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Ramping a physical parameter is one of the most common experimental protocols in studying a quantum system, and ramping dynamics has been widely used in preparing a quantum state and probing physical properties. Here, we present a novel method of probing quantum many-body correlation by ramping dynamics. We ramp a Hamiltonian parameter to the same target value from different initial values and with different velocities, and we show that the first-order correction on the finite ramping velocity is universal and path-independent, revealing a novel quantum many-body correlation function of the equilibrium phases at the target values. We term this method as the non-adiabatic linear response since this is the leading order correction beyond the adiabatic limit. We demonstrate this method experimentally by studying the Bose-Hubbard model with ultracold atoms in three-dimensional optical lattices. Unlike the conventional linear response that reveals whether the quasi-particle dispersion of a quantum phase is gapped or gapless, this probe is more sensitive to whether the quasi-particle lifetime is long enough such that the quantum phase possesses a well-defined quasi-particle description. In the Bose-Hubbard model, this non-adiabatic linear response is significant in the quantum critical regime where well-defined quasi-particles are absent. And in contrast, this response is vanishingly small in both superfluid and Mott insulators which possess well-defined quasi-particles. Because our proposal uses the most common experimental protocol, we envision that our method can find broad applications in probing various quantum systems., Comment: 7 pages for main text. Science Bulletin (2022)

A quantum gas microscope plays an important role in cold-atom experiments, which provides a high-resolution imaging of the spatial distributions of cold atoms. Here we design, build and calibrate an integrated microscope for quantum gases with all the optical components fixed outside the vacuum chamber. It provides large numerical aperture (NA) of 0.75, as well as good optical access from side for atom loading in cold-atom experiments due to long working distance (7 mm fused silica+6 mm vacuum) of the microscope objective. We make a special design of the vacuum viewport with a T-shape window, to suppress the window flatness distortion introduced by the metal-glass binding process, and protect the high-resolution imaging from distortions due to unflattened window. The achieved Strehl ratio is 0.9204 using scanning-near-field microscopy (SNOM) fiber coupling incoherent light as point light source.

We propose an entanglement-creation scheme in a multi-atom ensemble trapped in an optical cavity, named entanglement amplification, converting unentangled states into entangled states and amplifying less-entangled ones to maximally entangled Greenberger-Horne-Zeilinger (GHZ) states whose fidelity is logarithmically dependent on the atom number and robust against common experimental noises. The scheme starts with a multi-atom ensemble initialized in a coherent spin state. By shifting the energy of a particular Dicke state, we break the Hilbert space of the ensemble into two isolated subspaces to tear the coherent spin state into two components so that entanglement is introduced. After that, we utilize the isolated subspaces to further enhance the entanglement by coherently separating the two components. By single-particle Rabi drivings on atoms in a high-finesse optical cavity illuminated by a single-frequency light, 2000-atom GHZ states can be created with a fidelity above 80% in an experimentally achievable system, making resources of ensembles at Heisenberg limit practically available for quantum metrology.

Manipulation of ultracold atoms in optical lattices is one of the optimal ways to observe phase transitions of the Hubbard model which is useful in a variety of condensed-matter systems. Bosonic atoms in this model experience a phase transition from superfluids to Mott insulators by tuning systematic parameters. However, in conventional setups, phase transitions take place over a large range of parameters instead of one critical point due to the background inhomogeneity caused by the Gaussian shape of optical-lattice lasers. To probe the phase transition point more precisely in our lattice system, we apply a blue-detuned laser to compensate for this local Gaussian geometry. By inspecting the change of visibility, we find a sudden jump point at one particular trap depth of optical lattices, corresponding to the first appearance of Mott insulators in inhomogeneous systems. This provides a simple method to detect the phase transition point in such inhomogeneous systems. We believe it will be a useful tool for most cold atom experiments.

Defect-free atomic arrays have been demonstrated as a scalable and fully-controllable platform for quantum simulations and quantum computations. To push the qubit size limit of this platform further, we design an integrated measurement and feedback system, based on field programmable gate array (FPGA), to quickly assemble two-dimensional defect-free atomic array using maximum parallelisms. The total time cost of the rearrangement is first reduced by processing atom detection, atomic occupation analysis, rearrangement strategy formulation, and acousto-optic deflectors (AOD) driving signal generation in parallel in time. Then, by simultaneously moving multiple atoms in the same row (column), we save rearrangement time by parallelism in space. To best utilize these parallelisms, we propose a new algorithm named Tetris algorithm to reassemble atoms to arbitrary target array geometry from two-dimensional stochastically loaded atomic arrays. For an $L \times L$ target array geometry, the number of moves scales as $L$, and the total rearrangement time scales at most as $L^2$. We present the overall performance for different target geometries, and demonstrate a significant reduction in rearrangement time and the potential to scale up defect-free atomic array system to thousands of qubits.

