Observation and quantification of the pseudogap in unitary Fermi gases.

The microscopic origin of high-temperature superconductivity in cuprates remains unknown. It is widely believed that substantial progress could be achieved by better understanding of the pseudogap phase, a normal non-superconducting state of cuprates1,2. In particular, a central issue is whether the pseudogap could originate from strong pairing fluctuations3. Unitary Fermi gases4,5, in which the pseudogap-if it exists-necessarily arises from many-body pairing, offer ideal quantum simulators to address this question. Here we report the observation of a pair-fluctuation-driven pseudogap in homogeneous unitary Fermi gases of lithium-6 atoms, by precisely measuring the fermion spectral function through momentum-resolved microwave spectroscopy and without spurious effects from final-state interactions. The temperature dependence of the pairing gap, inverse pair lifetime and single-particle scattering rate are quantitatively determined by analysing the spectra. We find a large pseudogap above the superfluid transition temperature. The inverse pair lifetime exhibits a thermally activated exponential behaviour, uncovering the microscopic virtual pair breaking and recombination mechanism. The obtained large, temperature-independent single-particle scattering rate is comparable with that set by the Planckian limit6. Our findings quantitatively characterize the pseudogap in strongly interacting Fermi gases and they lend support for the role of preformed pairing as a precursor to superfluidity.

Antiferromagnetic phase transition in a 3D fermionic Hubbard model.

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.

Creation of memory-memory entanglement in a metropolitan quantum network.

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.

Generation of genuine entanglement up to 51 superconducting qubits.

Scalable generation of genuine multipartite entanglement with an increasing number of qubits is important for both fundamental interest and practical use in quantum-information technologies1,2. On the one hand, multipartite entanglement shows a strong contradiction between the prediction of quantum mechanics and local realization and can be used for the study of quantum-to-classical transition3,4. On the other hand, realizing large-scale entanglement is a benchmark for the quality and controllability of the quantum system and is essential for realizing universal quantum computing5-8. However, scalable generation of genuine multipartite entanglement on a state-of-the-art quantum device can be challenging, requiring accurate quantum gates and efficient verification protocols. Here we show a scalable approach for preparing and verifying intermediate-scale genuine entanglement on a 66-qubit superconducting quantum processor. We used high-fidelity parallel quantum gates and optimized the fidelitites of parallel single- and two-qubit gates to be 99.91% and 99.05%, respectively. With efficient randomized fidelity estimation9, we realized 51-qubit one-dimensional and 30-qubit two-dimensional cluster states and achieved fidelities of 0.637 ± 0.030 and 0.671 ± 0.006, respectively. On the basis of high-fidelity cluster states, we further show a proof-of-principle realization of measurement-based variational quantum eigensolver10 for perturbed planar codes. Our work provides a feasible approach for preparing and verifying entanglement with a few hundred qubits, enabling medium-scale quantum computing with superconducting quantum systems.

Evidence for the association of triatomic molecules in ultracold 23Na40K + 40K mixtures.

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.

Free-space dissemination of time and frequency with 10-19 instability over 113 km.

Networks of optical clocks find applications in precise navigation1,2, in efforts to redefine the fundamental unit of the 'second'3-6 and in gravitational tests7. As the frequency instability for state-of-the-art optical clocks has reached the 10-19 level8,9, the vision of a global-scale optical network that achieves comparable performances requires the dissemination of time and frequency over a long-distance free-space link with a similar instability of 10-19. However, previous attempts at free-space dissemination of time and frequency at high precision did not extend beyond dozens of kilometres10,11. Here we report time-frequency dissemination with an offset of 6.3 × 10-20 ± 3.4 × 10-19 and an instability of less than 4 × 10-19 at 10,000 s through a free-space link of 113 km. Key technologies essential to this achievement include the deployment of high-power frequency combs, high-stability and high-efficiency optical transceiver systems and efficient linear optical sampling. We observe that the stability we have reached is retained for channel losses up to 89 dB. The technique we report can not only be directly used in ground-based applications, but could also lay the groundwork for future satellite time-frequency dissemination.

