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The thermalization of an isolated quantum system is described by quantum mechanics and thermodynamics, while these two subjects are still not fully consistent with each other. This leaves a less-explored region where both quantum and thermal effects cannot be neglected, and the ultracold atom platform provides a suitable and versatile testbed to experimentally investigate these complex phenomena. Here we perform experiments based on ultracold atoms in optical lattices and observe a divergence of thermalization rates of quantum matters when the temperature approaches zero. By ramping an external parameter in the Hamiltonian, we observe the time delay between the internal relaxation and the external ramping. This provides us with a direct comparison of the thermalization rates of different quantum phases. We find that the quantum coherence and bosonic stimulation of superfluid induces the divergence while the finite temperature and the many-body interactions are suppressing the divergence. The quantum coherence and the thermal effects are competing with each other in this isolated thermal quantum system, which leads to the transition of thermalization rate from divergence to convergence.

We report the first experimental observation of dissipation-driven coherent quantum many-body oscillation, and this oscillation is manifested as the coherent exchange of atoms between the thermal and the condensate components in a three-dimensional partially condensed Bose gas. Firstly, we observe that the dissipation leads to two different atom loss rates between the thermal and the condensate components, such that the thermal fraction increases as dissipation time increases. Therefore, this dissipation process serves as a tool to uniformly ramp up the system's temperature without introducing extra density excitation. Subsequently, a coherent pair exchange of atoms between the thermal and the condensate components occurs, resulting in coherent oscillation of atom numbers in both components. This oscillation, permanently embedded in the atom loss process, is revealed clearly when we inset a duration of dissipation-free evolution into the entire dynamics, manifested as an oscillation of total atom number at the end. Finally, we also present a theoretical calculation to support this physical mechanism, which simultaneously includes dissipation, interaction, finite temperature, and harmonic trap effects. Our work introduces a highly controllable dissipation as a new tool to control quantum many-body dynamics., Comment: 11 pages, 5 figures, 1 table

To achieve scalable universal quantum computing, we need to implement a universal set of logical gates fault-tolerantly, for which the main difficulty lies with non-Clifford gates. We demonstrate that several characteristic features of the reconfigurable atom array platform are inherently well-suited for addressing this key challenge, potentially leading to significant advantages in fidelity and efficiency. Specifically, we consider a series of different strategies including magic state distillation, concatenated code array, and fault-tolerant logical multi-controlled-$Z$ gates, leveraging key platform features such as non-local connectivity, parallel gate action, collective mobility, and native multi-controlled-$Z$ gates. Our analysis provides valuable insights into the efficient experimental realization of logical gates, serving as a guide for the full-cycle demonstration of fault-tolerant quantum computation with reconfigurable atom arrays.

Dissipation is unavoidable in quantum systems. It usually induces decoherences and changes quantum correlations. To access the information of strongly correlated quantum matters, one has to overcome or suppress dissipation to extract out the underlying quantum phenomena. However, here we find an opposite effect that dissipation can be utilized as a powerful tool to probe the intrinsic correlations of quantum many-body systems. Applying highly-controllable dissipation in ultracold atomic systems, we observe a universal dissipative dynamics in strongly correlated one-dimensional quantum gases. The total particle number of this system follows a universal stretched-exponential decay, and the stretched exponent measures the anomalous dimension of the spectral function, a critical exponent characterizing strong quantum fluctuations of this system. This method could have broad applications in detecting strongly correlated features, including spin-charge separations and Fermi arcs in quantum materials.

Cold atoms in an optical cavity have been widely used for quantum simulations of many-body physics, where the quantum control capability has been advancing rapidly in recent years. Here, we show the atom cavity system is universal for quantum optimization with arbitrary connectivity. We consider a single-mode cavity and develop a Raman coupling scheme by which the engineered quantum Hamiltonian for atoms directly encodes number partition problems (NPPs). The programmability is introduced by placing the atoms at different positions in the cavity with optical tweezers. The NPP solution is encoded in the ground state of atomic qubits coupled through a photonic cavity mode, that can be reached by adiabatic quantum computing (AQC). We construct an explicit mapping for the 3-SAT and vertex cover problems to be efficiently encoded by the cavity system, which costs linear overhead in the number of atomic qubits. The atom cavity encoding is further extended to quadratic unconstrained binary optimization (QUBO) problems. The encoding protocol is optimal in the cost of atom number scaling with the number of binary degrees of freedom of the computation problem. Our theory implies the atom cavity system is a promising quantum optimization platform searching for practical quantum advantage., Comment: 13 pages, 2 figures

