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.

Interrelated Thermalization and Quantum Criticality in a Lattice Gauge Simulator.

Gauge theory and thermalization are both topics of essential importance for modern quantum science and technology. The recently realized atomic quantum simulator for lattice gauge theories provides a unique opportunity for studying thermalization in gauge theory, in which theoretical studies have shown that quantum thermalization can signal the quantum phase transition. Nevertheless, the experimental study remains a challenge to accurately determine the critical point and controllably explore the thermalization dynamics due to the lack of techniques for locally manipulating and detecting matter and gauge fields. We report an experimental investigation of the quantum criticality in the lattice gauge theory from both equilibrium and nonequilibrium thermalization perspectives, with the help of the single-site addressing and atom-number-resolved detection capabilities. We accurately determine the quantum critical point and observe that the Néel state thermalizes only in the critical regime. This result manifests the interplay between quantum many-body scars, quantum criticality, and symmetry breaking.

Scalable Multipartite Entanglement Created by Spin Exchange in an Optical Lattice.

Ultracold atoms in optical lattices form a competitive candidate for quantum computation owing to the excellent coherence properties, the highly parallel operations over spins, and the ultralow entropy achieved in qubit arrays. For this, a massive number of parallel entangled atom pairs have been realized in superlattices. However, the more formidable challenge is to scale up and detect multipartite entanglement, the basic resource for quantum computation, due to the lack of manipulations over local atomic spins in retroreflected bichromatic superlattices. In this Letter, we realize the functional building blocks in quantum-gate-based architecture by developing a cross-angle spin-dependent optical superlattice for implementing layers of quantum gates over moderately separated atoms incorporated with a quantum gas microscope for single-atom manipulation and detection. Bell states with a fidelity of 95.6(5)% and a lifetime of 2.20±0.13 s are prepared in parallel, and then connected to multipartite entangled states of one-dimensional ten-atom chains and two-dimensional plaquettes of 2×4 atoms. The multipartite entanglement is further verified with full bipartite nonseparability criteria. This offers a new platform toward scalable quantum computation and simulation.

Direct binary search method for high-resolution holographic image projection.

Complex-amplitude modulation of light fields with a digital micromirror device (DMD) has been widely used in holographic image projection. DMD is a binary-amplitude modulator, and its use for complex field modulation in a 4f configuration requires low-pass filtering. However, the reconstructed fields suffer from low resolution due to the limited bandwidth for the existing methods such as the Lee and superpixel methods. Here, we report a direct binary search (DBS) method to design high-resolution complex-amplitude holograms. The method is able to increase the spatial bandwidth up to twice that of the superpixel method. Numerical simulations and experiments are presented to demonstrate the method, which show that the errors are reduced by about 60% and 40% respectively for the test fields compared to the superpixel method. Furthermore, the measured efficiency of laser light can be improved by a maximum of 60%.

High-powered optical superlattice with robust phase stability for quantum gas microscopy.

Optical superlattice has a wide range of applications in the study of ultracold atom physics. Especially, it can be used to trap and manipulate thousands of atom pairs in parallel which constitutes a promising system for quantum simulation and quantum computation. In the present work, we report on a high-power optical superlattice formed by a 532-nm and 1064-nm dual-wavelength interferometer with a short lattice spacing of 630 nm. The short-term fluctuation (in 10 seconds) of the relative phase between the short lattice and the long lattice is measured to be 0.003π, which satisfies the needs for performing two-qubit gates among neighboring lattice sites. We further implement this superlattice in a 87Rb experiment with a quantum gas microscope of single-site resolution, where the high-power 532-nm laser is necessary for pinning atoms in the short lattice during imaging, providing a unique platform for engineering quantum states.

Quantum criticality and the Tomonaga-Luttinger liquid in one-dimensional Bose gases.

We experimentally investigate the quantum criticality and Tomonaga-Luttinger liquid (TLL) behavior within one-dimensional (1D) ultracold atomic gases. Based on the measured density profiles at different temperatures, the universal scaling laws of thermodynamic quantities are observed. The quantum critical regime and the relevant crossover temperatures are determined through the double-peak structure of the specific heat. In the TLL regime, we obtain the Luttinger parameter by probing sound propagation. Furthermore, a characteristic power-law behavior emerges in the measured momentum distributions of the 1D ultracold gas, confirming the existence of the TLL.

Quantum teleportation between remote atomic-ensemble quantum memories.