An integrated space-to-ground quantum communication network over 4,600 kilometres.

Quantum key distribution (QKD)1,2 has the potential to enable secure communication and information transfer3. In the laboratory, the feasibility of point-to-point QKD is evident from the early proof-of-concept demonstration in the laboratory over 32 centimetres4; this distance was later extended to the 100-kilometre scale5,6 with decoy-state QKD and more recently to the 500-kilometre scale7-10 with measurement-device-independent QKD. Several small-scale QKD networks have also been tested outside the laboratory11-14. However, a global QKD network requires a practically (not just theoretically) secure and reliable QKD network that can be used by a large number of users distributed over a wide area15. Quantum repeaters16,17 could in principle provide a viable option for such a global network, but they cannot be deployed using current technology18. Here we demonstrate an integrated space-to-ground quantum communication network that combines a large-scale fibre network of more than 700 fibre QKD links and two high-speed satellite-to-ground free-space QKD links. Using a trusted relay structure, the fibre network on the ground covers more than 2,000 kilometres, provides practical security against the imperfections of realistic devices, and maintains long-term reliability and stability. The satellite-to-ground QKD achieves an average secret-key rate of 47.8 kilobits per second for a typical satellite pass-more than 40 times higher than achieved previously. Moreover, its channel loss is comparable to that between a geostationary satellite and the ground, making the construction of more versatile and ultralong quantum links via geosynchronous satellites feasible. Finally, by integrating the fibre and free-space QKD links, the QKD network is extended to a remote node more than 2,600 kilometres away, enabling any user in the network to communicate with any other, up to a total distance of 4,600 kilometres.

Observation of gauge invariance in a 71-site Bose-Hubbard quantum simulator.

The modern description of elementary particles, as formulated in the standard model of particle physics, is built on gauge theories1. Gauge theories implement fundamental laws of physics by local symmetry constraints. For example, in quantum electrodynamics Gauss's law introduces an intrinsic local relation between charged matter and electromagnetic fields, which protects many salient physical properties, including massless photons and a long-ranged Coulomb law. Solving gauge theories using classical computers is an extremely arduous task2, which has stimulated an effort to simulate gauge-theory dynamics in microscopically engineered quantum devices3-6. Previous achievements implemented density-dependent Peierls phases without defining a local symmetry7,8, realized mappings onto effective models to integrate out either matter or electric fields9-12, or were limited to very small systems13-16. However, the essential gauge symmetry has not been observed experimentally. Here we report the quantum simulation of an extended U(1) lattice gauge theory, and experimentally quantify the gauge invariance in a many-body system comprising matter and gauge fields. These fields are realized in defect-free arrays of bosonic atoms in an optical superlattice of 71 sites. We demonstrate full tunability of the model parameters and benchmark the matter-gauge interactions by sweeping across a quantum phase transition. Using high-fidelity manipulation techniques, we measure the degree to which Gauss's law is violated by extracting probabilities of locally gauge-invariant states from correlated atom occupations. Our work provides a way to explore gauge symmetry in the interplay of fundamental particles using controllable large-scale quantum simulators.

Entanglement of two quantum memories via fibres over dozens of kilometres.

A quantum internet that connects remote quantum processors1,2 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 progress3-12, at present the maximal physical separation achieved between two nodes is 1.3 kilometres10, 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 entanglement13-15 and we use quantum frequency conversion16 to shift the atomic wavelength to telecommunications wavelengths. We realize entanglement over 22 kilometres of field-deployed fibres via two-photon interference17,18 and entanglement over 50 kilometres of coiled fibres via single-photon interference19. 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.

Entanglement-based secure quantum cryptography over 1,120 kilometres.