We develop a theoretical model for calibrating the absorption imaging of cold atoms under high magnetic fields. Comparing to zero or low magnetic fields, the efficiency of the absorption imaging becomes lower while it requires an additional correction factor to obtain the absolute atom number under the Beer-Lambert law. Our model is based on the rate equations and can account many experimental imperfections such as Zeeman level crossing, failures of hyperfine structures, off-resonant couplings, and low repumping efficiency, etc. Based on this method, we can precisely calculate the correction factor for atom number measurement without any empirical or fitting parameters. Meanwhile, we use a cold-atom apparatus of rubidium-85 to experimentally verify our model. Besides these, we find our work can also serve as a benchmark to measure the polarization impurity of a circular-polarized laser beam with high sensitivities. We believe this work will bring convenience for most of cold-atom experiments using absorption imaging., Comment: 9 pages, 5 figures

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.

Computing finite temperature properties of a quantum many-body system is key to describing a broad range of correlated quantum many-body physics from quantum chemistry and condensed matter to thermal quantum field theories. Quantum computing with rapid developments in recent years has a huge potential to impact the computation of quantum thermodynamics. To fulfill the potential impacts, it is crucial to design quantum algorithms that utilize the computation power of the quantum computing devices. Here we present a quantum kernel function expansion (QKFE) algorithm for solving thermodynamic properties of quantum many-body systems. In this quantum algorithm, the many-body density of states is approximated by a kernel-Fourier expansion, whose expansion moments are obtained by random state sampling and quantum interferometric measurements. As compared to its classical counterpart, namely the kernel polynomial method (KPM), QKFE has an exponential advantage in the cost of both time and memory. In computing low temperature properties, QKFE becomes inefficient, as similar to classical KPM. To resolve this difficulty, we further construct a thermal ensemble and approaches the low temperature regime step-by-step. For quantum Hamiltonians, whose ground states are preparable with polynomial quantum circuits, THEI has an overall polynomial complexity. We demonstrate its efficiency with applications to one and two-dimensional quantum spin models, and a fermionic lattice. With our analysis on the realization with digital and analogue quantum devices, we expect the quantum algorithm is accessible to current quantum technology., Comment: 11 pages, 5 figures

We observe and study a special ground state of bosons with two spin states in an optical lattice: the spin-Mott insulator, a state that consists of repulsively bound pairs which is insulating for both spin and charge transport. Because of the pairing gap created by the interaction anisotropy, it can be prepared with low entropy and can serve as a starting point for adiabatic state preparation. We find that the stability of the spin-Mott state depends on the pairing energy, and observe two qualitatively different decay regimes, one of which exhibits protection by the gap.

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)

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., Comment: 6 pages, 4 figures for main text

We propose a novel entanglement-creation scheme in a multi-atom ensemble, named entanglement amplification, which converts unentangled states into entangled states and amplifies less-entangled ones to maximally-entangled Greenberger-Horne-Zeilinger (GHZ) states. 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., Comment: 6 pages and 4 figures

Optical cavities are widely used to enhance the interaction between atoms and light. Typical designs using a geometrically symmetric structure in the near-concentric regime face a tradeoff between mechanical stability and high single-atom cooperativity. To overcome this limitation, we design and implement a geometrically asymmetric standing-wave cavity. This structure, with mirrors of very different radii of curvature, allows strong atom-light coupling while exhibiting good stability against misalignment. We observe effective cooperativities ranging from $\eta_{\rm eff}=10$ to $\eta_{\rm eff}=0.2$ by shifting the location of the atoms in the cavity mode. By loading $^{171}$Yb atoms directly from a mirror magneto-optical trap into a one-dimensional optical lattice along the cavity mode, we produce atomic ensembles with collective cooperativities up to $N\eta=2\times 10^4$. This system opens a way to preparing spin squeezing for an optical lattice clock and to accessing a range of nonclassical collective states., Comment: 8 pages, 7 figures, published version

We demonstrate direct laser cooling of a gas of rubidium 87 atoms to quantum degeneracy. The method does not involve evaporative cooling, is fast, and induces little atom loss. The atoms are trapped in a two-dimensional optical lattice that enables cycles of cloud compression to increase the density, followed by degenerate Raman sideband cooling to decrease the temperature. Light-induced loss at high atomic density is substantially reduced by using far red detuned optical pumping light. Starting with 2000 atoms, we prepare 1400 atoms in 300 ms at quantum degeneracy, as confirmed by the appearance of a bimodal velocity distribution as the system crosses over from a classical gas to a Bose-condensed, interacting one-dimensional gas with a macroscopic population of the quantum ground state. The method should be broadly applicable to many bosonic and fermionic species, and to systems where evaporative cooling is not possible., Comment: 5 pages, 3 figures (main text)