Quantum critical behavior of many-body phase transitions is one of the most fascinating yet challenging questions in quantum physics. Here, we improved the band-mapping method to investigate the quantum phase transition from superfluid to Mott insulators, and we observed the critical behaviors of quantum phase transitions in both dynamical steady-state-relaxation region and phase-oscillation region. Based on various observables, two different values for the same quantum critical parameter are observed. This result is beyond a universal-scaling-law description of quantum phase transitions known as the Kibble-Zurek mechanism, and suggests that multiple quantum critical mechanisms are competing in many-body quantum phase transition experiments in inhomogeneous systems., 6 pages, 4 figures for main text

We propose a scheme to realize bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices. This scheme does not require a very flat band, and the necessary long-range interaction relies on s-wave scattering, which is common in many ultracold-atom experiments. By filling the lattice at 1/4 with identical bosons under Feshbach resonance, two degenerate many-body ground states share one Chern number of 1 and correspond exactly to the fractional quantum Hall conductance of 1/2. Meanwhile, we prove that the fractional quantum Hall state can be prepared by adiabatically turning on the lattice shaking, and the fractional conductance is robust in the shaken lattice. This provides an easy way to initialize and prepare the fractional quantum Hall states in ultracold-atom platforms, and it paves the way to investigate and simulate strongly correlated quantum matters with degenerate quantum gas.

The exploration of quantum phenomena in a curved spacetime is an emerging interdisciplinary area at the interface between general relativity1–4, thermodynamics4–6 and quantum information7,8. One famous prediction in this field is Unruh thermal radiation3—the manifestation of thermal radiation from a Minkowski vacuum when viewed in an accelerating reference frame. Here, we report the experimental observation of a matter field with thermal fluctuations that agree with Unruh’s predictions. The matter field is generated within a framework for the simulation of quantum physics in a non-inertial frame, based on Bose–Einstein condensates that are parametrically modulated9 to make their evolution replicate the frame transformation. We further observe long-range phase coherence and temporal reversal of the matter-wave radiation, hallmarks that distinguish Unruh radiation from its classical counterpart. Our demonstration offers a new avenue for the investigation of the dynamics of quantum many-body systems in a curved spacetime. According to the Unruh effect, for an accelerating observer the vacuum is filled with thermal radiation. Experiments now simulate this effect, recreating the statistics of Unruh radiation in the matter-wave field of a Bose–Einstein condensate.

The Bose-Einstein condensation (BEC) of

Correlations in interacting many-body systems are key to the study of quantum materials and quantum information. More often than not, the complexity of the correlations grows quickly as the system evolves and thus presents a challenge for experimental characterization and intuitive understanding. In a strongly driven Bose-Einstein condensate, we observe the high harmonic generation of matter-wave jets with complex correlations as a result of bosonic stimulation. Based on a pattern recognition scheme, we identify a universal pattern of correlations which offers essential clues to unveiling the underlying secondary scattering processes and high-order correlations. We show that the pattern recognition offers a versatile strategy to visualize and analyze the quantum dynamics of a many-body system., Comment: 14 pages, 4 figures in the main text, and 3 figures in the supplement

Pattern formation is ubiquitous in nature from morphogenesis and cloud formation to galaxy filamentation. More often than not, patterns arise in a medium driven far from equilibrium due to the interplay of dynamical instability and nonlinear wave mixing. We report, based on momentum and real space pattern recognition, formation of density patterns with two- (D$_2$), four- (D$_4$) and six-fold (D$_6$) symmetries in Bose-Einstein condensates (BECs) with atomic interactions driven at two frequencies. The symmetry of the pattern is controlled by the ratio of the frequencies. The D$_6$ density waves, in particular, arise from a resonant wave mixing process that coherently correlates and enhances the excitations that respect the symmetry., Main text: 6 pages, 4 figures; Supplement: 10 pages, 5 figures