Quantum key distribution (QKD)1-3 is a theoretically secure way of sharing secret keys between remote users. It has been demonstrated in a laboratory over a coiled optical fibre up to 404 kilometres long4-7. In the field, point-to-point QKD has been achieved from a satellite to a ground station up to 1,200 kilometres away8-10. However, real-world QKD-based cryptography targets physically separated users on the Earth, for which the maximum distance has been about 100 kilometres11,12. The use of trusted relays can extend these distances from across a typical metropolitan area13-16 to intercity17 and even intercontinental distances18. However, relays pose security risks, which can be avoided by using entanglement-based QKD, which has inherent source-independent security19,20. Long-distance entanglement distribution can be realized using quantum repeaters21, but the related technology is still immature for practical implementations22. The obvious alternative for extending the range of quantum communication without compromising its security is satellite-based QKD, but so far satellite-based entanglement distribution has not been efficient23 enough to support QKD. Here we demonstrate entanglement-based QKD between two ground stations separated by 1,120 kilometres at a finite secret-key rate of 0.12 bits per second, without the need for trusted relays. Entangled photon pairs were distributed via two bidirectional downlinks from the Micius satellite to two ground observatories in Delingha and Nanshan in China. The development of a high-efficiency telescope and follow-up optics crucially improved the link efficiency. The generated keys are secure for realistic devices, because our ground receivers were carefully designed to guarantee fair sampling and immunity to all known side channels24,25. Our method not only increases the secure distance on the ground tenfold but also increases the practical security of QKD to an unprecedented level.

Solving independent set problems with photonic quantum circuits.

An independent set (IS) is a set of vertices in a graph such that no edge connects any two vertices. In adiabatic quantum computation [E. Farhi, et al., Science 292, 472-475 (2001); A. Das, B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061-1081 (2008)], a given graph G(V, E) can be naturally mapped onto a many-body Hamiltonian [Formula: see text], with edges [Formula: see text] being the two-body interactions between adjacent vertices [Formula: see text]. Thus, solving the IS problem is equivalent to finding all the computational basis ground states of [Formula: see text]. Very recently, non-Abelian adiabatic mixing (NAAM) has been proposed to address this task, exploiting an emergent non-Abelian gauge symmetry of [Formula: see text] [B. Wu, H. Yu, F. Wilczek, Phys. Rev. A 101, 012318 (2020)]. Here, we solve a representative IS problem [Formula: see text] by simulating the NAAM digitally using a linear optical quantum network, consisting of three C-Phase gates, four deterministic two-qubit gate arrays (DGA), and ten single rotation gates. The maximum IS has been successfully identified with sufficient Trotterization steps and a carefully chosen evolution path. Remarkably, we find IS with a total probability of 0.875(16), among which the nontrivial ones have a considerable weight of about 31.4%. Our experiment demonstrates the potential advantage of NAAM for solving IS-equivalent problems.

Device-independent quantum randomness-enhanced zero-knowledge proof.

Zero-knowledge proof (ZKP) is a fundamental cryptographic primitive that allows a prover to convince a verifier of the validity of a statement without leaking any further information. As an efficient variant of ZKP, noninteractive zero-knowledge proof (NIZKP) adopting the Fiat-Shamir heuristic is essential to a wide spectrum of applications, such as federated learning, blockchain, and social networks. However, the heuristic is typically built upon the random oracle model that makes ideal assumptions about hash functions, which does not hold in reality and thus undermines the security of the protocol. Here, we present a quantum solution to the problem. Instead of resorting to a random oracle model, we implement a quantum randomness service. This service generates random numbers certified by the loophole-free Bell test and delivers them with postquantum cryptography (PQC) authentication. By employing this service, we conceive and implement NIZKP of the three-coloring problem. By bridging together three prominent research themes, quantum nonlocality, PQC, and ZKP, we anticipate this work to inspire more innovative applications that combine quantum information science and the cryptography field.

Observation of Photoassociation Resonances in Ultracold Atom-Molecule Collisions.