Quantum teleportation and quantum memory are two crucial elements for large-scale quantum networks. With the help of prior distributed entanglement as a "quantum channel," quantum teleportation provides an intriguing means to faithfully transfer quantum states among distant locations without actual transmission of the physical carriers [Bennett CH, et al. (1993) Phys Rev Lett 70(13):1895-1899]. Quantum memory enables controlled storage and retrieval of fast-flying photonic quantum bits with stationary matter systems, which is essential to achieve the scalability required for large-scale quantum networks. Combining these two capabilities, here we realize quantum teleportation between two remote atomic-ensemble quantum memory nodes, each composed of ∼10(8) rubidium atoms and connected by a 150-m optical fiber. The spin wave state of one atomic ensemble is mapped to a propagating photon and subjected to Bell state measurements with another single photon that is entangled with the spin wave state of the other ensemble. Two-photon detection events herald the success of teleportation with an average fidelity of 88(7)%. Besides its fundamental interest as a teleportation between two remote macroscopic objects, our technique may be useful for quantum information transfer between different nodes in quantum networks and distributed quantum computing.

Experimental demonstration of a BDCZ quantum repeater node.

Quantum communication is a method that offers efficient and secure ways for the exchange of information in a network. Large-scale quantum communication (of the order of 100 km) has been achieved; however, serious problems occur beyond this distance scale, mainly due to inevitable photon loss in the transmission channel. Quantum communication eventually fails when the probability of a dark count in the photon detectors becomes comparable to the probability that a photon is correctly detected. To overcome this problem, Briegel, Dür, Cirac and Zoller (BDCZ) introduced the concept of quantum repeaters, combining entanglement swapping and quantum memory to efficiently extend the achievable distances. Although entanglement swapping has been experimentally demonstrated, the implementation of BDCZ quantum repeaters has proved challenging owing to the difficulty of integrating a quantum memory. Here we realize entanglement swapping with storage and retrieval of light, a building block of the BDCZ quantum repeater. We follow a scheme that incorporates the strategy of BDCZ with atomic quantum memories. Two atomic ensembles, each originally entangled with a single emitted photon, are projected into an entangled state by performing a joint Bell state measurement on the two single photons after they have passed through a 300-m fibre-based communication channel. The entanglement is stored in the atomic ensembles and later verified by converting the atomic excitations into photons. Our method is intrinsically phase insensitive and establishes the essential element needed to realize quantum repeaters with stationary atomic qubits as quantum memories and flying photonic qubits as quantum messengers.

A compact gain-enhanced microwave helical antenna for 87Rb atomic experiments.

We present a compact and gain-enhanced microwave helical antenna for manipulating ultracold 87Rb atoms coherently. By replacing the reflecting plate with an enhancing cup, the voltage standing wave ratio is reduced by 0.5 in the frequency range of 6.73-6.93 GHz, which covers the resonant frequency between the ground-state hyperfine levels of the 87Rb atom. The gain of the helical antenna is increased by 1.25-1.63 dBi, whose length is 89 mm. Applying the antenna to ultracold 87Rb atomic experiments, we achieve a Rabi frequency of 60(1) ×2π kHz of the oscillation between the hyperfine levels.

Thermalization dynamics of a gauge theory on a quantum simulator.

Gauge theories form the foundation of modern physics, with applications ranging from elementary particle physics and early-universe cosmology to condensed matter systems. We perform quantum simulations of the unitary dynamics of a U(1) symmetric gauge field theory and demonstrate emergent irreversible behavior. The highly constrained gauge theory dynamics are encoded in a one-dimensional Bose-Hubbard simulator, which couples fermionic matter fields through dynamical gauge fields. We investigated global quantum quenches and the equilibration to a steady state well approximated by a thermal ensemble. Our work may enable the investigation of elusive phenomena, such as Schwinger pair production and string breaking, and paves the way for simulating more complex, higher-dimensional gauge theories on quantum synthetic matter devices.

Low-noise and high-power second harmonic generation of 532 nm laser for trapping ultracold atoms.

Optical lattices for coherently manipulating ultracold atoms demand high-power, low-noise, narrow-line-width, and continuous-wave lasers. Here, we report the implementation of a 30 W 532 nm low-noise laser by second harmonic generation from a 1064 nm fiber laser, which is capable to generate optical lattices for a quantum gas microscope of Rb87 atoms. The overall conversion efficiency is 59% at an input power of 51 W with a lithium triborate crystal coupled to a ring cavity. The relative intensity noise of the output laser is suppressed to -120 dBc/Hz in the range of 10 Hz-100 kHz with a high dynamic range of over 50 dB, which is suitable for long-term trapping and coherent manipulation of the quantum gases.

A high-power and low-noise 532-nm continuous-wave laser for quantum gas microscopy.

Low-noise, high-power 532-nm lasers are of great interest in many scientific research studies, such as gravitational wave detection and ultracold atom experiments. In particular, in the experiments of quantum gas microscopy, a large power of laser is necessary during the imaging process, while low noise is important for preventing the atoms from being heated up. In this work, we report on the generation of such a 532-nm continuous-wave laser by coherently combining two laser beams produced by single-pass second-harmonic generation. The power of the combined laser is up to 17 W. With the help of intensity stabilization, we are able to suppress the relative intensity noise to below -120 dBc/Hz. The generated laser satisfies the experimental requirements for integrating optical superlattices with a quantum gas microscope.