This dataset contains data shown in all our publishing figures as well as the MATLAB program used to process the data. Here is a list of the figures and the corresponding data. In the main text: Figure 1: Figure1.xlsx; Figure 2: Figure2.xlsx; Figure 3: Figure3.xlsx; Figure 4: Figure4.xlsx. In the supplementary material: Figure S1: N/A Figure S2: FigureS2.xlsx; Figure S3: Figure4.xlsx; Figure S4: Figure4.xlsx. Essential MATLAB code for analyzing experimental data are included in MatlabScripts.zip.&nbsp

A Bose condensate, subject to periodic modulation of the two-body interactions, was recently observed to emit matter-wave jets resembling fireworks [Nature (London) 551, 356 (2017)NATUAS0028-083610.1038/nature24272]. In this Letter, combining experiment with numerical simulation, we demonstrate that these "Bose fireworks" represent a late stage in a complex time evolution of the driven condensate. We identify a "density wave" stage which precedes jet emission and results from the interference of matter waves. The density waves self-organize and self-amplify without breaking long range translational symmetry. This density wave structure deterministically establishes the template for the subsequent patterns of the emitted jets. Moreover, our simulations, in good agreement with experiment, address an apparent asymmetry in the jet pattern, and show that it is fully consistent with momentum conservation.

The detection of a single photon from a laser interacting with an atomic ensemble is shown to produce entanglement of almost 3,000 atoms; in contrast to previous production of multi-atom entanglement, the highly non-classical nature of the present entangled state is verified by measurement of a negative quasiprobability distribution. Entanglement is the crucial resource that quantum technologies harness for classically impossible applications. Large ensembles of entangled particles promise to be useful in quantum metrology, but they are difficult to produce. Vladan Vuletic and colleagues demonstrate how the detection of a single photon from a laser interacting with an atomic ensemble can produce entanglement of almost 3,000 atoms. Entanglements of atomic ensembles with many atoms have been produced before, but they showed only weak signs of non-classicality, as quantified by the Wigner function. The entangled atoms described here, however, show a negative Wigner function and are thus highly non-classical, providing a realistic route to 'Schrodinger's cat' states in large atomic ensembles. The result has yet to be optimized to yield a quantum advantage in metrology applications but it is an important step towards this goal. Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized1,2,3,4,5,6,7,8,9,10, but these states display Gaussian spin distribution functions with a non-negative Wigner quasiprobability distribution function. Non-Gaussian entangled states have been produced in small ensembles of ions11,12, and very recently in large atomic ensembles13,14,15. Here we generate entanglement in a large atomic ensemble via an interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function—an important hallmark of non-classicality—and verify an entanglement depth (the minimum number of mutually entangled atoms) of 2,910 ± 190 out of 3,100 atoms. Attaining such a negative Wigner function and the mutual entanglement of virtually all atoms is unprecedented for an ensemble containing more than a few particles. Although the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrodinger cat states for quantum metrology and information processing. More generally, our results demonstrate the power of heralded methods for entanglement generation, and illustrate how the information contained in a single photon can drastically alter the quantum state of a large system.

We experimentally demonstrate the strictly nonclassical behavior in a many-atom system using a recently derived criterion [E. Kot et al., Phys. Rev. Lett. 108, 233601 (2012)] that explicitly does not make use of quantum mechanics. We thereby show that the magnetic moment distribution measured by McConnell et al. [R. McConnell et al., Nature 519, 439 (2015)] in a system with a total mass of $2.6\times 10^5$ atomic mass units is inconsistent with classical physics. Notably, the strictly nonclassical behavior affects an area in phase space $10^3$ times larger than the Planck quantum $\hbar$., 5 pages

The decoy-state method of quantum key distribution(QKD) successfully solves the loophole of Photon-Number-Splitting attack and it also makes people to demonstrate QKD with a long distance. In this paper, we review the development of QKD, from BB84 protocol to the demonstration of three-intensity decoy-state method. We also explain how to get the final security key rate from the input parameters.

We analyze the problem of approximate quantum cloning when the quantum state is between two latitudes on the Bloch's sphere. We present an analytical formula for the optimized 1-to-2 cloning. The formula unifies the universal quantum cloning (UQCM) and the phase covariant quantum cloning.