We report on the observation of photoassociation resonances in ultracold collisions between ^{23}Na^{40}K molecules and ^{40}K atoms. We perform photoassociation in a long-wavelength optical dipole trap to form deeply bound triatomic molecules in electronically excited states. The atom-molecule Feshbach resonance is used to enhance the free-bound Franck-Condon overlap. The photoassociation into well-defined quantum states of excited triatomic molecules is identified by observing resonantly enhanced loss features. These loss features depend on the polarization of the photoassociation lasers, allowing us to assign rotational quantum numbers. The observation of ultracold atom-molecule photoassociation resonances paves the way toward preparing ground-state triatomic molecules, provides a new high-resolution spectroscopy technique for polyatomic molecules, and is also important to atom-molecule Feshbach resonances.

Single-Shot Readout of a Nuclear Spin in Silicon Carbide.

Solid-state qubits with a photonic interface is very promising for quantum networks. Color centers in silicon carbide have shown excellent optical and spin coherence, even when integrated with membranes and nanostructures. Additionally, nuclear spins coupled with electron spins can serve as long-lived quantum memories. Pioneering work previously has realized the initialization of a single nuclear spin and demonstrated its entanglement with an electron spin. In this Letter, we report the first realization of single-shot readout for a nuclear spin in SiC. We obtain a deterministic nuclear spin initialization and readout fidelity of 94.95% with a measurement duration of 1 ms. With a dual-step readout scheme, we obtain a readout fidelity as high as 99.03% within 0.28 ms by sacrificing the success efficiency. Our Letter complements the experimental toolbox of harnessing both electron and nuclear spins in SiC for future quantum networks.

Twin-Field Quantum Key Distribution with Local Frequency Reference.

Twin-field quantum key distribution (TFQKD) overcomes the linear rate-loss limit, which promises a boost of secure key rate over long distance. However, the complexity of eliminating the frequency differences between the independent laser sources hinders its practical application. We analyzed and determined the frequency stability requirements for implementing TFQKD using frequency-stabilized lasers. Based on this analysis, we proposed and demonstrated a simple and practical approach that utilizes the saturated absorption spectroscopy of acetylene as an absolute reference, eliminating the need for fast frequency locking to achieve TFQKD. Adopting the 4-intensity sending-or-not-sending TFQKD protocol, we experimentally demonstrated the TFQKD over 502, 301, and 201 km ultralow-loss optical fiber, respectively. We expect this high-performance scheme will find widespread usage in future intercity and free-space quantum communication networks.

Non-Line-of-Sight Imaging and Vibrometry Using a Comb-Calibrated Coherent Sensor.

Non-line-of-sight (NLOS) imaging has the ability to reconstruct hidden objects, allowing a wide range of applications. Existing NLOS systems rely on pulsed lasers and time-resolved single-photon detectors to capture the information encoded in the time of flight of scattered photons. Despite remarkable advances, the pulsed time-of-flight LIDAR approach has limited temporal resolution and struggles to detect the frequency-associated information directly. Here, we propose and demonstrate the coherent scheme-frequency-modulated continuous wave calibrated by optical frequency comb-for high-resolution NLOS imaging, velocimetry, and vibrometry. Our comb-calibrated coherent sensor presents a system temporal resolution at subpicosecond and its superior signal-to-noise ratio permits NLOS imaging of complex scenes under strong ambient light. We show the capability of NLOS localization and 3D imaging at submillimeter scale and demonstrate NLOS vibrometry sensing at an accuracy of dozen Hertz. Our approach unlocks the coherent LIDAR techniques for widespread use in imaging science and optical sensing.

Transition from Flat-Band Localization to Anderson Localization in a One-Dimensional Tasaki Lattice.

We report an extensive experimental investigation on the transition from flat-band localization (FBL) to Anderson localization (AL) in a one-dimensional synthetic lattice in the momentum dimension. By driving multiple Bragg processes between designated momentum states, an effective one-dimensional Tasaki lattice is implemented with highly tunable parameters, including nearest-neighbor and next-nearest-neighbor coupling coefficients and onsite energy potentials. With that, a flat-band localization phase is realized and demonstrated via the evolution dynamics of the particle population over different momentum states. The localization effect is undermined when a moderate disorder is introduced to the onsite potential and restored under a strong disorder. We find clear signatures of the FBL-AL transition in the density profile evolution, the inverse participation ratio, and the von Neumann entropy, where good agreement is obtained with theoretical predictions.