Heralded generation of an atomic NOON state.

We report the heralded generation of an atomic NOON state by observation of phase super resolution in a motion-sensitive spin-wave (SW) interferometer. The SW interferometer is implemented by generating a superposition of two SWs and observing the interference between them, where the interference fringe is sensitive to the atomic collective motion. By heralded generation of a second order NOON state in the SW interferometer, we observe the interference pattern which provides strong evidence of phase super resolution. The demonstrated SW interferometer can in principle be scaled up to a highly entangled state, and thus is of fundamental importance, and might be used as an inertial sensor.

Cooling and entangling ultracold atoms in optical lattices.

Scalable, coherent many-body systems can enable the realization of previously unexplored quantum phases and have the potential to exponentially speed up information processing. Thermal fluctuations are negligible and quantum effects govern the behavior of such systems with extremely low temperature. We report the cooling of a quantum simulator with 10,000 atoms and mass production of high-fidelity entangled pairs. In a two-dimensional plane, we cool Mott insulator samples by immersing them into removable superfluid reservoirs, achieving an entropy per particle of [Formula: see text] The atoms are then rearranged into a two-dimensional lattice free of defects. We further demonstrate a two-qubit gate with a fidelity of 0.993 ± 0.001 for entangling 1250 atom pairs. Our results offer a setting for exploring low-energy many-body phases and may enable the creation of large-scale entanglement.

Quantum memory with optically trapped atoms.

We report the experimental demonstration of quantum memory for collective atomic states in a far-detuned optical dipole trap. Generation of the collective atomic state is heralded by the detection of a Raman scattered photon and accompanied by storage in the ensemble of atoms. The optical dipole trap provides confinement for the atoms during the quantum storage while retaining the atomic coherence. We probe the quantum storage by cross correlation of the photon pair arising from the Raman scattering and the retrieval of the atomic state stored in the memory. Nonclassical correlations are observed for storage times up to 60 mus.

Demonstration of a stable atom-photon entanglement source for quantum repeaters.

We demonstrate a novel way to efficiently create a robust entanglement between an atomic and a photonic qubit. A single laser beam is used to excite one atomic ensemble and two different modes of Raman fields are collected to generate the atom-photon entanglement. With the help of built-in quantum memory, the entanglement still exists after 20.5 micros storage time which is further proved by the violation of Clauser-Horne-Shimony-Holt type Bell's inequality. The entanglement procedure can serve as a building block for a novel robust quantum repeater architecture [Zhao, Phys. Rev. Lett. 98, 240502 (2007)10.1103/PhysRevLett.98.240502] and can be extended to generate high-dimensional atom-photon entanglements.

Synchronized independent narrow-band single photons and efficient generation of photonic entanglement.

We create independent, synchronized single-photon sources with built-in quantum memory based on two remote cold atomic ensembles. The synchronized single photons are used to demonstrate efficient generation of entanglement. The resulting entangled photon pairs violate a Bell's inequality by 5 standard deviations. Our synchronized single photons with their long coherence time of 25 ns and the efficient creation of entanglement serve as an ideal building block for scalable linear optical quantum information processing.

Optical oscillator strengths for valence-shell and Br-3d inner-shell excitations of HCl and HBr.

Absolute optical oscillator strength density spectra for valence-shell excitations of HCl and HBr, as well as for Br-3d inner-shell excitations of HBr, have been determined by high-resolution electron-energy-loss-spectroscopy method in the dipole limit. Absolute optical oscillator strengths for the discrete transitions of HCl and HBr are reported and compared with the previous results determined by the photoabsorption method.

Deterministic and storable single-photon source based on a quantum memory.

A single-photon source is realized with a cold atomic ensemble (87Rb atoms). A single excitation, written in an atomic quantum memory by Raman scattering of a laser pulse, is retrieved deterministically as a single photon at a predetermined time. It is shown that the production rate of single photons can be enhanced considerably by a feedback circuit while the single-photon quality is conserved. Such a single-photon source is well suited for future large-scale realization of quantum communication and linear optical quantum computation.

Electron-impact excitation of D1delta <-- X1sigma+ in carbon monoxide.

The dipole-forbidden transition of D1delta <-- X1sigma+ of CO has been observed by a fast electron-energy-loss spectrometer at a large scattering angle of 7 degrees and with an energy resolution of 60 meV. The energy levels and the relative intensity distribution of D1delta, v'=9-25 have been determined, most of the results are reported for the first time.