We consider the optical generation and verification of entanglement in atomic ensembles under non-uniform interaction between the ensemble and an optical mode. We show that for a wide range of parameters a system of non-uniformly coupled atomic spins can be described as an ensemble of uniformly coupled spins with a reduced effective atom-light coupling and a reduced effective atom number, with a reduction factor of order unity given by the ensemble-mode geometry. This description is valid even for complex entangled states with arbitrary phase-space distribution functions as long as the detection does not resolve single spins. Furthermore, we derive an analytic formula for the observable entanglement in the case, of relevance in practice, where the ensemble-mode coupling differs between state generation and measurement., Comment: 5 pages, 3 figures

We propose a versatile and efficient method to generate a broad class of complex entangled states of many atoms via the detection of a single photon. For an atomic ensemble contained in a strongly coupled optical cavity illuminated by weak single- or multi-frequency light, the atom-light interaction entangles the frequency spectrum of a transmitted photon with the collective spin of the atomic ensemble. Simple time-resolved detection of the transmitted photon then projects the atomic ensemble into a desired pure entangled state. This method can be implemented with existing technology, yields high success probability per trials, and can generate complex entangled states such as multicomponent Schr\"{o}dinger cat states with high fidelity., Comment: 3 figures

An arbitrary quantum-optical process (channel) can be completely characterized by probing it with coherent states using the recently developed coherent-state quantum process tomography (QPT) [Lobino et al., Science 322, 563 (2008)]. In general, precise QPT is possible if an infinite set of probes is available. Thus, realistic QPT of infinite-dimensional systems is approximate due to a finite experimentally-feasible set of coherent states and its related energy-cut-off approximation. We show with explicit formulas that one can completely identify a quantum-optical Gaussian process just with a few different coherent states without approximations like the energy cut-off. For tomography of multimode processes, our method exponentially reduces the number of different test states, compared with existing methods., 6 pages, 1 figure. Some parts of this article are based on our preliminary unpublished version arXiv:1010.0472v1

We propose and analyze a probabilistic but heralded scheme to generate pure, entangled, non-Gaussian states of collective spin in large atomic ensembles by means of single-photon detection. One photon announces the preparation of a Dicke state, while two or more photons announce Schr\"odinger cat states. The method produces pure states even for finite photon detection efficiency and weak atom-photon coupling. The entanglement generation can be made quasi-deterministic by means of repeated trial and feedback, enabling metrology beyond the standard quantum limit., Comment: 5 pages, 3 figures

Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions [11, 12], and very recently in large atomic ensembles [13, 14, 15]. Here, we generate entanglement in a large atomic ensemble via the interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function, an important hallmark of nonclassicality, and verify an entanglement depth (minimum number of mutually entangled atoms) of 2910 ± 190 out of 3100 atoms. Attaining such a negative Wigner function and the mutual entanglement of virtually all atoms is unprecedented for an ensemble containing more than a few particles. While the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrodinger cat states for quantum metrology and information processing.

We study the state decay of two qubits interacting with a common harmonic oscillator reservoir. We find both a decoherence error and the error caused by the amplitude change of the superradiant state. We show that frequent $\ensuremath{\pi}$-phase pulses can eliminate both types of errors and therefore protect a two-qubit odd-parity state more effectively than the frequent measurement method. This shows that the methods using dynamical decoupling and the quantum Zeno effects actually can give rather different results when the operation frequency is finite.

We present an upper bound of the entanglement evolution for two-mode Gaussian pure states under a one-sided Gaussian map. Based on this, the optimization of entanglement evolution is studied. Even if complete information about the one-sided Gaussian noisy channel does not exist, one can still maximize the entanglement distribution by testing the channel with only two specific states.

We present an improved formula for the lower bound of the fraction of single-photon counts in a decoy-state protocol with an unstable source. Based on the formula, we study two-intensity protocol and three-intensity protocol. The major formula in the passive two-intensity protocol proposed by Adachi, Yamamoto, Koashi, and Imoto (AYKI) [Phys. Rev. Lett. 99, 180503 (2007)] actually always holds with whatever intensity fluctuation of pump light. Therefore, the protocol can always work securely without monitoring the source state or switching the source intensity. We also show that our result can greatly improve the key rate of the three-intensity protocol with a fluctuating coherent-state source.

Nature 519, 439–442 (2015); doi:10.1038/nature14293 In Fig. 2a of this Letter, the solid blue line in the linear plot was inadvertently removed during the production process; this figure has now been corrected in the online versions of the manuscript.