Experimental Generation of Spin-Photon Entanglement in Silicon Carbide.

A solid-state approach for quantum networks is advantageous, as it allows the integration of nanophotonics to enhance the photon emission and the utilization of weakly coupled nuclear spins for long-lived storage. Silicon carbide, specifically point defects within it, shows great promise in this regard due to the easy of availability and well-established nanofabrication techniques. Despite of remarkable progresses made, achieving spin-photon entanglement remains a crucial aspect to be realized. In this Letter, we experimentally generate entanglement between a silicon vacancy defect in silicon carbide and a scattered single photon in the zero-phonon line. The spin state is measured by detecting photons scattered in the phonon sideband. The photonic qubit is encoded in the time-bin degree of freedom and measured using an unbalanced Mach-Zehnder interferometer. Photonic correlations not only reveal the quality of the entanglement but also verify the deterministic nature of the entanglement creation process. By harnessing two pairs of such spin-photon entanglement, it becomes straightforward to entangle remote quantum nodes at long distance.

Heralded Three-Photon Entanglement from a Single-Photon Source on a Photonic Chip.

In the quest to build general-purpose photonic quantum computers, fusion-based quantum computation has risen to prominence as a promising strategy. This model allows a ballistic construction of large cluster states which are universal for quantum computation, in a scalable and loss-tolerant way without feed forward, by fusing many small n-photon entangled resource states. However, a key obstacle to this architecture lies in efficiently generating the required essential resource states on photonic chips. One such critical seed state that has not yet been achieved is the heralded three-photon Greenberger-Horne-Zeilinger (3-GHZ) state. Here, we address this elementary resource gap, by reporting the first experimental realization of a heralded 3-GHZ state. Our implementation employs a low-loss and fully programmable photonic chip that manipulates six indistinguishable single photons of wavelengths in the telecommunication regime. Conditional on the heralding detection, we obtain the desired 3-GHZ state with a fidelity 0.573±0.024. Our Letter marks an important step for the future fault-tolerant photonic quantum computing, leading to the acceleration of building a large-scale optical quantum computer.

Device-independent quantum random-number generation.

Randomness is important for many information processing applications, including numerical modelling and cryptography1,2. Device-independent quantum random-number generation (DIQRNG)3,4 based on the loophole-free violation of a Bell inequality produces genuine, unpredictable randomness without requiring any assumptions about the inner workings of the devices, and is therefore an ultimate goal in the field of quantum information science5-7. Previously reported experimental demonstrations of DIQRNG8,9 were not provably secure against the most general adversaries or did not close the 'locality' loophole of the Bell test. Here we present DIQRNG that is secure against quantum and classical adversaries10-12. We use state-of-the-art quantum optical technology to create, modulate and detect entangled photon pairs, achieving an efficiency of more than 78 per cent from creation to detection at a distance of about 200 metres that greatly exceeds the threshold for closing the 'detection' loophole of the Bell test. By independently and randomly choosing the base settings for measuring the entangled photon pairs and by ensuring space-like separation between the measurement events, we also satisfy the no-signalling condition and close the 'locality' loophole of the Bell test, thus enabling the realization of the loophole-free violation of a Bell inequality. This, along with a high-voltage, high-repetition-rate Pockels cell modulation set-up, allows us to accumulate sufficient data in the experimental time to extract genuine quantum randomness that is secure against the most general adversaries. By applying a large (137.90 gigabits × 62.469 megabits) Toeplitz-matrix hashing technique, we obtain 6.2469 × 107 quantum-certified random bits in 96 hours with a total failure probability (of producing a random number that is not guaranteed to be perfectly secure) of less than 10-5. Our demonstration is a crucial step towards transforming DIQRNG from a concept to a key aspect of practical applications that require high levels of security and thus genuine randomness7. Our work may also help to improve our understanding of the origin of randomness from a fundamental perspective.