We investigate the generation of entanglement (spin squeezing) in an optical-transition atomic clock through the coupling to a vacuum electromagnetic field that is enhanced by an optical cavity. We show that if each atom is prepared in a superposition of the ground state and a long-lived electronic excited state, and viewed as a spin-1/2 system, then the collective vacuum light shift entangles the atoms, resulting in a squeezed distribution of the ensemble collective spin. This scheme reveals that even a vacuum field can be a useful resource for entanglement and quantum manipulation. The method is simple and robust since it requires neither the application of light nor precise frequency control of the ultra-high-finesse cavity. Furthermore, the scheme can be used to implement two-axis twisting by rotating the spin direction while coupling to the vacuum, resulting in stronger squeezing.

We demonstrate a new way to extend the coherence time of separated Bose-Einstein condensates that involves immersion into a superfluid bath. When both the system and the bath have similar scattering lengths, immersion in a superfluid bath cancels out inhomogeneous potentials either imposed by external fields or inherent in density fluctuations due to atomic shot noise. This effect, which we call superfluid shielding, allows for coherence lifetimes beyond the projection noise limit. We probe the coherence between separated condensates in different sites of an optical lattice by monitoring the contrast and decay of Bloch oscillations. Our technique demonstrates a new way that interactions can improve the performance of quantum devices., Comment: 4 pages, 4 figures plus 2 page supplement

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 $\hbar$., Comment: 5 pages

We report the continuous and partially nondestructive measurement of optical photons. For a weak light pulse traveling through a slow-light optical medium (signal), the associated atomic-excitation component is detected by another light beam (probe) with the aid of an optical cavity. We observe strong correlations of $g^{(2)}_{sp}=4.4(5)$ between the transmitted signal and probe photons. The observed (intrinsic) conditional nondestructive quantum efficiency ranges between 13% and 1% (65% and 5%) for a signal transmission range of 2% to 35%, at a typical time resolution of 2.5 $\mu$s. The maximal observed (intrinsic) device nondestructive quantum efficiency, defined as the product of the conditional nondestructive quantum efficiency and the signal transmission, is 0.5% (2.4%). The normalized cross-correlation function violates the Cauchy-Schwarz inequality, confirming the non-classical character of the correlations.

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

The realization of an all-optical transistor where one 'gate' photon controls a 'source' light beam, is a long-standing goal in optics. By stopping a light pulse in an atomic ensemble contained inside an optical resonator, we realize a device in which one stored gate photon controls the resonator transmission of subsequently applied source photons. A weak gate pulse induces bimodal transmission distribution, corresponding to zero and one gate photons. One stored gate photon produces fivefold source attenuation, and can be retrieved from the atomic ensemble after switching more than one source photon. Without retrieval, one stored gate photon can switch several hundred source photons. With improved storage and retrieval efficiency, our work may enable various new applications, including photonic quantum gates, and deterministic multiphoton entanglement., Comment: 20 pages, 5 figures. Published in Science. Includes supplemental information

Photons are excellent information carriers but normally pass through each other without consequence. Engineered interactions between photons would enable applications from quantum information processing to simulation of condensed matter systems. Using an ensemble of cold atoms strongly coupled to an optical cavity, we demonstrate experimentally that the transmission of light through a medium may be controlled with few photons and even by the electromagnetic vacuum field. The vacuum induces a group delay of 25 ns on the input optical pulse, corresponding to a light velocity of 1600 m/s, and a transparency of 40% that increases to 80% when the resonator is filled with 10 photons. This strongly nonlinear effect provides prospects for advanced quantum devices such as photon-number-state filters., Comment: 13 pages, 4 figures

We present a novel technique to phase-lock two lasers with controllable frequency difference. In our setup, one sideband of a current modulated Vertical-Cavity Surface-Emitting Laser (VCSEL) is phase locked to the master laser by injection seeding, while another sideband of the VCSEL is used to phase lock the slave laser. The slave laser is therefore locked in phase with the master laser, with a frequency difference tunable up to about 35 GHz. The sideband suppression rate of the slave laser is more than 30dB at 30 uW seed power. The heterodyne spectrum between master and slave has a linewidth of less than 1 Hz. A coherent population trapping resonance of rubidium is achieved using such beams., Comment: 4 pages, 4 Encapsulated PostScript figures