Jennewein; Anton Zeilinger Quantum teleportation [1] is central to quantum communication, and plays an important role in a number of [...]

Author(s): Jian-Wei Pan; Christoph Simon [1]; Časlav Brukner; Anton Zeilinger (corresponding author) The distribution of entangled states between distant locations will be essential for the future large-scale realization of quantum [...]

Author(s): Jian-Wei Pan [1]; Dik Bouwmeester [2]; Matthew Daniell [1]; Harald Weinfurter [3]; Anton Zeilinger (corresponding author) [1] Bell's theorem [1] states that certain statistical correlations predicted by quantum physics [...]

Ultracold assembly of diatomic molecules has enabled great advances in controlled chemistry, ultracold chemical physics and quantum simulation with molecules1–3. Extending the ultracold association to triatomic molecules will offer many new research opportunities and challenges in these fields. A possible approach is to form triatomic molecules in a mixture of ultracold atoms and diatomic molecules by using a Feshbach resonance between them4,5. Although ultracold atom–diatomic-molecule Feshbach resonances have been observed recently6,7, using these resonances to form triatomic molecules remains challenging. Here we report on evidence of the association of triatomic molecules near the Feshbach resonance between 23Na40K molecules in the rovibrational ground state and 40K atoms. We apply a radio-frequency pulse to drive the free-bound transition in ultracold mixtures of 23Na40K and 40K and monitor the loss of 23Na40K molecules. The association of triatomic molecules manifests itself as an additional loss feature in the radio-frequency spectra, which can be distinguished from the atomic loss feature. The observation that the distance between the association feature and the atomic transition changes with the magnetic field provides strong evidence for the formation of triatomic molecules. The binding energy of the triatomic molecules is estimated from the measurements. Our work contributes to the understanding of the complex ultracold atom–molecule Feshbach resonances and may open up an avenue towards the preparation and control of ultracold triatomic molecules.Evidence is presented for the association of triatomic molecules near the Feshbach resonance in an ultracold gas comprising a mixture of 23Na40K molecules and 40K atoms, along with an estimation of the binding energy of the triatomic molecules. [ABSTRACT FROM AUTHOR]

Superposition is one of the most distinctive features of quantum theory and has been demonstrated in numerous single-particle interference experiments. Quantum entanglement, the coherent superposition of states in multi-particle systems, yields more complex phenomena. One important type of multi-particle experiment uses path-entangled number states, which exhibit pure higher-order interference and the potential for applications in metrology and imaging; these include quantum interferometry and spectroscopy with phase sensitivity at the Heisenberg limit, or quantum lithography beyond the classical diffraction limit. It has been generally understood that in optical implementations of such schemes, lower-order interference effects always decrease the overall performance at higher particle numbers. Such experiments have therefore been limited to two photons. Here we overcome this limitation, demonstrating a four-photon interferometer based on linear optics. We observe interference fringes with a periodicity of one-quarter of the single-photon wavelength, confirming the presence of a four-particle mode-entangled state. We anticipate that this scheme should be extendable to arbitrary photon numbers, holding promise for realizable applications with entanglement-enhanced performance. [ABSTRACT FROM AUTHOR]